Tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d52afe38",
   "metadata": {},
   "source": [
    "## JuliaCon 2021: [DataFrames.jl](https://github.com/JuliaData/DataFrames.jl) 1.4 tutorial for Julia 1.8\n",
    "\n",
    "### [Bogumił Kamiński](http://bogumilkaminski.pl/about/)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c76a224",
   "metadata": {},
   "source": [
    "## Before you start\n",
    "\n",
    "In this tutorial we will use the following statistical concepts:\n",
    "\n",
    "* [confidence intervals](https://en.wikipedia.org/wiki/Confidence_interval)\n",
    "* [density estimators](https://en.wikipedia.org/wiki/Density_estimation)\n",
    "* [probit model](https://en.wikipedia.org/wiki/Probit_model)\n",
    "* [bootstrapping](https://en.wikipedia.org/wiki/Bootstrapping_(statistics))\n",
    "\n",
    "If you want to follow the material smoothly it is recommended that you review them before continuing."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e146d08",
   "metadata": {},
   "source": [
    "The objective of the tutorial is to give you an overview of the ecosystem. This means that I will show many things but will not discuss them deeply."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5f34908",
   "metadata": {},
   "source": [
    "The tutorial was developed and tested under Julia 1.8.2 and should be run with Project.toml and Manifest.toml files present in the working directory of the notebook (the files are provided in the https://github.com/bkamins/Julia-DataFrames-Tutorial repository)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c15f51a4",
   "metadata": {},
   "source": [
    "Load the packages we will use:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "17f829f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "using Bootstrap\n",
    "using CSV\n",
    "using CategoricalArrays\n",
    "using Chain\n",
    "using DataFrames\n",
    "import Downloads\n",
    "using GLM\n",
    "using Plots\n",
    "using Random\n",
    "using StatsPlots\n",
    "using Statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "817c9b66",
   "metadata": {},
   "source": [
    "## Data preprocessing"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1932e1fa",
   "metadata": {},
   "source": [
    "Download the file we will work with to our working directory. Note that in Julia 1.6 the `download` function is deprecated in Base, so we use the `Downloads` module that is guaraneed to stay stable in the future."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "03d78f18",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"participation.csv\""
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Downloads.download(\"https://vincentarelbundock.github.io/Rdatasets/csv/Ecdat/Participation.csv\", \"participation.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc309205",
   "metadata": {},
   "source": [
    "We will work with the classic *participation.csv* data.\n",
    "\n",
    "The description of the data set can be found here: https://vincentarelbundock.github.io/Rdatasets/doc/Ecdat/Participation.html."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e861458e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "873-element Vector{String}:\n",
       " \"\\\"\\\",\\\"lfp\\\",\\\"lnnlinc\\\",\\\"age\\\",\\\"educ\\\",\\\"nyc\\\",\\\"noc\\\",\\\"foreign\\\"\"\n",
       " \"\\\"1\\\",\\\"no\\\",10.787497,3,8,1,1,\\\"no\\\"\"\n",
       " \"\\\"2\\\",\\\"yes\\\",10.524251,4.5,8,0,1,\\\"no\\\"\"\n",
       " \"\\\"3\\\",\\\"no\\\",10.968578,4.6,9,0,0,\\\"no\\\"\"\n",
       " \"\\\"4\\\",\\\"no\\\",11.104999,3.1,11,2,0,\\\"no\\\"\"\n",
       " \"\\\"5\\\",\\\"no\\\",11.10847,4.4,12,0,2,\\\"no\\\"\"\n",
       " \"\\\"6\\\",\\\"yes\\\",11.028254,4.2,12,0,1,\\\"no\\\"\"\n",
       " \"\\\"7\\\",\\\"no\\\",11.454707,5.1,8,0,0,\\\"no\\\"\"\n",
       " \"\\\"8\\\",\\\"yes\\\",10.490918,3.2,8,0,2,\\\"no\\\"\"\n",
       " \"\\\"9\\\",\\\"no\\\",10.62474,3.9,12,0,0,\\\"no\\\"\"\n",
       " \"\\\"10\\\",\\\"no\\\",10.48642,4.3,11,0,2,\\\"no\\\"\"\n",
       " \"\\\"11\\\",\\\"no\\\",10.660618,4.5,11,0,2,\\\"no\\\"\"\n",
       " \"\\\"12\\\",\\\"no\\\",10.467589,6,12,0,0,\\\"no\\\"\"\n",
       " ⋮\n",
       " \"\\\"861\\\",\\\"yes\\\",10.528899,3.4,9,1,1,\\\"yes\\\"\"\n",
       " \"\\\"862\\\",\\\"yes\\\",10.468534,3.3,6,0,2,\\\"yes\\\"\"\n",
       " \"\\\"863\\\",\\\"no\\\",11.110955,3.5,10,1,1,\\\"yes\\\"\"\n",
       " \"\\\"864\\\",\\\"no\\\",10.471365,5.1,9,0,1,\\\"yes\\\"\"\n",
       " \"\\\"865\\\",\\\"no\\\",10.147503,4.1,5,1,0,\\\"yes\\\"\"\n",
       " \"\\\"866\\\",\\\"yes\\\",10.69323,3.5,9,0,2,\\\"yes\\\"\"\n",
       " \"\\\"867\\\",\\\"yes\\\",10.027595,4.2,14,0,0,\\\"yes\\\"\"\n",
       " \"\\\"868\\\",\\\"no\\\",10.597393,2.4,4,2,1,\\\"yes\\\"\"\n",
       " \"\\\"869\\\",\\\"yes\\\",10.377773,4.8,8,0,0,\\\"yes\\\"\"\n",
       " \"\\\"870\\\",\\\"no\\\",10.13374,2.4,6,2,0,\\\"yes\\\"\"\n",
       " \"\\\"871\\\",\\\"yes\\\",10.932351,4.1,10,0,1,\\\"yes\\\"\"\n",
       " \"\\\"872\\\",\\\"no\\\",11.220691,5.1,10,0,0,\\\"yes\\\"\""
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "readlines(\"participation.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "793ac352",
   "metadata": {},
   "source": [
    "Our objective is to build a model predicting the `:lfp` variable (labor force participation)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46ffdb56",
   "metadata": {},
   "source": [
    "First read in the data into a data frame:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "52586b96",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>872×8 DataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">847 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">Column1</th><th style = \"text-align: left;\">lfp</th><th style = \"text-align: left;\">lnnlinc</th><th style = \"text-align: left;\">age</th><th style = \"text-align: left;\">educ</th><th style = \"text-align: left;\">nyc</th><th style = \"text-align: left;\">noc</th><th style = \"text-align: left;\">foreign</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"String3\" style = \"text-align: left;\">String3</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"String3\" style = \"text-align: left;\">String3</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td><td style = \"text-align: right;\">10.7875</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">yes</td><td style = \"text-align: right;\">10.5243</td><td style = \"text-align: right;\">4.5</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">3</td><td style = \"text-align: left;\">no</td><td style = \"text-align: right;\">10.9686</td><td style = \"text-align: right;\">4.6</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">4</td><td style = \"text-align: left;\">no</td><td style = \"text-align: right;\">11.105</td><td style = \"text-align: right;\">3.1</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">5</td><td style = \"text-align: left;\">no</td><td style = \"text-align: right;\">11.1085</td><td style = \"text-align: right;\">4.4</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">6</td><td style = \"text-align: left;\">yes</td><td style = \"text-align: right;\">11.0283</td><td style = \"text-align: right;\">4.2</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">7</td><td style = \"text-align: left;\">no</td><td style = \"text-align: right;\">11.4547</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">8</td><td style = \"text-align: left;\">yes</td><td style = \"text-align: right;\">10.4909</td><td style = \"text-align: right;\">3.2</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">9</td><td style = \"text-align: left;\">no</td><td style = \"text-align: right;\">10.6247</td><td style = \"text-align: right;\">3.9</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">10</td><td style = \"text-align: left;\">no</td><td style = \"text-align: right;\">10.4864</td><td style = \"text-align: right;\">4.3</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">11</td><td style = \"text-align: left;\">no</td><td style = \"text-align: right;\">10.6606</td><td style = \"text-align: right;\">4.5</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: right;\">12</td><td style = \"text-align: left;\">no</td><td style = \"text-align: right;\">10.4676</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; 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text-align: right;\">862</td><td style = \"text-align: right;\">862</td><td style = \"text-align: left;\">yes</td><td style = \"text-align: right;\">10.4685</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">863</td><td style = \"text-align: right;\">863</td><td style = \"text-align: left;\">no</td><td style = \"text-align: right;\">11.111</td><td style = \"text-align: right;\">3.5</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">864</td><td style = \"text-align: right;\">864</td><td style = \"text-align: left;\">no</td><td style = \"text-align: right;\">10.4714</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">865</td><td style = \"text-align: right;\">865</td><td style = \"text-align: left;\">no</td><td style = \"text-align: right;\">10.1475</td><td style = \"text-align: right;\">4.1</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">866</td><td style = \"text-align: right;\">866</td><td style = \"text-align: left;\">yes</td><td style = \"text-align: right;\">10.6932</td><td style = \"text-align: right;\">3.5</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">867</td><td style = \"text-align: right;\">867</td><td style = \"text-align: left;\">yes</td><td style = \"text-align: right;\">10.0276</td><td style = \"text-align: right;\">4.2</td><td style = \"text-align: right;\">14</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">868</td><td style = \"text-align: right;\">868</td><td style = \"text-align: left;\">no</td><td style = \"text-align: right;\">10.5974</td><td style = \"text-align: right;\">2.4</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">869</td><td style = \"text-align: right;\">869</td><td style = \"text-align: left;\">yes</td><td style = \"text-align: right;\">10.3778</td><td style = \"text-align: right;\">4.8</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">870</td><td style = \"text-align: right;\">870</td><td style = \"text-align: left;\">no</td><td style = \"text-align: right;\">10.1337</td><td style = \"text-align: right;\">2.4</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">871</td><td style = \"text-align: right;\">871</td><td style = \"text-align: left;\">yes</td><td style = \"text-align: right;\">10.9324</td><td style = \"text-align: right;\">4.1</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">872</td><td style = \"text-align: right;\">872</td><td style = \"text-align: left;\">no</td><td style = \"text-align: right;\">11.2207</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& Column1 & lfp & lnnlinc & age & educ & nyc & noc & foreign\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & String3 & Float64 & Float64 & Int64 & Int64 & Int64 & String3\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & no & 10.7875 & 3.0 & 8 & 1 & 1 & no \\\\\n",
       "\t2 & 2 & yes & 10.5243 & 4.5 & 8 & 0 & 1 & no \\\\\n",
       "\t3 & 3 & no & 10.9686 & 4.6 & 9 & 0 & 0 & no \\\\\n",
       "\t4 & 4 & no & 11.105 & 3.1 & 11 & 2 & 0 & no \\\\\n",
       "\t5 & 5 & no & 11.1085 & 4.4 & 12 & 0 & 2 & no \\\\\n",
       "\t6 & 6 & yes & 11.0283 & 4.2 & 12 & 0 & 1 & no \\\\\n",
       "\t7 & 7 & no & 11.4547 & 5.1 & 8 & 0 & 0 & no \\\\\n",
       "\t8 & 8 & yes & 10.4909 & 3.2 & 8 & 0 & 2 & no \\\\\n",
       "\t9 & 9 & no & 10.6247 & 3.9 & 12 & 0 & 0 & no \\\\\n",
       "\t10 & 10 & no & 10.4864 & 4.3 & 11 & 0 & 2 & no \\\\\n",
       "\t11 & 11 & no & 10.6606 & 4.5 & 11 & 0 & 2 & no \\\\\n",
       "\t12 & 12 & no & 10.4676 & 6.0 & 12 & 0 & 0 & no \\\\\n",
       "\t13 & 13 & no & 11.2296 & 3.3 & 11 & 2 & 0 & no \\\\\n",
       "\t14 & 14 & no & 11.9065 & 5.6 & 14 & 0 & 0 & no \\\\\n",
       "\t15 & 15 & no & 11.5016 & 5.6 & 11 & 0 & 0 & no \\\\\n",
       "\t16 & 16 & no & 11.2935 & 4.7 & 11 & 0 & 1 & no \\\\\n",
       "\t17 & 17 & no & 10.8613 & 5.0 & 8 & 0 & 0 & no \\\\\n",
       "\t18 & 18 & yes & 11.844 & 3.9 & 12 & 0 & 0 & no \\\\\n",
       "\t19 & 19 & no & 11.0486 & 4.7 & 8 & 0 & 1 & no \\\\\n",
       "\t20 & 20 & yes & 10.9578 & 5.3 & 11 & 0 & 0 & no \\\\\n",
       "\t21 & 21 & no & 10.8601 & 2.9 & 19 & 0 & 0 & no \\\\\n",
       "\t22 & 22 & yes & 11.1081 & 4.6 & 11 & 0 & 1 & no \\\\\n",
       "\t23 & 23 & no & 10.8486 & 4.4 & 8 & 0 & 2 & no \\\\\n",
       "\t24 & 24 & no & 10.4824 & 2.0 & 12 & 1 & 0 & no \\\\\n",
       "\t25 & 25 & yes & 10.484 & 5.4 & 8 & 0 & 0 & no \\\\\n",
       "\t26 & 26 & yes & 10.6012 & 4.7 & 8 & 0 & 0 & no \\\\\n",
       "\t27 & 27 & no & 10.5406 & 2.8 & 9 & 2 & 0 & no \\\\\n",
       "\t28 & 28 & no & 11.2243 & 4.7 & 8 & 0 & 1 & no \\\\\n",
       "\t29 & 29 & yes & 10.8411 & 4.9 & 12 & 0 & 0 & no \\\\\n",
       "\t30 & 30 & no & 10.5663 & 3.0 & 11 & 0 & 1 & no \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m872×8 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m Column1 \u001b[0m\u001b[1m lfp     \u001b[0m\u001b[1m lnnlinc \u001b[0m\u001b[1m age     \u001b[0m\u001b[1m educ  \u001b[0m\u001b[1m nyc   \u001b[0m\u001b[1m noc   \u001b[0m\u001b[1m foreign \u001b[0m\n",
       "     │\u001b[90m Int64   \u001b[0m\u001b[90m String3 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m String3 \u001b[0m\n",
       "─────┼──────────────────────────────────────────────────────────────────\n",
       "   1 │       1  no       10.7875      3.0      8      1      1  no\n",
       "   2 │       2  yes      10.5243      4.5      8      0      1  no\n",
       "   3 │       3  no       10.9686      4.6      9      0      0  no\n",
       "   4 │       4  no       11.105       3.1     11      2      0  no\n",
       "   5 │       5  no       11.1085      4.4     12      0      2  no\n",
       "   6 │       6  yes      11.0283      4.2     12      0      1  no\n",
       "   7 │       7  no       11.4547      5.1      8      0      0  no\n",
       "   8 │       8  yes      10.4909      3.2      8      0      2  no\n",
       "   9 │       9  no       10.6247      3.9     12      0      0  no\n",
       "  10 │      10  no       10.4864      4.3     11      0      2  no\n",
       "  11 │      11  no       10.6606      4.5     11      0      2  no\n",
       "  ⋮  │    ⋮        ⋮        ⋮        ⋮       ⋮      ⋮      ⋮       ⋮\n",
       " 863 │     863  no       11.111       3.5     10      1      1  yes\n",
       " 864 │     864  no       10.4714      5.1      9      0      1  yes\n",
       " 865 │     865  no       10.1475      4.1      5      1      0  yes\n",
       " 866 │     866  yes      10.6932      3.5      9      0      2  yes\n",
       " 867 │     867  yes      10.0276      4.2     14      0      0  yes\n",
       " 868 │     868  no       10.5974      2.4      4      2      1  yes\n",
       " 869 │     869  yes      10.3778      4.8      8      0      0  yes\n",
       " 870 │     870  no       10.1337      2.4      6      2      0  yes\n",
       " 871 │     871  yes      10.9324      4.1     10      0      1  yes\n",
       " 872 │     872  no       11.2207      5.1     10      0      0  yes\n",
       "\u001b[36m                                                        851 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_raw = CSV.read(\"participation.csv\", DataFrame)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92c5f692",
   "metadata": {},
   "source": [
    "Inspect the contents of the data set to make sure it got loaded correctly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "983c1fa5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>8×7 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">variable</th><th style = \"text-align: left;\">mean</th><th style = \"text-align: left;\">min</th><th style = \"text-align: left;\">median</th><th style = \"text-align: left;\">max</th><th style = \"text-align: left;\">nmissing</th><th style = \"text-align: left;\">eltype</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Symbol\" style = \"text-align: left;\">Symbol</th><th title = \"Union{Nothing, Float64}\" style = \"text-align: left;\">Union…</th><th title = \"Any\" style = \"text-align: left;\">Any</th><th title = \"Union{Nothing, Float64}\" style = \"text-align: left;\">Union…</th><th title = \"Any\" style = \"text-align: left;\">Any</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"DataType\" style = \"text-align: left;\">DataType</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">Column1</td><td style = \"text-align: left;\">436.5</td><td style = \"text-align: left;\">1</td><td style = \"text-align: left;\">436.5</td><td style = \"text-align: left;\">872</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">Int64</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">lfp</td><td style = \"font-style: italic; text-align: left;\"></td><td style = \"text-align: left;\">no</td><td style = \"font-style: italic; text-align: left;\"></td><td style = \"text-align: left;\">yes</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">String3</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">lnnlinc</td><td style = \"text-align: left;\">10.6856</td><td style = \"text-align: left;\">7.1869</td><td style = \"text-align: left;\">10.6431</td><td style = \"text-align: left;\">12.3757</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">Float64</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">age</td><td style = \"text-align: left;\">3.99553</td><td style = \"text-align: left;\">2.0</td><td style = \"text-align: left;\">3.9</td><td style = \"text-align: left;\">6.2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">Float64</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">educ</td><td style = \"text-align: left;\">9.30734</td><td style = \"text-align: left;\">1</td><td style = \"text-align: left;\">9.0</td><td style = \"text-align: left;\">21</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">Int64</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: left;\">nyc</td><td style = \"text-align: left;\">0.311927</td><td style = \"text-align: left;\">0</td><td style = \"text-align: left;\">0.0</td><td style = \"text-align: left;\">3</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">Int64</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: left;\">noc</td><td style = \"text-align: left;\">0.982798</td><td style = \"text-align: left;\">0</td><td style = \"text-align: left;\">1.0</td><td style = \"text-align: left;\">6</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">Int64</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: left;\">foreign</td><td style = \"font-style: italic; text-align: left;\"></td><td style = \"text-align: left;\">no</td><td style = \"font-style: italic; text-align: left;\"></td><td style = \"text-align: left;\">yes</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">String3</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccccc}\n",
       "\t& variable & mean & min & median & max & nmissing & eltype\\\\\n",
       "\t\\hline\n",
       "\t& Symbol & Union… & Any & Union… & Any & Int64 & DataType\\\\\n",
       "\t\\hline\n",
       "\t1 & Column1 & 436.5 & 1 & 436.5 & 872 & 0 & Int64 \\\\\n",
       "\t2 & lfp &  & no &  & yes & 0 & String3 \\\\\n",
       "\t3 & lnnlinc & 10.6856 & 7.1869 & 10.6431 & 12.3757 & 0 & Float64 \\\\\n",
       "\t4 & age & 3.99553 & 2.0 & 3.9 & 6.2 & 0 & Float64 \\\\\n",
       "\t5 & educ & 9.30734 & 1 & 9.0 & 21 & 0 & Int64 \\\\\n",
       "\t6 & nyc & 0.311927 & 0 & 0.0 & 3 & 0 & Int64 \\\\\n",
       "\t7 & noc & 0.982798 & 0 & 1.0 & 6 & 0 & Int64 \\\\\n",
       "\t8 & foreign &  & no &  & yes & 0 & String3 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m8×7 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m variable \u001b[0m\u001b[1m mean     \u001b[0m\u001b[1m min    \u001b[0m\u001b[1m median  \u001b[0m\u001b[1m max     \u001b[0m\u001b[1m nmissing \u001b[0m\u001b[1m eltype   \u001b[0m\n",
       "     │\u001b[90m Symbol   \u001b[0m\u001b[90m Union…   \u001b[0m\u001b[90m Any    \u001b[0m\u001b[90m Union…  \u001b[0m\u001b[90m Any     \u001b[0m\u001b[90m Int64    \u001b[0m\u001b[90m DataType \u001b[0m\n",
       "─────┼──────────────────────────────────────────────────────────────────\n",
       "   1 │ Column1   436.5     1       436.5    872             0  Int64\n",
       "   2 │ lfp      \u001b[90m          \u001b[0m no     \u001b[90m         \u001b[0m yes             0  String3\n",
       "   3 │ lnnlinc   10.6856   7.1869  10.6431  12.3757         0  Float64\n",
       "   4 │ age       3.99553   2.0     3.9      6.2             0  Float64\n",
       "   5 │ educ      9.30734   1       9.0      21              0  Int64\n",
       "   6 │ nyc       0.311927  0       0.0      3               0  Int64\n",
       "   7 │ noc       0.982798  0       1.0      6               0  Int64\n",
       "   8 │ foreign  \u001b[90m          \u001b[0m no     \u001b[90m         \u001b[0m yes             0  String3"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "describe(df_raw)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "494399ae",
   "metadata": {},
   "source": [
    "Now transform the data set. We use the `select` function and perform the following transformations:\n",
    "* recode `:lfp` variable from text to binary;\n",
    "* add square of `:age` column;\n",
    "* change `:foreign` column to be categorical;\n",
    "* all other columns are left as they are.\n",
    "\n",
    "The general syntax of column transformation options is:\n",
    "```\n",
    "source columns => transformation => target columns name\n",
    "```\n",
    "(the `transformation` and `target columns name` can be dropped)\n",
    "\n",
    "Also note the `ByRow` wrapper which tells `select` to perform the operation row-wise (by default operations are performed on whole columns).\n",
    "\n",
    "In [this post](https://bkamins.github.io/julialang/2020/12/24/minilanguage.html) you can find an explanation of the most typical cases of supported transformation specifications."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "01bc9d07",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>872×8 DataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">847 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">lfp</th><th style = \"text-align: left;\">lnnlinc</th><th style = \"text-align: left;\">age</th><th style = \"text-align: left;\">age²</th><th style = \"text-align: left;\">educ</th><th style = \"text-align: left;\">nyc</th><th style = \"text-align: left;\">noc</th><th style = \"text-align: left;\">foreign</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"CategoricalValue{String3, UInt32}\" style = \"text-align: left;\">Cat…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.7875</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.5243</td><td style = \"text-align: right;\">4.5</td><td style = \"text-align: right;\">20.25</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.9686</td><td style = \"text-align: right;\">4.6</td><td style = \"text-align: right;\">21.16</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; 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text-align: right;\">7</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.4547</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.4909</td><td style = \"text-align: right;\">3.2</td><td style = \"text-align: right;\">10.24</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.6247</td><td style = \"text-align: right;\">3.9</td><td style = \"text-align: right;\">15.21</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; 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text-align: right;\">13</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.2296</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">10.89</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">861</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.5289</td><td style = \"text-align: right;\">3.4</td><td style = \"text-align: right;\">11.56</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">862</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.4685</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">10.89</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">863</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.111</td><td style = \"text-align: right;\">3.5</td><td style = \"text-align: right;\">12.25</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">864</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.4714</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">865</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.1475</td><td style = \"text-align: right;\">4.1</td><td style = \"text-align: right;\">16.81</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">866</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.6932</td><td style = \"text-align: right;\">3.5</td><td style = \"text-align: right;\">12.25</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">867</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.0276</td><td style = \"text-align: right;\">4.2</td><td style = \"text-align: right;\">17.64</td><td style = \"text-align: right;\">14</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">868</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.5974</td><td style = \"text-align: right;\">2.4</td><td style = \"text-align: right;\">5.76</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">869</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.3778</td><td style = \"text-align: right;\">4.8</td><td style = \"text-align: right;\">23.04</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">870</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.1337</td><td style = \"text-align: right;\">2.4</td><td style = \"text-align: right;\">5.76</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">871</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.9324</td><td style = \"text-align: right;\">4.1</td><td style = \"text-align: right;\">16.81</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">872</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.2207</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& lfp & lnnlinc & age & age² & educ & nyc & noc & foreign\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64 & Float64 & Float64 & Int64 & Int64 & Int64 & Cat…\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & 10.7875 & 3.0 & 9.0 & 8 & 1 & 1 & no \\\\\n",
       "\t2 & 1 & 10.5243 & 4.5 & 20.25 & 8 & 0 & 1 & no \\\\\n",
       "\t3 & 0 & 10.9686 & 4.6 & 21.16 & 9 & 0 & 0 & no \\\\\n",
       "\t4 & 0 & 11.105 & 3.1 & 9.61 & 11 & 2 & 0 & no \\\\\n",
       "\t5 & 0 & 11.1085 & 4.4 & 19.36 & 12 & 0 & 2 & no \\\\\n",
       "\t6 & 1 & 11.0283 & 4.2 & 17.64 & 12 & 0 & 1 & no \\\\\n",
       "\t7 & 0 & 11.4547 & 5.1 & 26.01 & 8 & 0 & 0 & no \\\\\n",
       "\t8 & 1 & 10.4909 & 3.2 & 10.24 & 8 & 0 & 2 & no \\\\\n",
       "\t9 & 0 & 10.6247 & 3.9 & 15.21 & 12 & 0 & 0 & no \\\\\n",
       "\t10 & 0 & 10.4864 & 4.3 & 18.49 & 11 & 0 & 2 & no \\\\\n",
       "\t11 & 0 & 10.6606 & 4.5 & 20.25 & 11 & 0 & 2 & no \\\\\n",
       "\t12 & 0 & 10.4676 & 6.0 & 36.0 & 12 & 0 & 0 & no \\\\\n",
       "\t13 & 0 & 11.2296 & 3.3 & 10.89 & 11 & 2 & 0 & no \\\\\n",
       "\t14 & 0 & 11.9065 & 5.6 & 31.36 & 14 & 0 & 0 & no \\\\\n",
       "\t15 & 0 & 11.5016 & 5.6 & 31.36 & 11 & 0 & 0 & no \\\\\n",
       "\t16 & 0 & 11.2935 & 4.7 & 22.09 & 11 & 0 & 1 & no \\\\\n",
       "\t17 & 0 & 10.8613 & 5.0 & 25.0 & 8 & 0 & 0 & no \\\\\n",
       "\t18 & 1 & 11.844 & 3.9 & 15.21 & 12 & 0 & 0 & no \\\\\n",
       "\t19 & 0 & 11.0486 & 4.7 & 22.09 & 8 & 0 & 1 & no \\\\\n",
       "\t20 & 1 & 10.9578 & 5.3 & 28.09 & 11 & 0 & 0 & no \\\\\n",
       "\t21 & 0 & 10.8601 & 2.9 & 8.41 & 19 & 0 & 0 & no \\\\\n",
       "\t22 & 1 & 11.1081 & 4.6 & 21.16 & 11 & 0 & 1 & no \\\\\n",
       "\t23 & 0 & 10.8486 & 4.4 & 19.36 & 8 & 0 & 2 & no \\\\\n",
       "\t24 & 0 & 10.4824 & 2.0 & 4.0 & 12 & 1 & 0 & no \\\\\n",
       "\t25 & 1 & 10.484 & 5.4 & 29.16 & 8 & 0 & 0 & no \\\\\n",
       "\t26 & 1 & 10.6012 & 4.7 & 22.09 & 8 & 0 & 0 & no \\\\\n",
       "\t27 & 0 & 10.5406 & 2.8 & 7.84 & 9 & 2 & 0 & no \\\\\n",
       "\t28 & 0 & 11.2243 & 4.7 & 22.09 & 8 & 0 & 1 & no \\\\\n",
       "\t29 & 1 & 10.8411 & 4.9 & 24.01 & 12 & 0 & 0 & no \\\\\n",
       "\t30 & 0 & 10.5663 & 3.0 & 9.0 & 11 & 0 & 1 & no \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m872×8 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m lfp   \u001b[0m\u001b[1m lnnlinc \u001b[0m\u001b[1m age     \u001b[0m\u001b[1m age²    \u001b[0m\u001b[1m educ  \u001b[0m\u001b[1m nyc   \u001b[0m\u001b[1m noc   \u001b[0m\u001b[1m foreign \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Cat…    \u001b[0m\n",
       "─────┼────────────────────────────────────────────────────────────────\n",
       "   1 │     0  10.7875      3.0     9.0       8      1      1  no\n",
       "   2 │     1  10.5243      4.5    20.25      8      0      1  no\n",
       "   3 │     0  10.9686      4.6    21.16      9      0      0  no\n",
       "   4 │     0  11.105       3.1     9.61     11      2      0  no\n",
       "   5 │     0  11.1085      4.4    19.36     12      0      2  no\n",
       "   6 │     1  11.0283      4.2    17.64     12      0      1  no\n",
       "   7 │     0  11.4547      5.1    26.01      8      0      0  no\n",
       "   8 │     1  10.4909      3.2    10.24      8      0      2  no\n",
       "   9 │     0  10.6247      3.9    15.21     12      0      0  no\n",
       "  10 │     0  10.4864      4.3    18.49     11      0      2  no\n",
       "  11 │     0  10.6606      4.5    20.25     11      0      2  no\n",
       "  ⋮  │   ⋮       ⋮        ⋮        ⋮       ⋮      ⋮      ⋮       ⋮\n",
       " 863 │     0  11.111       3.5    12.25     10      1      1  yes\n",
       " 864 │     0  10.4714      5.1    26.01      9      0      1  yes\n",
       " 865 │     0  10.1475      4.1    16.81      5      1      0  yes\n",
       " 866 │     1  10.6932      3.5    12.25      9      0      2  yes\n",
       " 867 │     1  10.0276      4.2    17.64     14      0      0  yes\n",
       " 868 │     0  10.5974      2.4     5.76      4      2      1  yes\n",
       " 869 │     1  10.3778      4.8    23.04      8      0      0  yes\n",
       " 870 │     0  10.1337      2.4     5.76      6      2      0  yes\n",
       " 871 │     1  10.9324      4.1    16.81     10      0      1  yes\n",
       " 872 │     0  11.2207      5.1    26.01     10      0      0  yes\n",
       "\u001b[36m                                                      851 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = select(df_raw,\n",
    "            :lfp => (x -> recode(x, \"yes\" => 1, \"no\" => 0)) => :lfp,\n",
    "            :lnnlinc,\n",
    "            :age,\n",
    "            :age => ByRow(x -> x^2) => :age²,\n",
    "            Between(:educ, :noc),\n",
    "            :foreign => categorical => :foreign)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c071c39e",
   "metadata": {},
   "source": [
    "If we want to leave column names unchanged we can use `renamecols=false` keyword argument, and in this case the target column name can be dropped:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "96c9a4e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>872×8 DataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">847 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">lfp</th><th style = \"text-align: left;\">lnnlinc</th><th style = \"text-align: left;\">age</th><th style = \"text-align: left;\">age²</th><th style = \"text-align: left;\">educ</th><th style = \"text-align: left;\">nyc</th><th style = \"text-align: left;\">noc</th><th style = \"text-align: left;\">foreign</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"CategoricalValue{String3, UInt32}\" style = \"text-align: left;\">Cat…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.7875</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.5243</td><td style = \"text-align: right;\">4.5</td><td style = \"text-align: right;\">20.25</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.9686</td><td style = \"text-align: right;\">4.6</td><td style = \"text-align: right;\">21.16</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.105</td><td style = \"text-align: right;\">3.1</td><td style = \"text-align: right;\">9.61</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.1085</td><td style = \"text-align: right;\">4.4</td><td style = \"text-align: right;\">19.36</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">11.0283</td><td style = \"text-align: right;\">4.2</td><td style = \"text-align: right;\">17.64</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.4547</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.4909</td><td style = \"text-align: right;\">3.2</td><td style = \"text-align: right;\">10.24</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.6247</td><td style = \"text-align: right;\">3.9</td><td style = \"text-align: right;\">15.21</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.4864</td><td style = \"text-align: right;\">4.3</td><td style = \"text-align: right;\">18.49</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.6606</td><td style = \"text-align: right;\">4.5</td><td style = \"text-align: right;\">20.25</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.4676</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">36.0</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.2296</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">10.89</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">861</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.5289</td><td style = \"text-align: right;\">3.4</td><td style = \"text-align: right;\">11.56</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">862</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.4685</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">10.89</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">863</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.111</td><td style = \"text-align: right;\">3.5</td><td style = \"text-align: right;\">12.25</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">864</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.4714</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">865</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.1475</td><td style = \"text-align: right;\">4.1</td><td style = \"text-align: right;\">16.81</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">866</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.6932</td><td style = \"text-align: right;\">3.5</td><td style = \"text-align: right;\">12.25</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">867</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.0276</td><td style = \"text-align: right;\">4.2</td><td style = \"text-align: right;\">17.64</td><td style = \"text-align: right;\">14</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">868</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.5974</td><td style = \"text-align: right;\">2.4</td><td style = \"text-align: right;\">5.76</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">869</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.3778</td><td style = \"text-align: right;\">4.8</td><td style = \"text-align: right;\">23.04</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">870</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.1337</td><td style = \"text-align: right;\">2.4</td><td style = \"text-align: right;\">5.76</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">871</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.9324</td><td style = \"text-align: right;\">4.1</td><td style = \"text-align: right;\">16.81</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">872</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.2207</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& lfp & lnnlinc & age & age² & educ & nyc & noc & foreign\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64 & Float64 & Float64 & Int64 & Int64 & Int64 & Cat…\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & 10.7875 & 3.0 & 9.0 & 8 & 1 & 1 & no \\\\\n",
       "\t2 & 1 & 10.5243 & 4.5 & 20.25 & 8 & 0 & 1 & no \\\\\n",
       "\t3 & 0 & 10.9686 & 4.6 & 21.16 & 9 & 0 & 0 & no \\\\\n",
       "\t4 & 0 & 11.105 & 3.1 & 9.61 & 11 & 2 & 0 & no \\\\\n",
       "\t5 & 0 & 11.1085 & 4.4 & 19.36 & 12 & 0 & 2 & no \\\\\n",
       "\t6 & 1 & 11.0283 & 4.2 & 17.64 & 12 & 0 & 1 & no \\\\\n",
       "\t7 & 0 & 11.4547 & 5.1 & 26.01 & 8 & 0 & 0 & no \\\\\n",
       "\t8 & 1 & 10.4909 & 3.2 & 10.24 & 8 & 0 & 2 & no \\\\\n",
       "\t9 & 0 & 10.6247 & 3.9 & 15.21 & 12 & 0 & 0 & no \\\\\n",
       "\t10 & 0 & 10.4864 & 4.3 & 18.49 & 11 & 0 & 2 & no \\\\\n",
       "\t11 & 0 & 10.6606 & 4.5 & 20.25 & 11 & 0 & 2 & no \\\\\n",
       "\t12 & 0 & 10.4676 & 6.0 & 36.0 & 12 & 0 & 0 & no \\\\\n",
       "\t13 & 0 & 11.2296 & 3.3 & 10.89 & 11 & 2 & 0 & no \\\\\n",
       "\t14 & 0 & 11.9065 & 5.6 & 31.36 & 14 & 0 & 0 & no \\\\\n",
       "\t15 & 0 & 11.5016 & 5.6 & 31.36 & 11 & 0 & 0 & no \\\\\n",
       "\t16 & 0 & 11.2935 & 4.7 & 22.09 & 11 & 0 & 1 & no \\\\\n",
       "\t17 & 0 & 10.8613 & 5.0 & 25.0 & 8 & 0 & 0 & no \\\\\n",
       "\t18 & 1 & 11.844 & 3.9 & 15.21 & 12 & 0 & 0 & no \\\\\n",
       "\t19 & 0 & 11.0486 & 4.7 & 22.09 & 8 & 0 & 1 & no \\\\\n",
       "\t20 & 1 & 10.9578 & 5.3 & 28.09 & 11 & 0 & 0 & no \\\\\n",
       "\t21 & 0 & 10.8601 & 2.9 & 8.41 & 19 & 0 & 0 & no \\\\\n",
       "\t22 & 1 & 11.1081 & 4.6 & 21.16 & 11 & 0 & 1 & no \\\\\n",
       "\t23 & 0 & 10.8486 & 4.4 & 19.36 & 8 & 0 & 2 & no \\\\\n",
       "\t24 & 0 & 10.4824 & 2.0 & 4.0 & 12 & 1 & 0 & no \\\\\n",
       "\t25 & 1 & 10.484 & 5.4 & 29.16 & 8 & 0 & 0 & no \\\\\n",
       "\t26 & 1 & 10.6012 & 4.7 & 22.09 & 8 & 0 & 0 & no \\\\\n",
       "\t27 & 0 & 10.5406 & 2.8 & 7.84 & 9 & 2 & 0 & no \\\\\n",
       "\t28 & 0 & 11.2243 & 4.7 & 22.09 & 8 & 0 & 1 & no \\\\\n",
       "\t29 & 1 & 10.8411 & 4.9 & 24.01 & 12 & 0 & 0 & no \\\\\n",
       "\t30 & 0 & 10.5663 & 3.0 & 9.0 & 11 & 0 & 1 & no \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m872×8 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m lfp   \u001b[0m\u001b[1m lnnlinc \u001b[0m\u001b[1m age     \u001b[0m\u001b[1m age²    \u001b[0m\u001b[1m educ  \u001b[0m\u001b[1m nyc   \u001b[0m\u001b[1m noc   \u001b[0m\u001b[1m foreign \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Cat…    \u001b[0m\n",
       "─────┼────────────────────────────────────────────────────────────────\n",
       "   1 │     0  10.7875      3.0     9.0       8      1      1  no\n",
       "   2 │     1  10.5243      4.5    20.25      8      0      1  no\n",
       "   3 │     0  10.9686      4.6    21.16      9      0      0  no\n",
       "   4 │     0  11.105       3.1     9.61     11      2      0  no\n",
       "   5 │     0  11.1085      4.4    19.36     12      0      2  no\n",
       "   6 │     1  11.0283      4.2    17.64     12      0      1  no\n",
       "   7 │     0  11.4547      5.1    26.01      8      0      0  no\n",
       "   8 │     1  10.4909      3.2    10.24      8      0      2  no\n",
       "   9 │     0  10.6247      3.9    15.21     12      0      0  no\n",
       "  10 │     0  10.4864      4.3    18.49     11      0      2  no\n",
       "  11 │     0  10.6606      4.5    20.25     11      0      2  no\n",
       "  ⋮  │   ⋮       ⋮        ⋮        ⋮       ⋮      ⋮      ⋮       ⋮\n",
       " 863 │     0  11.111       3.5    12.25     10      1      1  yes\n",
       " 864 │     0  10.4714      5.1    26.01      9      0      1  yes\n",
       " 865 │     0  10.1475      4.1    16.81      5      1      0  yes\n",
       " 866 │     1  10.6932      3.5    12.25      9      0      2  yes\n",
       " 867 │     1  10.0276      4.2    17.64     14      0      0  yes\n",
       " 868 │     0  10.5974      2.4     5.76      4      2      1  yes\n",
       " 869 │     1  10.3778      4.8    23.04      8      0      0  yes\n",
       " 870 │     0  10.1337      2.4     5.76      6      2      0  yes\n",
       " 871 │     1  10.9324      4.1    16.81     10      0      1  yes\n",
       " 872 │     0  11.2207      5.1    26.01     10      0      0  yes\n",
       "\u001b[36m                                                      851 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = select(df_raw,\n",
    "            :lfp => x -> recode(x, \"yes\" => 1, \"no\" => 0),\n",
    "            :lnnlinc,\n",
    "            :age,\n",
    "            :age => ByRow(x -> x^2) => :age²,\n",
    "            Between(:educ, :noc),\n",
    "            :foreign => categorical,\n",
    "            renamecols=false)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8cf42c7e",
   "metadata": {},
   "source": [
    "Check the summary statistics of the updated table:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2eac1062",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>8×7 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">variable</th><th style = \"text-align: left;\">mean</th><th style = \"text-align: left;\">min</th><th style = \"text-align: left;\">median</th><th style = \"text-align: left;\">max</th><th style = \"text-align: left;\">nmissing</th><th style = \"text-align: left;\">eltype</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Symbol\" style = \"text-align: left;\">Symbol</th><th title = \"Union{Nothing, Float64}\" style = \"text-align: left;\">Union…</th><th title = \"Any\" style = \"text-align: left;\">Any</th><th title = \"Union{Nothing, Float64}\" style = \"text-align: left;\">Union…</th><th title = \"Any\" style = \"text-align: left;\">Any</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"DataType\" style = \"text-align: left;\">DataType</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">lfp</td><td style = \"text-align: left;\">0.459862</td><td style = \"text-align: left;\">0</td><td style = \"text-align: left;\">0.0</td><td style = \"text-align: left;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">Int64</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">lnnlinc</td><td style = \"text-align: left;\">10.6856</td><td style = \"text-align: left;\">7.1869</td><td style = \"text-align: left;\">10.6431</td><td style = \"text-align: left;\">12.3757</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">Float64</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">age</td><td style = \"text-align: left;\">3.99553</td><td style = \"text-align: left;\">2.0</td><td style = \"text-align: left;\">3.9</td><td style = \"text-align: left;\">6.2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">Float64</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">age²</td><td style = \"text-align: left;\">17.0763</td><td style = \"text-align: left;\">4.0</td><td style = \"text-align: left;\">15.21</td><td style = \"text-align: left;\">38.44</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">Float64</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">educ</td><td style = \"text-align: left;\">9.30734</td><td style = \"text-align: left;\">1</td><td style = \"text-align: left;\">9.0</td><td style = \"text-align: left;\">21</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">Int64</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: left;\">nyc</td><td style = \"text-align: left;\">0.311927</td><td style = \"text-align: left;\">0</td><td style = \"text-align: left;\">0.0</td><td style = \"text-align: left;\">3</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">Int64</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: left;\">noc</td><td style = \"text-align: left;\">0.982798</td><td style = \"text-align: left;\">0</td><td style = \"text-align: left;\">1.0</td><td style = \"text-align: left;\">6</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">Int64</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: left;\">foreign</td><td style = \"font-style: italic; text-align: left;\"></td><td style = \"text-align: left;\">no</td><td style = \"font-style: italic; text-align: left;\"></td><td style = \"text-align: left;\">yes</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">CategoricalValue{String3, UInt32}</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccccc}\n",
       "\t& variable & mean & min & median & max & nmissing & eltype\\\\\n",
       "\t\\hline\n",
       "\t& Symbol & Union… & Any & Union… & Any & Int64 & DataType\\\\\n",
       "\t\\hline\n",
       "\t1 & lfp & 0.459862 & 0 & 0.0 & 1 & 0 & Int64 \\\\\n",
       "\t2 & lnnlinc & 10.6856 & 7.1869 & 10.6431 & 12.3757 & 0 & Float64 \\\\\n",
       "\t3 & age & 3.99553 & 2.0 & 3.9 & 6.2 & 0 & Float64 \\\\\n",
       "\t4 & age² & 17.0763 & 4.0 & 15.21 & 38.44 & 0 & Float64 \\\\\n",
       "\t5 & educ & 9.30734 & 1 & 9.0 & 21 & 0 & Int64 \\\\\n",
       "\t6 & nyc & 0.311927 & 0 & 0.0 & 3 & 0 & Int64 \\\\\n",
       "\t7 & noc & 0.982798 & 0 & 1.0 & 6 & 0 & Int64 \\\\\n",
       "\t8 & foreign &  & no &  & yes & 0 & CategoricalValue\\{String3, UInt32\\} \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m8×7 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m variable \u001b[0m\u001b[1m mean     \u001b[0m\u001b[1m min    \u001b[0m\u001b[1m median  \u001b[0m\u001b[1m max     \u001b[0m\u001b[1m nmissing \u001b[0m\u001b[1m eltype         \u001b[0m ⋯\n",
       "     │\u001b[90m Symbol   \u001b[0m\u001b[90m Union…   \u001b[0m\u001b[90m Any    \u001b[0m\u001b[90m Union…  \u001b[0m\u001b[90m Any     \u001b[0m\u001b[90m Int64    \u001b[0m\u001b[90m DataType       \u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │ lfp       0.459862  0       0.0      1               0  Int64           ⋯\n",
       "   2 │ lnnlinc   10.6856   7.1869  10.6431  12.3757         0  Float64\n",
       "   3 │ age       3.99553   2.0     3.9      6.2             0  Float64\n",
       "   4 │ age²      17.0763   4.0     15.21    38.44           0  Float64\n",
       "   5 │ educ      9.30734   1       9.0      21              0  Int64           ⋯\n",
       "   6 │ nyc       0.311927  0       0.0      3               0  Int64\n",
       "   7 │ noc       0.982798  0       1.0      6               0  Int64\n",
       "   8 │ foreign  \u001b[90m          \u001b[0m no     \u001b[90m         \u001b[0m yes             0  CategoricalValu\n",
       "\u001b[36m                                                                1 column omitted\u001b[0m"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "describe(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63ded484",
   "metadata": {},
   "source": [
    "## Exploratory data analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8880bd35",
   "metadata": {},
   "source": [
    "We want to compute the mean of numeric columns by `:lfp` to initialy check in what direction they influence the target.\n",
    "\n",
    "In the example we use the following:\n",
    "* the `@chain` macro from the [Chain.jl](https://github.com/jkrumbiegel/Chain.jl) package; it allows for convenient piping of operations;\n",
    "* the `groupby` function that adds the key column to the data frame (groups the data frame by the passed column)\n",
    "* the `combine` function that combines the rows of a data frame by some function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6868bd67",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>2×6 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">lfp</th><th style = \"text-align: left;\">lnnlinc_mean</th><th style = \"text-align: left;\">age_mean</th><th style = \"text-align: left;\">educ_mean</th><th style = \"text-align: left;\">nyc_mean</th><th style = \"text-align: left;\">noc_mean</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.7513</td><td style = \"text-align: right;\">4.08535</td><td style = \"text-align: right;\">9.59448</td><td style = \"text-align: right;\">0.409766</td><td style = \"text-align: right;\">0.902335</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.6083</td><td style = \"text-align: right;\">3.89002</td><td style = \"text-align: right;\">8.97007</td><td style = \"text-align: right;\">0.197007</td><td style = \"text-align: right;\">1.07731</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccc}\n",
       "\t& lfp & lnnlinc\\_mean & age\\_mean & educ\\_mean & nyc\\_mean & noc\\_mean\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64 & Float64 & Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & 10.7513 & 4.08535 & 9.59448 & 0.409766 & 0.902335 \\\\\n",
       "\t2 & 1 & 10.6083 & 3.89002 & 8.97007 & 0.197007 & 1.07731 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×6 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m lfp   \u001b[0m\u001b[1m lnnlinc_mean \u001b[0m\u001b[1m age_mean \u001b[0m\u001b[1m educ_mean \u001b[0m\u001b[1m nyc_mean \u001b[0m\u001b[1m noc_mean \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Float64      \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼──────────────────────────────────────────────────────────────\n",
       "   1 │     0       10.7513   4.08535    9.59448  0.409766  0.902335\n",
       "   2 │     1       10.6083   3.89002    8.97007  0.197007  1.07731"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@chain df begin\n",
    "    groupby(:lfp)\n",
    "    combine([:lnnlinc, :age, :educ, :nyc, :noc] .=> mean)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3d9934a",
   "metadata": {},
   "source": [
    "Observe that the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b1720dff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element Vector{Pair{Symbol, typeof(mean)}}:\n",
       " :lnnlinc => Statistics.mean\n",
       "     :age => Statistics.mean\n",
       "    :educ => Statistics.mean\n",
       "     :nyc => Statistics.mean\n",
       "     :noc => Statistics.mean"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[:lnnlinc, :age, :educ, :nyc, :noc] .=> mean"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fc5b3cc",
   "metadata": {},
   "source": [
    "is a convenient way to specify multiple similar transformations using the broadcasting syntax provided by Julia.\n",
    "\n",
    "You can find more examples of this pattern at work [here](https://bkamins.github.io/julialang/2021/07/09/multicol.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0a602c4",
   "metadata": {},
   "source": [
    "If we did not want to list all the columns manually we could have written (note that `:lfp` was included as it is binary):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "fc12c922",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>2×8 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">lfp</th><th style = \"text-align: left;\">lfp_mean</th><th style = \"text-align: left;\">lnnlinc_mean</th><th style = \"text-align: left;\">age_mean</th><th style = \"text-align: left;\">age²_mean</th><th style = \"text-align: left;\">educ_mean</th><th style = \"text-align: left;\">nyc_mean</th><th style = \"text-align: left;\">noc_mean</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0.0</td><td style = \"text-align: right;\">10.7513</td><td style = \"text-align: right;\">4.08535</td><td style = \"text-align: right;\">18.0357</td><td style = \"text-align: right;\">9.59448</td><td style = \"text-align: right;\">0.409766</td><td style = \"text-align: right;\">0.902335</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1.0</td><td style = \"text-align: right;\">10.6083</td><td style = \"text-align: right;\">3.89002</td><td style = \"text-align: right;\">15.9496</td><td style = \"text-align: right;\">8.97007</td><td style = \"text-align: right;\">0.197007</td><td style = \"text-align: right;\">1.07731</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& lfp & lfp\\_mean & lnnlinc\\_mean & age\\_mean & age²\\_mean & educ\\_mean & nyc\\_mean & noc\\_mean\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & 0.0 & 10.7513 & 4.08535 & 18.0357 & 9.59448 & 0.409766 & 0.902335 \\\\\n",
       "\t2 & 1 & 1.0 & 10.6083 & 3.89002 & 15.9496 & 8.97007 & 0.197007 & 1.07731 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×8 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m lfp   \u001b[0m\u001b[1m lfp_mean \u001b[0m\u001b[1m lnnlinc_mean \u001b[0m\u001b[1m age_mean \u001b[0m\u001b[1m age²_mean \u001b[0m\u001b[1m educ_mean \u001b[0m\u001b[1m nyc_mean\u001b[0m ⋯\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Float64      \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64 \u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │     0       0.0       10.7513   4.08535    18.0357    9.59448  0.409766 ⋯\n",
       "   2 │     1       1.0       10.6083   3.89002    15.9496    8.97007  0.197007\n",
       "\u001b[36m                                                                1 column omitted\u001b[0m"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@chain df begin\n",
    "    groupby(:lfp)\n",
    "    combine(names(df, Real) .=> mean)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb1eddd8",
   "metadata": {},
   "source": [
    "Now handle the categorical variable `:foreign`.\n",
    "\n",
    "Note that this time we pass just `nrow` to combine, which has a special treatement and returns the number of rows in each group."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "84bb013e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>4×3 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">lfp</th><th style = \"text-align: left;\">foreign</th><th style = \"text-align: left;\">nrow</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"CategoricalValue{String3, UInt32}\" style = \"text-align: left;\">Cat…</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td><td style = \"text-align: right;\">402</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td><td style = \"text-align: right;\">69</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td><td style = \"text-align: right;\">254</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td><td style = \"text-align: right;\">147</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& lfp & foreign & nrow\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Cat… & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & no & 402 \\\\\n",
       "\t2 & 0 & yes & 69 \\\\\n",
       "\t3 & 1 & no & 254 \\\\\n",
       "\t4 & 1 & yes & 147 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m4×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m lfp   \u001b[0m\u001b[1m foreign \u001b[0m\u001b[1m nrow  \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Cat…    \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼───────────────────────\n",
       "   1 │     0  no         402\n",
       "   2 │     0  yes         69\n",
       "   3 │     1  no         254\n",
       "   4 │     1  yes        147"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@chain df begin\n",
    "    groupby([:lfp, :foreign])\n",
    "    combine(nrow)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f3f983a",
   "metadata": {},
   "source": [
    "If we wanted to create a cross-tabulation of the data we can put:\n",
    "* the `:lfp` variable as rows,\n",
    "* the `:foreign` variable as columns,\n",
    "* the `:nrow` variable as values,\n",
    "\n",
    "using the `unstack` function.\n",
    "\n",
    "More advanced examples of reshaping of data frames are presented [here](https://bkamins.github.io/julialang/2021/05/28/pivot.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "81d473d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>2×3 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">lfp</th><th style = \"text-align: left;\">no</th><th style = \"text-align: left;\">yes</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">402</td><td style = \"text-align: right;\">69</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">254</td><td style = \"text-align: right;\">147</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& lfp & no & yes\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64? & Int64?\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & 402 & 69 \\\\\n",
       "\t2 & 1 & 254 & 147 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m lfp   \u001b[0m\u001b[1m no     \u001b[0m\u001b[1m yes    \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64? \u001b[0m\u001b[90m Int64? \u001b[0m\n",
       "─────┼───────────────────────\n",
       "   1 │     0     402      69\n",
       "   2 │     1     254     147"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@chain df begin\n",
    "    groupby([:lfp, :foreign])\n",
    "    combine(nrow)\n",
    "    unstack(:lfp, :foreign, :nrow)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1c1edb6",
   "metadata": {},
   "source": [
    "or just:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c9319cbe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>2×3 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">lfp</th><th style = \"text-align: left;\">no</th><th style = \"text-align: left;\">yes</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">402</td><td style = \"text-align: right;\">69</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">254</td><td style = \"text-align: right;\">147</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& lfp & no & yes\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64? & Int64?\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & 402 & 69 \\\\\n",
       "\t2 & 1 & 254 & 147 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m lfp   \u001b[0m\u001b[1m no     \u001b[0m\u001b[1m yes    \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64? \u001b[0m\u001b[90m Int64? \u001b[0m\n",
       "─────┼───────────────────────\n",
       "   1 │     0     402      69\n",
       "   2 │     1     254     147"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unstack(df, :lfp, :foreign, :foreign, combine=length)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "037fdf0e",
   "metadata": {},
   "source": [
    "Finally let us add another step to our `@chain`, which will create a fraction of `:yes` answers in each group.\n",
    "\n",
    "Note that in this example we show how to pass more than one column to a transformation function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "f3667883",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>2×2 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">lfp</th><th style = \"text-align: left;\">foreign_yes</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0.146497</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.366584</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& lfp & foreign\\_yes\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & 0.146497 \\\\\n",
       "\t2 & 1 & 0.366584 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×2 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m lfp   \u001b[0m\u001b[1m foreign_yes \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Float64     \u001b[0m\n",
       "─────┼────────────────────\n",
       "   1 │     0     0.146497\n",
       "   2 │     1     0.366584"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@chain df begin\n",
    "    groupby([:lfp, :foreign])\n",
    "    combine(nrow)\n",
    "    unstack(:lfp, :foreign, :nrow)\n",
    "    select(:lfp, [:no, :yes] => ByRow((x, y) -> y / (x + y)) => :foreign_yes)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4a112c6",
   "metadata": {},
   "source": [
    "An observant reader will notice that we could have done it in one step like this (the benefit of being verbose was that we have learned more features of DataFrames.jl):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "3a70f926",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>2×2 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">lfp</th><th style = \"text-align: left;\">foreign_yes</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0.146497</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0.366584</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& lfp & foreign\\_yes\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & 0.146497 \\\\\n",
       "\t2 & 1 & 0.366584 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×2 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m lfp   \u001b[0m\u001b[1m foreign_yes \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Float64     \u001b[0m\n",
       "─────┼────────────────────\n",
       "   1 │     0     0.146497\n",
       "   2 │     1     0.366584"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@chain df begin\n",
    "    groupby(:lfp)\n",
    "    combine(:foreign => (x -> mean(x .== \"yes\")) => :foreign_yes)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98cfef8a",
   "metadata": {},
   "source": [
    "The `GroupedDataFrame` that is created by the `groupby` function can be a useful object to work with on its own."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "b37c320a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p><b>GroupedDataFrame with 2 groups based on key: lfp</b></p><div><div style = \"float: left;\"><span>First Group (471 rows): lfp = 0</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">446 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">lfp</th><th style = \"text-align: left;\">lnnlinc</th><th style = \"text-align: left;\">age</th><th style = \"text-align: left;\">age²</th><th style = \"text-align: left;\">educ</th><th style = \"text-align: left;\">nyc</th><th style = \"text-align: left;\">noc</th><th style = \"text-align: left;\">foreign</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"CategoricalValue{String3, UInt32}\" style = \"text-align: left;\">Cat…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.7875</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.9686</td><td style = \"text-align: right;\">4.6</td><td style = \"text-align: right;\">21.16</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.105</td><td style = \"text-align: right;\">3.1</td><td style = \"text-align: right;\">9.61</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.1085</td><td style = \"text-align: right;\">4.4</td><td style = \"text-align: right;\">19.36</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.4547</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.6247</td><td style = \"text-align: right;\">3.9</td><td style = \"text-align: right;\">15.21</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.4864</td><td style = \"text-align: right;\">4.3</td><td style = \"text-align: right;\">18.49</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.6606</td><td style = \"text-align: right;\">4.5</td><td style = \"text-align: right;\">20.25</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.4676</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">36.0</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.2296</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">10.89</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.9065</td><td style = \"text-align: right;\">5.6</td><td style = \"text-align: right;\">31.36</td><td style = \"text-align: right;\">14</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.5016</td><td style = \"text-align: right;\">5.6</td><td style = \"text-align: right;\">31.36</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.2935</td><td style = \"text-align: right;\">4.7</td><td style = \"text-align: right;\">22.09</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">460</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.5008</td><td style = \"text-align: right;\">4.9</td><td style = \"text-align: right;\">24.01</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">461</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.3173</td><td style = \"text-align: right;\">5.5</td><td style = \"text-align: right;\">30.25</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">462</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.0104</td><td style = \"text-align: right;\">5.7</td><td style = \"text-align: right;\">32.49</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">463</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.5593</td><td style = \"text-align: right;\">3.2</td><td style = \"text-align: right;\">10.24</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">464</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.2158</td><td style = \"text-align: right;\">2.5</td><td style = \"text-align: right;\">6.25</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">465</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.9458</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">10.89</td><td style = \"text-align: right;\">14</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">466</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.111</td><td style = \"text-align: right;\">3.5</td><td style = \"text-align: right;\">12.25</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">467</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.4714</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">468</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.1475</td><td style = \"text-align: right;\">4.1</td><td style = \"text-align: right;\">16.81</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">469</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.5974</td><td style = \"text-align: right;\">2.4</td><td style = \"text-align: right;\">5.76</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">470</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.1337</td><td style = \"text-align: right;\">2.4</td><td style = \"text-align: right;\">5.76</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">471</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.2207</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr></tbody></table></div><p>&vellip;</p><div><div style = \"float: left;\"><span>Last Group (401 rows): lfp = 1</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">376 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">lfp</th><th style = \"text-align: left;\">lnnlinc</th><th style = \"text-align: left;\">age</th><th style = \"text-align: left;\">age²</th><th style = \"text-align: left;\">educ</th><th style = \"text-align: left;\">nyc</th><th style = \"text-align: left;\">noc</th><th style = \"text-align: left;\">foreign</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"CategoricalValue{String3, UInt32}\" style = \"text-align: left;\">Cat…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.5243</td><td style = \"text-align: right;\">4.5</td><td style = \"text-align: right;\">20.25</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">11.0283</td><td style = \"text-align: right;\">4.2</td><td style = \"text-align: right;\">17.64</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.4909</td><td style = \"text-align: right;\">3.2</td><td style = \"text-align: right;\">10.24</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">11.844</td><td style = \"text-align: right;\">3.9</td><td style = \"text-align: right;\">15.21</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.9578</td><td style = \"text-align: right;\">5.3</td><td style = \"text-align: right;\">28.09</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">11.1081</td><td style = \"text-align: right;\">4.6</td><td style = \"text-align: right;\">21.16</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.484</td><td style = \"text-align: right;\">5.4</td><td style = \"text-align: right;\">29.16</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.6012</td><td style = \"text-align: right;\">4.7</td><td style = \"text-align: right;\">22.09</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.8411</td><td style = \"text-align: right;\">4.9</td><td style = \"text-align: right;\">24.01</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">11.1566</td><td style = \"text-align: right;\">3.6</td><td style = \"text-align: right;\">12.96</td><td style = \"text-align: right;\">13</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">11.1063</td><td style = \"text-align: right;\">4.1</td><td style = \"text-align: right;\">16.81</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.6446</td><td style = \"text-align: right;\">4.2</td><td style = \"text-align: right;\">17.64</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.467</td><td style = \"text-align: right;\">3.2</td><td style = \"text-align: right;\">10.24</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">390</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.4837</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">10.89</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">3</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">391</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.7525</td><td style = \"text-align: right;\">4.1</td><td style = \"text-align: right;\">16.81</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">392</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">11.574</td><td style = \"text-align: right;\">4.7</td><td style = \"text-align: right;\">22.09</td><td style = \"text-align: right;\">13</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">393</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.806</td><td style = \"text-align: right;\">3.1</td><td style = \"text-align: right;\">9.61</td><td style = \"text-align: right;\">16</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">394</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.3799</td><td style = \"text-align: right;\">2.8</td><td style = \"text-align: right;\">7.84</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">395</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.7756</td><td style = \"text-align: right;\">3.8</td><td style = \"text-align: right;\">14.44</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">396</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.5289</td><td style = \"text-align: right;\">3.4</td><td style = \"text-align: right;\">11.56</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">397</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.4685</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">10.89</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">398</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.6932</td><td style = \"text-align: right;\">3.5</td><td style = \"text-align: right;\">12.25</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">399</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.0276</td><td style = \"text-align: right;\">4.2</td><td style = \"text-align: right;\">17.64</td><td style = \"text-align: right;\">14</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">400</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.3778</td><td style = \"text-align: right;\">4.8</td><td style = \"text-align: right;\">23.04</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">401</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.9324</td><td style = \"text-align: right;\">4.1</td><td style = \"text-align: right;\">16.81</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "GroupedDataFrame with 2 groups based on key: lfp\n",
       "\n",
       "First Group (471 rows): lfp = 0\n",
       "\n",
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& lfp & lnnlinc & age & age² & educ & nyc & noc & foreign\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64 & Float64 & Float64 & Int64 & Int64 & Int64 & Cat…\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & 10.7875 & 3.0 & 9.0 & 8 & 1 & 1 & no \\\\\n",
       "\t2 & 0 & 10.9686 & 4.6 & 21.16 & 9 & 0 & 0 & no \\\\\n",
       "\t3 & 0 & 11.105 & 3.1 & 9.61 & 11 & 2 & 0 & no \\\\\n",
       "\t4 & 0 & 11.1085 & 4.4 & 19.36 & 12 & 0 & 2 & no \\\\\n",
       "\t5 & 0 & 11.4547 & 5.1 & 26.01 & 8 & 0 & 0 & no \\\\\n",
       "\t6 & 0 & 10.6247 & 3.9 & 15.21 & 12 & 0 & 0 & no \\\\\n",
       "\t7 & 0 & 10.4864 & 4.3 & 18.49 & 11 & 0 & 2 & no \\\\\n",
       "\t8 & 0 & 10.6606 & 4.5 & 20.25 & 11 & 0 & 2 & no \\\\\n",
       "\t9 & 0 & 10.4676 & 6.0 & 36.0 & 12 & 0 & 0 & no \\\\\n",
       "\t10 & 0 & 11.2296 & 3.3 & 10.89 & 11 & 2 & 0 & no \\\\\n",
       "\t11 & 0 & 11.9065 & 5.6 & 31.36 & 14 & 0 & 0 & no \\\\\n",
       "\t12 & 0 & 11.5016 & 5.6 & 31.36 & 11 & 0 & 0 & no \\\\\n",
       "\t13 & 0 & 11.2935 & 4.7 & 22.09 & 11 & 0 & 1 & no \\\\\n",
       "\t14 & 0 & 10.8613 & 5.0 & 25.0 & 8 & 0 & 0 & no \\\\\n",
       "\t15 & 0 & 11.0486 & 4.7 & 22.09 & 8 & 0 & 1 & no \\\\\n",
       "\t16 & 0 & 10.8601 & 2.9 & 8.41 & 19 & 0 & 0 & no \\\\\n",
       "\t17 & 0 & 10.8486 & 4.4 & 19.36 & 8 & 0 & 2 & no \\\\\n",
       "\t18 & 0 & 10.4824 & 2.0 & 4.0 & 12 & 1 & 0 & no \\\\\n",
       "\t19 & 0 & 10.5406 & 2.8 & 7.84 & 9 & 2 & 0 & no \\\\\n",
       "\t20 & 0 & 11.2243 & 4.7 & 22.09 & 8 & 0 & 1 & no \\\\\n",
       "\t21 & 0 & 10.5663 & 3.0 & 9.0 & 11 & 0 & 1 & no \\\\\n",
       "\t22 & 0 & 11.7696 & 5.1 & 26.01 & 11 & 0 & 0 & no \\\\\n",
       "\t23 & 0 & 10.6671 & 2.8 & 7.84 & 11 & 0 & 2 & no \\\\\n",
       "\t24 & 0 & 10.6246 & 5.4 & 29.16 & 11 & 0 & 0 & no \\\\\n",
       "\t25 & 0 & 10.5371 & 4.9 & 24.01 & 8 & 0 & 0 & no \\\\\n",
       "\t26 & 0 & 11.1356 & 5.3 & 28.09 & 10 & 0 & 0 & no \\\\\n",
       "\t27 & 0 & 10.3153 & 5.5 & 30.25 & 8 & 0 & 0 & no \\\\\n",
       "\t28 & 0 & 10.3727 & 2.4 & 5.76 & 11 & 1 & 0 & no \\\\\n",
       "\t29 & 0 & 11.5071 & 5.0 & 25.0 & 8 & 0 & 1 & no \\\\\n",
       "\t30 & 0 & 10.4529 & 2.3 & 5.29 & 9 & 1 & 0 & no \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ \\\\\n",
       "\\end{tabular}\n",
       "\n",
       "$\\dots$\n",
       "\n",
       "Last Group (401 rows): lfp = 1\n",
       "\n",
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& lfp & lnnlinc & age & age² & educ & nyc & noc & foreign\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64 & Float64 & Float64 & Int64 & Int64 & Int64 & Cat…\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 10.5243 & 4.5 & 20.25 & 8 & 0 & 1 & no \\\\\n",
       "\t2 & 1 & 11.0283 & 4.2 & 17.64 & 12 & 0 & 1 & no \\\\\n",
       "\t3 & 1 & 10.4909 & 3.2 & 10.24 & 8 & 0 & 2 & no \\\\\n",
       "\t4 & 1 & 11.844 & 3.9 & 15.21 & 12 & 0 & 0 & no \\\\\n",
       "\t5 & 1 & 10.9578 & 5.3 & 28.09 & 11 & 0 & 0 & no \\\\\n",
       "\t6 & 1 & 11.1081 & 4.6 & 21.16 & 11 & 0 & 1 & no \\\\\n",
       "\t7 & 1 & 10.484 & 5.4 & 29.16 & 8 & 0 & 0 & no \\\\\n",
       "\t8 & 1 & 10.6012 & 4.7 & 22.09 & 8 & 0 & 0 & no \\\\\n",
       "\t9 & 1 & 10.8411 & 4.9 & 24.01 & 12 & 0 & 0 & no \\\\\n",
       "\t10 & 1 & 11.1566 & 3.6 & 12.96 & 13 & 0 & 2 & no \\\\\n",
       "\t11 & 1 & 11.1063 & 4.1 & 16.81 & 12 & 0 & 2 & no \\\\\n",
       "\t12 & 1 & 10.6446 & 4.2 & 17.64 & 10 & 0 & 2 & no \\\\\n",
       "\t13 & 1 & 10.467 & 3.2 & 10.24 & 8 & 0 & 1 & no \\\\\n",
       "\t14 & 1 & 10.4782 & 3.4 & 11.56 & 9 & 0 & 2 & no \\\\\n",
       "\t15 & 1 & 10.4355 & 4.4 & 19.36 & 9 & 0 & 1 & no \\\\\n",
       "\t16 & 1 & 10.4273 & 5.8 & 33.64 & 12 & 0 & 0 & no \\\\\n",
       "\t17 & 1 & 10.4718 & 4.4 & 19.36 & 9 & 0 & 2 & no \\\\\n",
       "\t18 & 1 & 11.4112 & 4.0 & 16.0 & 13 & 0 & 2 & no \\\\\n",
       "\t19 & 1 & 10.4933 & 3.5 & 12.25 & 4 & 0 & 2 & no \\\\\n",
       "\t20 & 1 & 10.7186 & 3.1 & 9.61 & 10 & 1 & 1 & no \\\\\n",
       "\t21 & 1 & 10.8147 & 5.5 & 30.25 & 10 & 0 & 1 & no \\\\\n",
       "\t22 & 1 & 10.4729 & 3.5 & 12.25 & 9 & 0 & 2 & no \\\\\n",
       "\t23 & 1 & 10.5176 & 5.6 & 31.36 & 9 & 0 & 0 & no \\\\\n",
       "\t24 & 1 & 10.9099 & 4.3 & 18.49 & 8 & 0 & 0 & no \\\\\n",
       "\t25 & 1 & 10.3636 & 2.4 & 5.76 & 12 & 0 & 0 & no \\\\\n",
       "\t26 & 1 & 9.64615 & 5.4 & 29.16 & 8 & 0 & 0 & no \\\\\n",
       "\t27 & 1 & 10.2798 & 5.2 & 27.04 & 7 & 0 & 2 & no \\\\\n",
       "\t28 & 1 & 10.5409 & 3.4 & 11.56 & 10 & 0 & 0 & no \\\\\n",
       "\t29 & 1 & 11.2358 & 4.9 & 24.01 & 12 & 0 & 2 & no \\\\\n",
       "\t30 & 1 & 10.3482 & 4.8 & 23.04 & 8 & 0 & 0 & no \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "GroupedDataFrame with 2 groups based on key: lfp\n",
       "First Group (471 rows): lfp = 0\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m lfp   \u001b[0m\u001b[1m lnnlinc \u001b[0m\u001b[1m age     \u001b[0m\u001b[1m age²    \u001b[0m\u001b[1m educ  \u001b[0m\u001b[1m nyc   \u001b[0m\u001b[1m noc   \u001b[0m\u001b[1m foreign \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Cat…    \u001b[0m\n",
       "─────┼────────────────────────────────────────────────────────────────\n",
       "   1 │     0  10.7875      3.0     9.0       8      1      1  no\n",
       "   2 │     0  10.9686      4.6    21.16      9      0      0  no\n",
       "   3 │     0  11.105       3.1     9.61     11      2      0  no\n",
       "   4 │     0  11.1085      4.4    19.36     12      0      2  no\n",
       "  ⋮  │   ⋮       ⋮        ⋮        ⋮       ⋮      ⋮      ⋮       ⋮\n",
       " 469 │     0  10.5974      2.4     5.76      4      2      1  yes\n",
       " 470 │     0  10.1337      2.4     5.76      6      2      0  yes\n",
       " 471 │     0  11.2207      5.1    26.01     10      0      0  yes\n",
       "\u001b[36m                                                      464 rows omitted\u001b[0m\n",
       "⋮\n",
       "Last Group (401 rows): lfp = 1\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m lfp   \u001b[0m\u001b[1m lnnlinc \u001b[0m\u001b[1m age     \u001b[0m\u001b[1m age²    \u001b[0m\u001b[1m educ  \u001b[0m\u001b[1m nyc   \u001b[0m\u001b[1m noc   \u001b[0m\u001b[1m foreign \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Cat…    \u001b[0m\n",
       "─────┼────────────────────────────────────────────────────────────────\n",
       "   1 │     1  10.5243      4.5    20.25      8      0      1  no\n",
       "   2 │     1  11.0283      4.2    17.64     12      0      1  no\n",
       "   3 │     1  10.4909      3.2    10.24      8      0      2  no\n",
       "  ⋮  │   ⋮       ⋮        ⋮        ⋮       ⋮      ⋮      ⋮       ⋮\n",
       " 399 │     1  10.0276      4.2    17.64     14      0      0  yes\n",
       " 400 │     1  10.3778      4.8    23.04      8      0      0  yes\n",
       " 401 │     1  10.9324      4.1    16.81     10      0      1  yes\n",
       "\u001b[36m                                                      395 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gd = groupby(df, :lfp)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fbf26849",
   "metadata": {},
   "source": [
    "Note that you can conveniently index into it to get the groups."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3e8a75f",
   "metadata": {},
   "source": [
    "First we use the standard indexing syntax:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7fbdffdc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>471×8 SubDataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">446 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">lfp</th><th style = \"text-align: left;\">lnnlinc</th><th style = \"text-align: left;\">age</th><th style = \"text-align: left;\">age²</th><th style = \"text-align: left;\">educ</th><th style = \"text-align: left;\">nyc</th><th style = \"text-align: left;\">noc</th><th style = \"text-align: left;\">foreign</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"CategoricalValue{String3, UInt32}\" style = \"text-align: left;\">Cat…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.7875</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.9686</td><td style = \"text-align: right;\">4.6</td><td style = \"text-align: right;\">21.16</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.105</td><td style = \"text-align: right;\">3.1</td><td style = \"text-align: right;\">9.61</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.1085</td><td style = \"text-align: right;\">4.4</td><td style = \"text-align: right;\">19.36</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.4547</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.6247</td><td style = \"text-align: right;\">3.9</td><td style = \"text-align: right;\">15.21</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.4864</td><td style = \"text-align: right;\">4.3</td><td style = \"text-align: right;\">18.49</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.6606</td><td style = \"text-align: right;\">4.5</td><td style = \"text-align: right;\">20.25</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.4676</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">36.0</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.2296</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">10.89</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.9065</td><td style = \"text-align: right;\">5.6</td><td style = \"text-align: right;\">31.36</td><td style = \"text-align: right;\">14</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.5016</td><td style = \"text-align: right;\">5.6</td><td style = \"text-align: right;\">31.36</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.2935</td><td style = \"text-align: right;\">4.7</td><td style = \"text-align: right;\">22.09</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">460</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.5008</td><td style = \"text-align: right;\">4.9</td><td style = \"text-align: right;\">24.01</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">461</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.3173</td><td style = \"text-align: right;\">5.5</td><td style = \"text-align: right;\">30.25</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">462</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.0104</td><td style = \"text-align: right;\">5.7</td><td style = \"text-align: right;\">32.49</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">463</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.5593</td><td style = \"text-align: right;\">3.2</td><td style = \"text-align: right;\">10.24</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">464</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.2158</td><td style = \"text-align: right;\">2.5</td><td style = \"text-align: right;\">6.25</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">465</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.9458</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">10.89</td><td style = \"text-align: right;\">14</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">466</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.111</td><td style = \"text-align: right;\">3.5</td><td style = \"text-align: right;\">12.25</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">467</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.4714</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">468</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.1475</td><td style = \"text-align: right;\">4.1</td><td style = \"text-align: right;\">16.81</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">469</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.5974</td><td style = \"text-align: right;\">2.4</td><td style = \"text-align: right;\">5.76</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">470</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.1337</td><td style = \"text-align: right;\">2.4</td><td style = \"text-align: right;\">5.76</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">471</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.2207</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& lfp & lnnlinc & age & age² & educ & nyc & noc & foreign\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64 & Float64 & Float64 & Int64 & Int64 & Int64 & Cat…\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & 10.7875 & 3.0 & 9.0 & 8 & 1 & 1 & no \\\\\n",
       "\t2 & 0 & 10.9686 & 4.6 & 21.16 & 9 & 0 & 0 & no \\\\\n",
       "\t3 & 0 & 11.105 & 3.1 & 9.61 & 11 & 2 & 0 & no \\\\\n",
       "\t4 & 0 & 11.1085 & 4.4 & 19.36 & 12 & 0 & 2 & no \\\\\n",
       "\t5 & 0 & 11.4547 & 5.1 & 26.01 & 8 & 0 & 0 & no \\\\\n",
       "\t6 & 0 & 10.6247 & 3.9 & 15.21 & 12 & 0 & 0 & no \\\\\n",
       "\t7 & 0 & 10.4864 & 4.3 & 18.49 & 11 & 0 & 2 & no \\\\\n",
       "\t8 & 0 & 10.6606 & 4.5 & 20.25 & 11 & 0 & 2 & no \\\\\n",
       "\t9 & 0 & 10.4676 & 6.0 & 36.0 & 12 & 0 & 0 & no \\\\\n",
       "\t10 & 0 & 11.2296 & 3.3 & 10.89 & 11 & 2 & 0 & no \\\\\n",
       "\t11 & 0 & 11.9065 & 5.6 & 31.36 & 14 & 0 & 0 & no \\\\\n",
       "\t12 & 0 & 11.5016 & 5.6 & 31.36 & 11 & 0 & 0 & no \\\\\n",
       "\t13 & 0 & 11.2935 & 4.7 & 22.09 & 11 & 0 & 1 & no \\\\\n",
       "\t14 & 0 & 10.8613 & 5.0 & 25.0 & 8 & 0 & 0 & no \\\\\n",
       "\t15 & 0 & 11.0486 & 4.7 & 22.09 & 8 & 0 & 1 & no \\\\\n",
       "\t16 & 0 & 10.8601 & 2.9 & 8.41 & 19 & 0 & 0 & no \\\\\n",
       "\t17 & 0 & 10.8486 & 4.4 & 19.36 & 8 & 0 & 2 & no \\\\\n",
       "\t18 & 0 & 10.4824 & 2.0 & 4.0 & 12 & 1 & 0 & no \\\\\n",
       "\t19 & 0 & 10.5406 & 2.8 & 7.84 & 9 & 2 & 0 & no \\\\\n",
       "\t20 & 0 & 11.2243 & 4.7 & 22.09 & 8 & 0 & 1 & no \\\\\n",
       "\t21 & 0 & 10.5663 & 3.0 & 9.0 & 11 & 0 & 1 & no \\\\\n",
       "\t22 & 0 & 11.7696 & 5.1 & 26.01 & 11 & 0 & 0 & no \\\\\n",
       "\t23 & 0 & 10.6671 & 2.8 & 7.84 & 11 & 0 & 2 & no \\\\\n",
       "\t24 & 0 & 10.6246 & 5.4 & 29.16 & 11 & 0 & 0 & no \\\\\n",
       "\t25 & 0 & 10.5371 & 4.9 & 24.01 & 8 & 0 & 0 & no \\\\\n",
       "\t26 & 0 & 11.1356 & 5.3 & 28.09 & 10 & 0 & 0 & no \\\\\n",
       "\t27 & 0 & 10.3153 & 5.5 & 30.25 & 8 & 0 & 0 & no \\\\\n",
       "\t28 & 0 & 10.3727 & 2.4 & 5.76 & 11 & 1 & 0 & no \\\\\n",
       "\t29 & 0 & 11.5071 & 5.0 & 25.0 & 8 & 0 & 1 & no \\\\\n",
       "\t30 & 0 & 10.4529 & 2.3 & 5.29 & 9 & 1 & 0 & no \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m471×8 SubDataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m lfp   \u001b[0m\u001b[1m lnnlinc \u001b[0m\u001b[1m age     \u001b[0m\u001b[1m age²    \u001b[0m\u001b[1m educ  \u001b[0m\u001b[1m nyc   \u001b[0m\u001b[1m noc   \u001b[0m\u001b[1m foreign \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Cat…    \u001b[0m\n",
       "─────┼────────────────────────────────────────────────────────────────\n",
       "   1 │     0  10.7875      3.0     9.0       8      1      1  no\n",
       "   2 │     0  10.9686      4.6    21.16      9      0      0  no\n",
       "   3 │     0  11.105       3.1     9.61     11      2      0  no\n",
       "   4 │     0  11.1085      4.4    19.36     12      0      2  no\n",
       "   5 │     0  11.4547      5.1    26.01      8      0      0  no\n",
       "   6 │     0  10.6247      3.9    15.21     12      0      0  no\n",
       "   7 │     0  10.4864      4.3    18.49     11      0      2  no\n",
       "   8 │     0  10.6606      4.5    20.25     11      0      2  no\n",
       "   9 │     0  10.4676      6.0    36.0      12      0      0  no\n",
       "  10 │     0  11.2296      3.3    10.89     11      2      0  no\n",
       "  11 │     0  11.9065      5.6    31.36     14      0      0  no\n",
       "  ⋮  │   ⋮       ⋮        ⋮        ⋮       ⋮      ⋮      ⋮       ⋮\n",
       " 462 │     0  10.0104      5.7    32.49      6      0      1  yes\n",
       " 463 │     0  10.5593      3.2    10.24     12      1      0  yes\n",
       " 464 │     0  10.2158      2.5     6.25     11      1      0  yes\n",
       " 465 │     0  10.9458      3.3    10.89     14      0      2  yes\n",
       " 466 │     0  11.111       3.5    12.25     10      1      1  yes\n",
       " 467 │     0  10.4714      5.1    26.01      9      0      1  yes\n",
       " 468 │     0  10.1475      4.1    16.81      5      1      0  yes\n",
       " 469 │     0  10.5974      2.4     5.76      4      2      1  yes\n",
       " 470 │     0  10.1337      2.4     5.76      6      2      0  yes\n",
       " 471 │     0  11.2207      5.1    26.01     10      0      0  yes\n",
       "\u001b[36m                                                      450 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gd[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8742860f",
   "metadata": {},
   "source": [
    "Now we we use a special indexing syntax that efficiently selects groups by their value (not position):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7547996f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>471×8 SubDataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">446 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">lfp</th><th style = \"text-align: left;\">lnnlinc</th><th style = \"text-align: left;\">age</th><th style = \"text-align: left;\">age²</th><th style = \"text-align: left;\">educ</th><th style = \"text-align: left;\">nyc</th><th style = \"text-align: left;\">noc</th><th style = \"text-align: left;\">foreign</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"CategoricalValue{String3, UInt32}\" style = \"text-align: left;\">Cat…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.7875</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.9686</td><td style = \"text-align: right;\">4.6</td><td style = \"text-align: right;\">21.16</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.105</td><td style = \"text-align: right;\">3.1</td><td style = \"text-align: right;\">9.61</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.1085</td><td style = \"text-align: right;\">4.4</td><td style = \"text-align: right;\">19.36</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.4547</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.6247</td><td style = \"text-align: right;\">3.9</td><td style = \"text-align: right;\">15.21</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.4864</td><td style = \"text-align: right;\">4.3</td><td style = \"text-align: right;\">18.49</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.6606</td><td style = \"text-align: right;\">4.5</td><td style = \"text-align: right;\">20.25</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.4676</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">36.0</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.2296</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">10.89</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.9065</td><td style = \"text-align: right;\">5.6</td><td style = \"text-align: right;\">31.36</td><td style = \"text-align: right;\">14</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.5016</td><td style = \"text-align: right;\">5.6</td><td style = \"text-align: right;\">31.36</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.2935</td><td style = \"text-align: right;\">4.7</td><td style = \"text-align: right;\">22.09</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">460</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.5008</td><td style = \"text-align: right;\">4.9</td><td style = \"text-align: right;\">24.01</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">461</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.3173</td><td style = \"text-align: right;\">5.5</td><td style = \"text-align: right;\">30.25</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">462</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.0104</td><td style = \"text-align: right;\">5.7</td><td style = \"text-align: right;\">32.49</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">463</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.5593</td><td style = \"text-align: right;\">3.2</td><td style = \"text-align: right;\">10.24</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">464</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.2158</td><td style = \"text-align: right;\">2.5</td><td style = \"text-align: right;\">6.25</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">465</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.9458</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">10.89</td><td style = \"text-align: right;\">14</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">466</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.111</td><td style = \"text-align: right;\">3.5</td><td style = \"text-align: right;\">12.25</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">467</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.4714</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">468</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.1475</td><td style = \"text-align: right;\">4.1</td><td style = \"text-align: right;\">16.81</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">469</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.5974</td><td style = \"text-align: right;\">2.4</td><td style = \"text-align: right;\">5.76</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">470</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.1337</td><td style = \"text-align: right;\">2.4</td><td style = \"text-align: right;\">5.76</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">471</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.2207</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& lfp & lnnlinc & age & age² & educ & nyc & noc & foreign\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64 & Float64 & Float64 & Int64 & Int64 & Int64 & Cat…\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & 10.7875 & 3.0 & 9.0 & 8 & 1 & 1 & no \\\\\n",
       "\t2 & 0 & 10.9686 & 4.6 & 21.16 & 9 & 0 & 0 & no \\\\\n",
       "\t3 & 0 & 11.105 & 3.1 & 9.61 & 11 & 2 & 0 & no \\\\\n",
       "\t4 & 0 & 11.1085 & 4.4 & 19.36 & 12 & 0 & 2 & no \\\\\n",
       "\t5 & 0 & 11.4547 & 5.1 & 26.01 & 8 & 0 & 0 & no \\\\\n",
       "\t6 & 0 & 10.6247 & 3.9 & 15.21 & 12 & 0 & 0 & no \\\\\n",
       "\t7 & 0 & 10.4864 & 4.3 & 18.49 & 11 & 0 & 2 & no \\\\\n",
       "\t8 & 0 & 10.6606 & 4.5 & 20.25 & 11 & 0 & 2 & no \\\\\n",
       "\t9 & 0 & 10.4676 & 6.0 & 36.0 & 12 & 0 & 0 & no \\\\\n",
       "\t10 & 0 & 11.2296 & 3.3 & 10.89 & 11 & 2 & 0 & no \\\\\n",
       "\t11 & 0 & 11.9065 & 5.6 & 31.36 & 14 & 0 & 0 & no \\\\\n",
       "\t12 & 0 & 11.5016 & 5.6 & 31.36 & 11 & 0 & 0 & no \\\\\n",
       "\t13 & 0 & 11.2935 & 4.7 & 22.09 & 11 & 0 & 1 & no \\\\\n",
       "\t14 & 0 & 10.8613 & 5.0 & 25.0 & 8 & 0 & 0 & no \\\\\n",
       "\t15 & 0 & 11.0486 & 4.7 & 22.09 & 8 & 0 & 1 & no \\\\\n",
       "\t16 & 0 & 10.8601 & 2.9 & 8.41 & 19 & 0 & 0 & no \\\\\n",
       "\t17 & 0 & 10.8486 & 4.4 & 19.36 & 8 & 0 & 2 & no \\\\\n",
       "\t18 & 0 & 10.4824 & 2.0 & 4.0 & 12 & 1 & 0 & no \\\\\n",
       "\t19 & 0 & 10.5406 & 2.8 & 7.84 & 9 & 2 & 0 & no \\\\\n",
       "\t20 & 0 & 11.2243 & 4.7 & 22.09 & 8 & 0 & 1 & no \\\\\n",
       "\t21 & 0 & 10.5663 & 3.0 & 9.0 & 11 & 0 & 1 & no \\\\\n",
       "\t22 & 0 & 11.7696 & 5.1 & 26.01 & 11 & 0 & 0 & no \\\\\n",
       "\t23 & 0 & 10.6671 & 2.8 & 7.84 & 11 & 0 & 2 & no \\\\\n",
       "\t24 & 0 & 10.6246 & 5.4 & 29.16 & 11 & 0 & 0 & no \\\\\n",
       "\t25 & 0 & 10.5371 & 4.9 & 24.01 & 8 & 0 & 0 & no \\\\\n",
       "\t26 & 0 & 11.1356 & 5.3 & 28.09 & 10 & 0 & 0 & no \\\\\n",
       "\t27 & 0 & 10.3153 & 5.5 & 30.25 & 8 & 0 & 0 & no \\\\\n",
       "\t28 & 0 & 10.3727 & 2.4 & 5.76 & 11 & 1 & 0 & no \\\\\n",
       "\t29 & 0 & 11.5071 & 5.0 & 25.0 & 8 & 0 & 1 & no \\\\\n",
       "\t30 & 0 & 10.4529 & 2.3 & 5.29 & 9 & 1 & 0 & no \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m471×8 SubDataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m lfp   \u001b[0m\u001b[1m lnnlinc \u001b[0m\u001b[1m age     \u001b[0m\u001b[1m age²    \u001b[0m\u001b[1m educ  \u001b[0m\u001b[1m nyc   \u001b[0m\u001b[1m noc   \u001b[0m\u001b[1m foreign \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Cat…    \u001b[0m\n",
       "─────┼────────────────────────────────────────────────────────────────\n",
       "   1 │     0  10.7875      3.0     9.0       8      1      1  no\n",
       "   2 │     0  10.9686      4.6    21.16      9      0      0  no\n",
       "   3 │     0  11.105       3.1     9.61     11      2      0  no\n",
       "   4 │     0  11.1085      4.4    19.36     12      0      2  no\n",
       "   5 │     0  11.4547      5.1    26.01      8      0      0  no\n",
       "   6 │     0  10.6247      3.9    15.21     12      0      0  no\n",
       "   7 │     0  10.4864      4.3    18.49     11      0      2  no\n",
       "   8 │     0  10.6606      4.5    20.25     11      0      2  no\n",
       "   9 │     0  10.4676      6.0    36.0      12      0      0  no\n",
       "  10 │     0  11.2296      3.3    10.89     11      2      0  no\n",
       "  11 │     0  11.9065      5.6    31.36     14      0      0  no\n",
       "  ⋮  │   ⋮       ⋮        ⋮        ⋮       ⋮      ⋮      ⋮       ⋮\n",
       " 462 │     0  10.0104      5.7    32.49      6      0      1  yes\n",
       " 463 │     0  10.5593      3.2    10.24     12      1      0  yes\n",
       " 464 │     0  10.2158      2.5     6.25     11      1      0  yes\n",
       " 465 │     0  10.9458      3.3    10.89     14      0      2  yes\n",
       " 466 │     0  11.111       3.5    12.25     10      1      1  yes\n",
       " 467 │     0  10.4714      5.1    26.01      9      0      1  yes\n",
       " 468 │     0  10.1475      4.1    16.81      5      1      0  yes\n",
       " 469 │     0  10.5974      2.4     5.76      4      2      1  yes\n",
       " 470 │     0  10.1337      2.4     5.76      6      2      0  yes\n",
       " 471 │     0  11.2207      5.1    26.01     10      0      0  yes\n",
       "\u001b[36m                                                      450 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gd[(lfp=0,)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "68339a48",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>471×8 SubDataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">446 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">lfp</th><th style = \"text-align: left;\">lnnlinc</th><th style = \"text-align: left;\">age</th><th style = \"text-align: left;\">age²</th><th style = \"text-align: left;\">educ</th><th style = \"text-align: left;\">nyc</th><th style = \"text-align: left;\">noc</th><th style = \"text-align: left;\">foreign</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"CategoricalValue{String3, UInt32}\" style = \"text-align: left;\">Cat…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.7875</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.9686</td><td style = \"text-align: right;\">4.6</td><td style = \"text-align: right;\">21.16</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.105</td><td style = \"text-align: right;\">3.1</td><td style = \"text-align: right;\">9.61</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.1085</td><td style = \"text-align: right;\">4.4</td><td style = \"text-align: right;\">19.36</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.4547</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.6247</td><td style = \"text-align: right;\">3.9</td><td style = \"text-align: right;\">15.21</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.4864</td><td style = \"text-align: right;\">4.3</td><td style = \"text-align: right;\">18.49</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.6606</td><td style = \"text-align: right;\">4.5</td><td style = \"text-align: right;\">20.25</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.4676</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">36.0</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.2296</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">10.89</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.9065</td><td style = \"text-align: right;\">5.6</td><td style = \"text-align: right;\">31.36</td><td style = \"text-align: right;\">14</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.5016</td><td style = \"text-align: right;\">5.6</td><td style = \"text-align: right;\">31.36</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.2935</td><td style = \"text-align: right;\">4.7</td><td style = \"text-align: right;\">22.09</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">460</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.5008</td><td style = \"text-align: right;\">4.9</td><td style = \"text-align: right;\">24.01</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">461</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.3173</td><td style = \"text-align: right;\">5.5</td><td style = \"text-align: right;\">30.25</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">462</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.0104</td><td style = \"text-align: right;\">5.7</td><td style = \"text-align: right;\">32.49</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">463</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.5593</td><td style = \"text-align: right;\">3.2</td><td style = \"text-align: right;\">10.24</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">464</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.2158</td><td style = \"text-align: right;\">2.5</td><td style = \"text-align: right;\">6.25</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">465</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.9458</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">10.89</td><td style = \"text-align: right;\">14</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">466</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.111</td><td style = \"text-align: right;\">3.5</td><td style = \"text-align: right;\">12.25</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">467</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.4714</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">468</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.1475</td><td style = \"text-align: right;\">4.1</td><td style = \"text-align: right;\">16.81</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">469</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.5974</td><td style = \"text-align: right;\">2.4</td><td style = \"text-align: right;\">5.76</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">470</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.1337</td><td style = \"text-align: right;\">2.4</td><td style = \"text-align: right;\">5.76</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">471</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.2207</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& lfp & lnnlinc & age & age² & educ & nyc & noc & foreign\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64 & Float64 & Float64 & Int64 & Int64 & Int64 & Cat…\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & 10.7875 & 3.0 & 9.0 & 8 & 1 & 1 & no \\\\\n",
       "\t2 & 0 & 10.9686 & 4.6 & 21.16 & 9 & 0 & 0 & no \\\\\n",
       "\t3 & 0 & 11.105 & 3.1 & 9.61 & 11 & 2 & 0 & no \\\\\n",
       "\t4 & 0 & 11.1085 & 4.4 & 19.36 & 12 & 0 & 2 & no \\\\\n",
       "\t5 & 0 & 11.4547 & 5.1 & 26.01 & 8 & 0 & 0 & no \\\\\n",
       "\t6 & 0 & 10.6247 & 3.9 & 15.21 & 12 & 0 & 0 & no \\\\\n",
       "\t7 & 0 & 10.4864 & 4.3 & 18.49 & 11 & 0 & 2 & no \\\\\n",
       "\t8 & 0 & 10.6606 & 4.5 & 20.25 & 11 & 0 & 2 & no \\\\\n",
       "\t9 & 0 & 10.4676 & 6.0 & 36.0 & 12 & 0 & 0 & no \\\\\n",
       "\t10 & 0 & 11.2296 & 3.3 & 10.89 & 11 & 2 & 0 & no \\\\\n",
       "\t11 & 0 & 11.9065 & 5.6 & 31.36 & 14 & 0 & 0 & no \\\\\n",
       "\t12 & 0 & 11.5016 & 5.6 & 31.36 & 11 & 0 & 0 & no \\\\\n",
       "\t13 & 0 & 11.2935 & 4.7 & 22.09 & 11 & 0 & 1 & no \\\\\n",
       "\t14 & 0 & 10.8613 & 5.0 & 25.0 & 8 & 0 & 0 & no \\\\\n",
       "\t15 & 0 & 11.0486 & 4.7 & 22.09 & 8 & 0 & 1 & no \\\\\n",
       "\t16 & 0 & 10.8601 & 2.9 & 8.41 & 19 & 0 & 0 & no \\\\\n",
       "\t17 & 0 & 10.8486 & 4.4 & 19.36 & 8 & 0 & 2 & no \\\\\n",
       "\t18 & 0 & 10.4824 & 2.0 & 4.0 & 12 & 1 & 0 & no \\\\\n",
       "\t19 & 0 & 10.5406 & 2.8 & 7.84 & 9 & 2 & 0 & no \\\\\n",
       "\t20 & 0 & 11.2243 & 4.7 & 22.09 & 8 & 0 & 1 & no \\\\\n",
       "\t21 & 0 & 10.5663 & 3.0 & 9.0 & 11 & 0 & 1 & no \\\\\n",
       "\t22 & 0 & 11.7696 & 5.1 & 26.01 & 11 & 0 & 0 & no \\\\\n",
       "\t23 & 0 & 10.6671 & 2.8 & 7.84 & 11 & 0 & 2 & no \\\\\n",
       "\t24 & 0 & 10.6246 & 5.4 & 29.16 & 11 & 0 & 0 & no \\\\\n",
       "\t25 & 0 & 10.5371 & 4.9 & 24.01 & 8 & 0 & 0 & no \\\\\n",
       "\t26 & 0 & 11.1356 & 5.3 & 28.09 & 10 & 0 & 0 & no \\\\\n",
       "\t27 & 0 & 10.3153 & 5.5 & 30.25 & 8 & 0 & 0 & no \\\\\n",
       "\t28 & 0 & 10.3727 & 2.4 & 5.76 & 11 & 1 & 0 & no \\\\\n",
       "\t29 & 0 & 11.5071 & 5.0 & 25.0 & 8 & 0 & 1 & no \\\\\n",
       "\t30 & 0 & 10.4529 & 2.3 & 5.29 & 9 & 1 & 0 & no \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m471×8 SubDataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m lfp   \u001b[0m\u001b[1m lnnlinc \u001b[0m\u001b[1m age     \u001b[0m\u001b[1m age²    \u001b[0m\u001b[1m educ  \u001b[0m\u001b[1m nyc   \u001b[0m\u001b[1m noc   \u001b[0m\u001b[1m foreign \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Cat…    \u001b[0m\n",
       "─────┼────────────────────────────────────────────────────────────────\n",
       "   1 │     0  10.7875      3.0     9.0       8      1      1  no\n",
       "   2 │     0  10.9686      4.6    21.16      9      0      0  no\n",
       "   3 │     0  11.105       3.1     9.61     11      2      0  no\n",
       "   4 │     0  11.1085      4.4    19.36     12      0      2  no\n",
       "   5 │     0  11.4547      5.1    26.01      8      0      0  no\n",
       "   6 │     0  10.6247      3.9    15.21     12      0      0  no\n",
       "   7 │     0  10.4864      4.3    18.49     11      0      2  no\n",
       "   8 │     0  10.6606      4.5    20.25     11      0      2  no\n",
       "   9 │     0  10.4676      6.0    36.0      12      0      0  no\n",
       "  10 │     0  11.2296      3.3    10.89     11      2      0  no\n",
       "  11 │     0  11.9065      5.6    31.36     14      0      0  no\n",
       "  ⋮  │   ⋮       ⋮        ⋮        ⋮       ⋮      ⋮      ⋮       ⋮\n",
       " 462 │     0  10.0104      5.7    32.49      6      0      1  yes\n",
       " 463 │     0  10.5593      3.2    10.24     12      1      0  yes\n",
       " 464 │     0  10.2158      2.5     6.25     11      1      0  yes\n",
       " 465 │     0  10.9458      3.3    10.89     14      0      2  yes\n",
       " 466 │     0  11.111       3.5    12.25     10      1      1  yes\n",
       " 467 │     0  10.4714      5.1    26.01      9      0      1  yes\n",
       " 468 │     0  10.1475      4.1    16.81      5      1      0  yes\n",
       " 469 │     0  10.5974      2.4     5.76      4      2      1  yes\n",
       " 470 │     0  10.1337      2.4     5.76      6      2      0  yes\n",
       " 471 │     0  11.2207      5.1    26.01     10      0      0  yes\n",
       "\u001b[36m                                                      450 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gd[Dict(:lfp => 0)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "6a9aa27c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>471×8 SubDataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">446 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">lfp</th><th style = \"text-align: left;\">lnnlinc</th><th style = \"text-align: left;\">age</th><th style = \"text-align: left;\">age²</th><th style = \"text-align: left;\">educ</th><th style = \"text-align: left;\">nyc</th><th style = \"text-align: left;\">noc</th><th style = \"text-align: left;\">foreign</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"CategoricalValue{String3, UInt32}\" style = \"text-align: left;\">Cat…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.7875</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.9686</td><td style = \"text-align: right;\">4.6</td><td style = \"text-align: right;\">21.16</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.105</td><td style = \"text-align: right;\">3.1</td><td style = \"text-align: right;\">9.61</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.1085</td><td style = \"text-align: right;\">4.4</td><td style = \"text-align: right;\">19.36</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.4547</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.6247</td><td style = \"text-align: right;\">3.9</td><td style = \"text-align: right;\">15.21</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.4864</td><td style = \"text-align: right;\">4.3</td><td style = \"text-align: right;\">18.49</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.6606</td><td style = \"text-align: right;\">4.5</td><td style = \"text-align: right;\">20.25</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.4676</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">36.0</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.2296</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">10.89</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.9065</td><td style = \"text-align: right;\">5.6</td><td style = \"text-align: right;\">31.36</td><td style = \"text-align: right;\">14</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.5016</td><td style = \"text-align: right;\">5.6</td><td style = \"text-align: right;\">31.36</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">no</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.2935</td><td style = \"text-align: right;\">4.7</td><td style = \"text-align: right;\">22.09</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">no</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">460</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.5008</td><td style = \"text-align: right;\">4.9</td><td style = \"text-align: right;\">24.01</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; 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text-align: right;\">464</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.2158</td><td style = \"text-align: right;\">2.5</td><td style = \"text-align: right;\">6.25</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">465</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.9458</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">10.89</td><td style = \"text-align: right;\">14</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">466</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.111</td><td style = \"text-align: right;\">3.5</td><td style = \"text-align: right;\">12.25</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">467</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.4714</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">468</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.1475</td><td style = \"text-align: right;\">4.1</td><td style = \"text-align: right;\">16.81</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">469</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.5974</td><td style = \"text-align: right;\">2.4</td><td style = \"text-align: right;\">5.76</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">470</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">10.1337</td><td style = \"text-align: right;\">2.4</td><td style = \"text-align: right;\">5.76</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">471</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">11.2207</td><td style = \"text-align: right;\">5.1</td><td style = \"text-align: right;\">26.01</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">yes</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& lfp & lnnlinc & age & age² & educ & nyc & noc & foreign\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64 & Float64 & Float64 & Int64 & Int64 & Int64 & Cat…\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & 10.7875 & 3.0 & 9.0 & 8 & 1 & 1 & no \\\\\n",
       "\t2 & 0 & 10.9686 & 4.6 & 21.16 & 9 & 0 & 0 & no \\\\\n",
       "\t3 & 0 & 11.105 & 3.1 & 9.61 & 11 & 2 & 0 & no \\\\\n",
       "\t4 & 0 & 11.1085 & 4.4 & 19.36 & 12 & 0 & 2 & no \\\\\n",
       "\t5 & 0 & 11.4547 & 5.1 & 26.01 & 8 & 0 & 0 & no \\\\\n",
       "\t6 & 0 & 10.6247 & 3.9 & 15.21 & 12 & 0 & 0 & no \\\\\n",
       "\t7 & 0 & 10.4864 & 4.3 & 18.49 & 11 & 0 & 2 & no \\\\\n",
       "\t8 & 0 & 10.6606 & 4.5 & 20.25 & 11 & 0 & 2 & no \\\\\n",
       "\t9 & 0 & 10.4676 & 6.0 & 36.0 & 12 & 0 & 0 & no \\\\\n",
       "\t10 & 0 & 11.2296 & 3.3 & 10.89 & 11 & 2 & 0 & no \\\\\n",
       "\t11 & 0 & 11.9065 & 5.6 & 31.36 & 14 & 0 & 0 & no \\\\\n",
       "\t12 & 0 & 11.5016 & 5.6 & 31.36 & 11 & 0 & 0 & no \\\\\n",
       "\t13 & 0 & 11.2935 & 4.7 & 22.09 & 11 & 0 & 1 & no \\\\\n",
       "\t14 & 0 & 10.8613 & 5.0 & 25.0 & 8 & 0 & 0 & no \\\\\n",
       "\t15 & 0 & 11.0486 & 4.7 & 22.09 & 8 & 0 & 1 & no \\\\\n",
       "\t16 & 0 & 10.8601 & 2.9 & 8.41 & 19 & 0 & 0 & no \\\\\n",
       "\t17 & 0 & 10.8486 & 4.4 & 19.36 & 8 & 0 & 2 & no \\\\\n",
       "\t18 & 0 & 10.4824 & 2.0 & 4.0 & 12 & 1 & 0 & no \\\\\n",
       "\t19 & 0 & 10.5406 & 2.8 & 7.84 & 9 & 2 & 0 & no \\\\\n",
       "\t20 & 0 & 11.2243 & 4.7 & 22.09 & 8 & 0 & 1 & no \\\\\n",
       "\t21 & 0 & 10.5663 & 3.0 & 9.0 & 11 & 0 & 1 & no \\\\\n",
       "\t22 & 0 & 11.7696 & 5.1 & 26.01 & 11 & 0 & 0 & no \\\\\n",
       "\t23 & 0 & 10.6671 & 2.8 & 7.84 & 11 & 0 & 2 & no \\\\\n",
       "\t24 & 0 & 10.6246 & 5.4 & 29.16 & 11 & 0 & 0 & no \\\\\n",
       "\t25 & 0 & 10.5371 & 4.9 & 24.01 & 8 & 0 & 0 & no \\\\\n",
       "\t26 & 0 & 11.1356 & 5.3 & 28.09 & 10 & 0 & 0 & no \\\\\n",
       "\t27 & 0 & 10.3153 & 5.5 & 30.25 & 8 & 0 & 0 & no \\\\\n",
       "\t28 & 0 & 10.3727 & 2.4 & 5.76 & 11 & 1 & 0 & no \\\\\n",
       "\t29 & 0 & 11.5071 & 5.0 & 25.0 & 8 & 0 & 1 & no \\\\\n",
       "\t30 & 0 & 10.4529 & 2.3 & 5.29 & 9 & 1 & 0 & no \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m471×8 SubDataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m lfp   \u001b[0m\u001b[1m lnnlinc \u001b[0m\u001b[1m age     \u001b[0m\u001b[1m age²    \u001b[0m\u001b[1m educ  \u001b[0m\u001b[1m nyc   \u001b[0m\u001b[1m noc   \u001b[0m\u001b[1m foreign \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Cat…    \u001b[0m\n",
       "─────┼────────────────────────────────────────────────────────────────\n",
       "   1 │     0  10.7875      3.0     9.0       8      1      1  no\n",
       "   2 │     0  10.9686      4.6    21.16      9      0      0  no\n",
       "   3 │     0  11.105       3.1     9.61     11      2      0  no\n",
       "   4 │     0  11.1085      4.4    19.36     12      0      2  no\n",
       "   5 │     0  11.4547      5.1    26.01      8      0      0  no\n",
       "   6 │     0  10.6247      3.9    15.21     12      0      0  no\n",
       "   7 │     0  10.4864      4.3    18.49     11      0      2  no\n",
       "   8 │     0  10.6606      4.5    20.25     11      0      2  no\n",
       "   9 │     0  10.4676      6.0    36.0      12      0      0  no\n",
       "  10 │     0  11.2296      3.3    10.89     11      2      0  no\n",
       "  11 │     0  11.9065      5.6    31.36     14      0      0  no\n",
       "  ⋮  │   ⋮       ⋮        ⋮        ⋮       ⋮      ⋮      ⋮       ⋮\n",
       " 462 │     0  10.0104      5.7    32.49      6      0      1  yes\n",
       " 463 │     0  10.5593      3.2    10.24     12      1      0  yes\n",
       " 464 │     0  10.2158      2.5     6.25     11      1      0  yes\n",
       " 465 │     0  10.9458      3.3    10.89     14      0      2  yes\n",
       " 466 │     0  11.111       3.5    12.25     10      1      1  yes\n",
       " 467 │     0  10.4714      5.1    26.01      9      0      1  yes\n",
       " 468 │     0  10.1475      4.1    16.81      5      1      0  yes\n",
       " 469 │     0  10.5974      2.4     5.76      4      2      1  yes\n",
       " 470 │     0  10.1337      2.4     5.76      6      2      0  yes\n",
       " 471 │     0  11.2207      5.1    26.01     10      0      0  yes\n",
       "\u001b[36m                                                      450 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gd[(0,)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d282c50",
   "metadata": {},
   "source": [
    "Before we move forward let us investigate why we have added a square of `:age` to our data frame.\n",
    "\n",
    "For this we use density plot from the [StatsPlots.jl](https://github.com/JuliaPlots/StatsPlots.jl) package. This package contains statistical recepies that extend the [Plots.jl](https://github.com/JuliaPlots/Plots.jl) functionality."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "04ce9ddd",
   "metadata": {},
   "outputs": [
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       "  1155.77,667.452 1166.18,671.312 1176.59,674.214 1187,676.256 1197.41,677.537 1207.83,678.153 1218.24,678.191 1228.65,677.722 1239.06,676.803 1249.47,675.473 \n",
       "  1259.88,673.762 1270.29,671.685 1280.71,669.253 1291.12,666.479 1301.53,663.374 1311.94,659.963 1322.35,656.276 1332.76,652.362 1343.17,648.278 1353.58,644.098 \n",
       "  1364,639.905 1374.41,635.79 1384.82,631.852 1395.23,628.188 1405.64,624.896 1416.05,622.066 1426.46,619.78 1436.87,618.109 1447.29,617.107 1457.7,616.814 \n",
       "  1468.11,617.248 1478.52,618.408 1488.93,620.271 1499.34,622.791 1509.75,625.899 1520.16,629.506 1530.58,633.501 1540.99,637.758 1551.4,642.137 1561.81,646.495 \n",
       "  1572.22,650.688 1582.63,654.583 1593.04,658.066 1603.46,661.05 1613.87,663.483 1624.28,665.359 1634.69,666.718 1645.1,667.652 1655.51,668.305 1665.92,668.871 \n",
       "  1676.33,669.586 1686.75,670.722 1697.16,672.579 1707.57,675.467 1717.98,679.701 1728.39,685.58 1738.8,693.381 1749.21,703.345 1759.62,715.665 1770.04,730.482 \n",
       "  1780.45,747.874 1790.86,767.857 1801.27,790.381 1811.68,815.332 1822.09,842.534 1832.5,871.757 1842.91,902.718 1853.33,935.097 1863.74,968.538 1874.15,1002.67 \n",
       "  1884.56,1037.1 1894.97,1071.44 1905.38,1105.32 1915.79,1138.39 1926.21,1170.32 1936.62,1200.82 1947.03,1229.65 1957.44,1256.61 1967.85,1281.57 1978.26,1304.43 \n",
       "  1988.67,1325.13 1999.08,1343.7 2009.5,1360.17 2019.91,1374.63 2030.32,1387.18 2040.73,1397.96 2051.14,1407.12 2061.55,1414.82 2071.96,1421.23 2082.37,1426.49 \n",
       "  2092.79,1430.77 2103.2,1434.22 2113.61,1436.96 2124.02,1439.11 2134.43,1440.79 2144.84,1442.08 2155.25,1443.06 2165.67,1443.8 2176.08,1444.35 2186.49,1444.75 \n",
       "  2196.9,1445.04 2207.31,1445.26 2217.72,1445.41 2228.13,1445.51 2238.54,1445.58 2248.96,1445.63 2259.37,1445.67 2269.78,1445.69 2280.19,1445.7 2290.6,1445.7 \n",
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       "  391.037,1443.85 400.513,1443.04 409.988,1441.94 419.463,1440.48 428.939,1438.54 438.414,1436.04 447.889,1432.85 457.365,1428.85 466.84,1423.92 476.315,1417.94 \n",
       "  485.791,1410.81 495.266,1402.43 504.741,1392.76 514.217,1381.77 523.692,1369.5 533.167,1356 542.643,1341.39 552.118,1325.82 561.593,1309.47 571.069,1292.52 \n",
       "  580.544,1275.16 590.019,1257.57 599.495,1239.86 608.97,1222.13 618.445,1204.37 627.921,1186.54 637.396,1168.5 646.871,1150.06 656.347,1131.02 665.822,1111.12 \n",
       "  675.297,1090.16 684.773,1067.94 694.248,1044.38 703.723,1019.45 713.199,993.262 722.674,966.021 732.149,938.047 741.625,909.743 751.1,881.569 760.575,854.007 \n",
       "  770.051,827.515 779.526,802.49 789.001,779.231 798.477,757.905 807.952,738.53 817.427,720.972 826.902,704.947 836.378,690.039 845.853,675.738 855.328,661.469 \n",
       "  864.804,646.639 874.279,630.681 883.754,613.089 893.23,593.457 902.705,571.504 912.18,547.089 921.656,520.218 931.131,491.042 940.606,459.842 950.082,427.018 \n",
       "  959.557,393.06 969.032,358.526 978.508,324.015 987.983,290.142 997.458,257.51 1006.93,226.693 1016.41,198.208 1025.88,172.505 1035.36,149.946 1044.83,130.794 \n",
       "  1054.31,115.211 1063.79,103.245 1073.26,94.8403 1082.74,89.835 1092.21,87.9763 1101.69,88.9329 1111.16,92.3134 1120.64,97.6866 1130.11,104.603 1139.59,112.615 \n",
       "  1149.06,121.299 1158.54,130.267 1168.01,139.187 1177.49,147.782 1186.96,155.846 1196.44,163.238 1205.92,169.881 1215.39,175.764 1224.87,180.929 1234.34,185.474 \n",
       "  1243.82,189.539 1253.29,193.304 1262.77,196.982 1272.24,200.81 1281.72,205.042 1291.19,209.942 1300.67,215.77 1310.14,222.771 1319.62,231.168 1329.09,241.146 \n",
       "  1338.57,252.843 1348.05,266.345 1357.52,281.681 1367,298.821 1376.47,317.685 1385.95,338.145 1395.42,360.042 1404.9,383.197 1414.37,407.426 1423.85,432.552 \n",
       "  1433.32,458.421 1442.8,484.903 1452.27,511.9 1461.75,539.345 1471.22,567.192 1480.7,595.414 1490.18,623.989 1499.65,652.885 1509.13,682.053 1518.6,711.414 \n",
       "  1528.08,740.855 1537.55,770.22 1547.03,799.319 1556.5,827.927 1565.98,855.796 1575.45,882.667 1584.93,908.287 1594.4,932.42 1603.88,954.866 1613.35,975.475 \n",
       "  1622.83,994.156 1632.31,1010.88 1641.78,1025.7 1651.26,1038.72 1660.73,1050.12 1670.21,1060.13 1679.68,1069.03 1689.16,1077.1 1698.63,1084.68 1708.11,1092.08 \n",
       "  1717.58,1099.59 1727.06,1107.52 1736.53,1116.08 1746.01,1125.49 1755.48,1135.89 1764.96,1147.35 1774.44,1159.92 1783.91,1173.57 1793.39,1188.21 1802.86,1203.71 \n",
       "  1812.34,1219.91 1821.81,1236.6 1831.29,1253.57 1840.76,1270.58 1850.24,1287.41 1859.71,1303.83 1869.19,1319.65 1878.66,1334.71 1888.14,1348.84 1897.61,1361.95 \n",
       "  1907.09,1373.97 1916.57,1384.84 1926.04,1394.57 1935.52,1403.16 1944.99,1410.67 1954.47,1417.14 1963.94,1422.67 1973.42,1427.32 1982.89,1431.19 1992.37,1434.38 \n",
       "  2001.84,1436.96 2011.32,1439.04 2020.79,1440.68 2030.27,1441.97 2039.74,1442.96 2049.22,1443.71 2058.69,1444.28 2068.17,1444.7 2077.65,1445.01 2087.12,1445.23 \n",
       "  2096.6,1445.39 2106.07,1445.5 2115.55,1445.58 2125.02,1445.63 2134.5,1445.67 2143.97,1445.69 2153.45,1445.71 2162.92,1445.71 2172.4,1445.72 2181.87,1445.71 \n",
       "  \n",
       "  \"/>\n",
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      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@df df density(:age, group=:lfp)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5ec446e",
   "metadata": {},
   "source": [
    "## Building a predictive model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9564c27e",
   "metadata": {},
   "source": [
    "Now we are ready to create the probit model using the [GLM.jl](https://github.com/JuliaStats/GLM.jl) package:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "f3ab9ac4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "StatsModels.TableRegressionModel{GeneralizedLinearModel{GLM.GlmResp{Vector{Float64}, Binomial{Float64}, ProbitLink}, GLM.DensePredChol{Float64, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}}}, Matrix{Float64}}\n",
       "\n",
       "lfp ~ 1 + lnnlinc + age + age² + educ + nyc + noc + foreign\n",
       "\n",
       "Coefficients:\n",
       "────────────────────────────────────────────────────────────────────────────\n",
       "                   Coef.  Std. Error      z  Pr(>|z|)  Lower 95%   Upper 95%\n",
       "────────────────────────────────────────────────────────────────────────────\n",
       "(Intercept)    3.74896     1.40663     2.67    0.0077   0.992006   6.50591\n",
       "lnnlinc       -0.666932    0.13192    -5.06    <1e-06  -0.92549   -0.408374\n",
       "age            2.07531     0.405407    5.12    <1e-06   1.28073    2.86989\n",
       "age²          -0.294345    0.0499446  -5.89    <1e-08  -0.392235  -0.196456\n",
       "educ           0.0191963   0.0179255   1.07    0.2842  -0.015937   0.0543295\n",
       "nyc           -0.714465    0.100397   -7.12    <1e-11  -0.911238  -0.517691\n",
       "noc           -0.146985    0.0508854  -2.89    0.0039  -0.246718  -0.0472509\n",
       "foreign: yes   0.71438     0.121324    5.89    <1e-08   0.476589   0.95217\n",
       "────────────────────────────────────────────────────────────────────────────"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probit = glm(@formula(lfp ~ lnnlinc + age + age² + educ + nyc + noc + foreign),\n",
    "             df, Binomial(), ProbitLink())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68d6a9cb",
   "metadata": {},
   "source": [
    "In the example above we have entered the `@formula` by hand. However, it can be also programmatically generated like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "950d7378",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "StatsModels.TableRegressionModel{GeneralizedLinearModel{GLM.GlmResp{Vector{Float64}, Binomial{Float64}, ProbitLink}, GLM.DensePredChol{Float64, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}}}, Matrix{Float64}}\n",
       "\n",
       "lfp ~ 1 + lnnlinc + age + age² + educ + nyc + noc + foreign\n",
       "\n",
       "Coefficients:\n",
       "────────────────────────────────────────────────────────────────────────────\n",
       "                   Coef.  Std. Error      z  Pr(>|z|)  Lower 95%   Upper 95%\n",
       "────────────────────────────────────────────────────────────────────────────\n",
       "(Intercept)    3.74896     1.40663     2.67    0.0077   0.992006   6.50591\n",
       "lnnlinc       -0.666932    0.13192    -5.06    <1e-06  -0.92549   -0.408374\n",
       "age            2.07531     0.405407    5.12    <1e-06   1.28073    2.86989\n",
       "age²          -0.294345    0.0499446  -5.89    <1e-08  -0.392235  -0.196456\n",
       "educ           0.0191963   0.0179255   1.07    0.2842  -0.015937   0.0543295\n",
       "nyc           -0.714465    0.100397   -7.12    <1e-11  -0.911238  -0.517691\n",
       "noc           -0.146985    0.0508854  -2.89    0.0039  -0.246718  -0.0472509\n",
       "foreign: yes   0.71438     0.121324    5.89    <1e-08   0.476589   0.95217\n",
       "────────────────────────────────────────────────────────────────────────────"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probit = glm(Term(:lfp) ~ sum(Term.(propertynames(df)[2:end])),\n",
    "             df, Binomial(), ProbitLink())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "572cd1e7",
   "metadata": {},
   "source": [
    "Note the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "524621c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "FormulaTerm\n",
       "Response:\n",
       "  lfp(unknown)\n",
       "Predictors:\n",
       "  lnnlinc(unknown)\n",
       "  age(unknown)\n",
       "  age²(unknown)\n",
       "  educ(unknown)\n",
       "  nyc(unknown)\n",
       "  noc(unknown)\n",
       "  foreign(unknown)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Term(:lfp) ~ sum(Term.(propertynames(df)[2:end]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "646e96aa",
   "metadata": {},
   "source": [
    "vs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "853199f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "FormulaTerm\n",
       "Response:\n",
       "  lfp(unknown)\n",
       "Predictors:\n",
       "  lnnlinc(unknown)\n",
       "  age(unknown)\n",
       "  age²(unknown)\n",
       "  educ(unknown)\n",
       "  nyc(unknown)\n",
       "  noc(unknown)\n",
       "  foreign(unknown)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@formula(lfp ~ lnnlinc + age + age² + educ + nyc + noc + foreign)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16a31c85",
   "metadata": {},
   "source": [
    "Finally observe that `@formula` is powerful enough to automatically do the computation of the square of `:age`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "7286316c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "StatsModels.TableRegressionModel{GeneralizedLinearModel{GLM.GlmResp{Vector{Float64}, Binomial{Float64}, ProbitLink}, GLM.DensePredChol{Float64, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}}}, Matrix{Float64}}\n",
       "\n",
       "lfp ~ 1 + lnnlinc + age + :(age ^ 2) + educ + nyc + noc + foreign\n",
       "\n",
       "Coefficients:\n",
       "────────────────────────────────────────────────────────────────────────────\n",
       "                   Coef.  Std. Error      z  Pr(>|z|)  Lower 95%   Upper 95%\n",
       "────────────────────────────────────────────────────────────────────────────\n",
       "(Intercept)    3.74896     1.40663     2.67    0.0077   0.992006   6.50591\n",
       "lnnlinc       -0.666932    0.13192    -5.06    <1e-06  -0.92549   -0.408374\n",
       "age            2.07531     0.405407    5.12    <1e-06   1.28073    2.86989\n",
       "age ^ 2       -0.294345    0.0499446  -5.89    <1e-08  -0.392235  -0.196456\n",
       "educ           0.0191963   0.0179255   1.07    0.2842  -0.015937   0.0543295\n",
       "nyc           -0.714465    0.100397   -7.12    <1e-11  -0.911238  -0.517691\n",
       "noc           -0.146985    0.0508854  -2.89    0.0039  -0.246718  -0.0472509\n",
       "foreign: yes   0.71438     0.121324    5.89    <1e-08   0.476589   0.95217\n",
       "────────────────────────────────────────────────────────────────────────────"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probit = glm(@formula(lfp ~ lnnlinc + age + age^2 + educ + nyc + noc + foreign),\n",
    "             df, Binomial(), ProbitLink())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46612c86",
   "metadata": {},
   "source": [
    "We check the formula again:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "25cc1f58",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "FormulaTerm\n",
       "Response:\n",
       "  lfp(unknown)\n",
       "Predictors:\n",
       "  lnnlinc(unknown)\n",
       "  age(unknown)\n",
       "  (age)->age ^ 2\n",
       "  educ(unknown)\n",
       "  nyc(unknown)\n",
       "  noc(unknown)\n",
       "  foreign(unknown)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@formula(lfp ~ lnnlinc + age + age^2 + educ + nyc + noc + foreign)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b24f2bd5",
   "metadata": {},
   "source": [
    "Next we prepare a new data frame in which we will check how the prediction of our model changes as we modify `:age` while keeping all other variables constant:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "35e9072a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>421×6 DataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">396 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">lnnlinc</th><th style = \"text-align: left;\">age</th><th style = \"text-align: left;\">educ</th><th style = \"text-align: left;\">nyc</th><th style = \"text-align: left;\">noc</th><th style = \"text-align: left;\">foreign</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"String\" style = \"text-align: left;\">String</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">2.0</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">2.01</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">2.02</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">2.03</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">2.04</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">2.05</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">2.06</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">2.07</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">2.08</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">2.09</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">2.1</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">2.11</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">2.12</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">410</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">6.09</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">411</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">6.1</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">412</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">6.11</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">413</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">6.12</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">414</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">6.13</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">415</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">6.14</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">416</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">6.15</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">417</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">6.16</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">418</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">6.17</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">419</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">6.18</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">420</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">6.19</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">421</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">6.2</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">yes</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccc}\n",
       "\t& lnnlinc & age & educ & nyc & noc & foreign\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Int64 & Int64 & Int64 & String\\\\\n",
       "\t\\hline\n",
       "\t1 & 10.0 & 2.0 & 9 & 0 & 1 & yes \\\\\n",
       "\t2 & 10.0 & 2.01 & 9 & 0 & 1 & yes \\\\\n",
       "\t3 & 10.0 & 2.02 & 9 & 0 & 1 & yes \\\\\n",
       "\t4 & 10.0 & 2.03 & 9 & 0 & 1 & yes \\\\\n",
       "\t5 & 10.0 & 2.04 & 9 & 0 & 1 & yes \\\\\n",
       "\t6 & 10.0 & 2.05 & 9 & 0 & 1 & yes \\\\\n",
       "\t7 & 10.0 & 2.06 & 9 & 0 & 1 & yes \\\\\n",
       "\t8 & 10.0 & 2.07 & 9 & 0 & 1 & yes \\\\\n",
       "\t9 & 10.0 & 2.08 & 9 & 0 & 1 & yes \\\\\n",
       "\t10 & 10.0 & 2.09 & 9 & 0 & 1 & yes \\\\\n",
       "\t11 & 10.0 & 2.1 & 9 & 0 & 1 & yes \\\\\n",
       "\t12 & 10.0 & 2.11 & 9 & 0 & 1 & yes \\\\\n",
       "\t13 & 10.0 & 2.12 & 9 & 0 & 1 & yes \\\\\n",
       "\t14 & 10.0 & 2.13 & 9 & 0 & 1 & yes \\\\\n",
       "\t15 & 10.0 & 2.14 & 9 & 0 & 1 & yes \\\\\n",
       "\t16 & 10.0 & 2.15 & 9 & 0 & 1 & yes \\\\\n",
       "\t17 & 10.0 & 2.16 & 9 & 0 & 1 & yes \\\\\n",
       "\t18 & 10.0 & 2.17 & 9 & 0 & 1 & yes \\\\\n",
       "\t19 & 10.0 & 2.18 & 9 & 0 & 1 & yes \\\\\n",
       "\t20 & 10.0 & 2.19 & 9 & 0 & 1 & yes \\\\\n",
       "\t21 & 10.0 & 2.2 & 9 & 0 & 1 & yes \\\\\n",
       "\t22 & 10.0 & 2.21 & 9 & 0 & 1 & yes \\\\\n",
       "\t23 & 10.0 & 2.22 & 9 & 0 & 1 & yes \\\\\n",
       "\t24 & 10.0 & 2.23 & 9 & 0 & 1 & yes \\\\\n",
       "\t25 & 10.0 & 2.24 & 9 & 0 & 1 & yes \\\\\n",
       "\t26 & 10.0 & 2.25 & 9 & 0 & 1 & yes \\\\\n",
       "\t27 & 10.0 & 2.26 & 9 & 0 & 1 & yes \\\\\n",
       "\t28 & 10.0 & 2.27 & 9 & 0 & 1 & yes \\\\\n",
       "\t29 & 10.0 & 2.28 & 9 & 0 & 1 & yes \\\\\n",
       "\t30 & 10.0 & 2.29 & 9 & 0 & 1 & yes \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m421×6 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m lnnlinc \u001b[0m\u001b[1m age     \u001b[0m\u001b[1m educ  \u001b[0m\u001b[1m nyc   \u001b[0m\u001b[1m noc   \u001b[0m\u001b[1m foreign \u001b[0m\n",
       "     │\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m String  \u001b[0m\n",
       "─────┼────────────────────────────────────────────────\n",
       "   1 │    10.0     2.0       9      0      1  yes\n",
       "   2 │    10.0     2.01      9      0      1  yes\n",
       "   3 │    10.0     2.02      9      0      1  yes\n",
       "   4 │    10.0     2.03      9      0      1  yes\n",
       "   5 │    10.0     2.04      9      0      1  yes\n",
       "   6 │    10.0     2.05      9      0      1  yes\n",
       "   7 │    10.0     2.06      9      0      1  yes\n",
       "   8 │    10.0     2.07      9      0      1  yes\n",
       "   9 │    10.0     2.08      9      0      1  yes\n",
       "  10 │    10.0     2.09      9      0      1  yes\n",
       "  11 │    10.0     2.1       9      0      1  yes\n",
       "  ⋮  │    ⋮        ⋮       ⋮      ⋮      ⋮       ⋮\n",
       " 412 │    10.0     6.11      9      0      1  yes\n",
       " 413 │    10.0     6.12      9      0      1  yes\n",
       " 414 │    10.0     6.13      9      0      1  yes\n",
       " 415 │    10.0     6.14      9      0      1  yes\n",
       " 416 │    10.0     6.15      9      0      1  yes\n",
       " 417 │    10.0     6.16      9      0      1  yes\n",
       " 418 │    10.0     6.17      9      0      1  yes\n",
       " 419 │    10.0     6.18      9      0      1  yes\n",
       " 420 │    10.0     6.19      9      0      1  yes\n",
       " 421 │    10.0     6.2       9      0      1  yes\n",
       "\u001b[36m                                      400 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_pred = DataFrame(lnnlinc=10.0, age= 2.0:0.01:6.2, educ = 9, nyc = 0, noc = 1, foreign = \"yes\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ac9db26",
   "metadata": {},
   "source": [
    "We make a prediction along with its confidence interval:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "36377669",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>421×3 DataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">396 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">prediction</th><th style = \"text-align: left;\">lower</th><th style = \"text-align: left;\">upper</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Union{Missing, Float64}\" style = \"text-align: left;\">Float64?</th><th title = \"Union{Missing, Float64}\" style = \"text-align: left;\">Float64?</th><th title = \"Union{Missing, Float64}\" style = \"text-align: left;\">Float64?</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0.786122</td><td style = \"text-align: right;\">0.636712</td><td style = \"text-align: right;\">0.891844</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">0.78872</td><td style = \"text-align: right;\">0.641194</td><td style = \"text-align: right;\">0.892941</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">0.791282</td><td style = \"text-align: right;\">0.645623</td><td style = \"text-align: right;\">0.894026</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">0.79381</td><td style = \"text-align: right;\">0.650001</td><td style = \"text-align: right;\">0.895097</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">0.796302</td><td style = \"text-align: right;\">0.654325</td><td style = \"text-align: right;\">0.896155</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; 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text-align: right;\">421</td><td style = \"text-align: right;\">0.265032</td><td style = \"text-align: right;\">0.131668</td><td style = \"text-align: right;\">0.445407</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& prediction & lower & upper\\\\\n",
       "\t\\hline\n",
       "\t& Float64? & Float64? & Float64?\\\\\n",
       "\t\\hline\n",
       "\t1 & 0.786122 & 0.636712 & 0.891844 \\\\\n",
       "\t2 & 0.78872 & 0.641194 & 0.892941 \\\\\n",
       "\t3 & 0.791282 & 0.645623 & 0.894026 \\\\\n",
       "\t4 & 0.79381 & 0.650001 & 0.895097 \\\\\n",
       "\t5 & 0.796302 & 0.654325 & 0.896155 \\\\\n",
       "\t6 & 0.79876 & 0.658597 & 0.8972 \\\\\n",
       "\t7 & 0.801183 & 0.662817 & 0.898233 \\\\\n",
       "\t8 & 0.803572 & 0.666983 & 0.899252 \\\\\n",
       "\t9 & 0.805928 & 0.671097 & 0.90026 \\\\\n",
       "\t10 & 0.808251 & 0.675159 & 0.901254 \\\\\n",
       "\t11 & 0.81054 & 0.679167 & 0.902237 \\\\\n",
       "\t12 & 0.812797 & 0.683124 & 0.903207 \\\\\n",
       "\t13 & 0.815021 & 0.687028 & 0.904166 \\\\\n",
       "\t14 & 0.817213 & 0.690879 & 0.905113 \\\\\n",
       "\t15 & 0.819373 & 0.694678 & 0.906048 \\\\\n",
       "\t16 & 0.821502 & 0.698426 & 0.906971 \\\\\n",
       "\t17 & 0.8236 & 0.702121 & 0.907883 \\\\\n",
       "\t18 & 0.825667 & 0.705765 & 0.908784 \\\\\n",
       "\t19 & 0.827703 & 0.709358 & 0.909674 \\\\\n",
       "\t20 & 0.82971 & 0.712899 & 0.910552 \\\\\n",
       "\t21 & 0.831686 & 0.716389 & 0.91142 \\\\\n",
       "\t22 & 0.833633 & 0.719829 & 0.912277 \\\\\n",
       "\t23 & 0.835551 & 0.723218 & 0.913123 \\\\\n",
       "\t24 & 0.83744 & 0.726558 & 0.913959 \\\\\n",
       "\t25 & 0.8393 & 0.729847 & 0.914785 \\\\\n",
       "\t26 & 0.841133 & 0.733087 & 0.9156 \\\\\n",
       "\t27 & 0.842937 & 0.736278 & 0.916405 \\\\\n",
       "\t28 & 0.844714 & 0.739421 & 0.9172 \\\\\n",
       "\t29 & 0.846463 & 0.742515 & 0.917985 \\\\\n",
       "\t30 & 0.848186 & 0.74556 & 0.91876 \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m421×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m prediction \u001b[0m\u001b[1m lower    \u001b[0m\u001b[1m upper    \u001b[0m\n",
       "     │\u001b[90m Float64?   \u001b[0m\u001b[90m Float64? \u001b[0m\u001b[90m Float64? \u001b[0m\n",
       "─────┼────────────────────────────────\n",
       "   1 │   0.786122  0.636712  0.891844\n",
       "   2 │   0.78872   0.641194  0.892941\n",
       "   3 │   0.791282  0.645623  0.894026\n",
       "   4 │   0.79381   0.650001  0.895097\n",
       "   5 │   0.796302  0.654325  0.896155\n",
       "   6 │   0.79876   0.658597  0.8972\n",
       "   7 │   0.801183  0.662817  0.898233\n",
       "   8 │   0.803572  0.666983  0.899252\n",
       "   9 │   0.805928  0.671097  0.90026\n",
       "  10 │   0.808251  0.675159  0.901254\n",
       "  11 │   0.81054   0.679167  0.902237\n",
       "  ⋮  │     ⋮          ⋮         ⋮\n",
       " 412 │   0.312569  0.171341  0.488718\n",
       " 413 │   0.307192  0.166677  0.483938\n",
       " 414 │   0.301835  0.162074  0.479148\n",
       " 415 │   0.2965    0.157534  0.474349\n",
       " 416 │   0.291189  0.153057  0.469542\n",
       " 417 │   0.285902  0.148645  0.464727\n",
       " 418 │   0.280642  0.144299  0.459905\n",
       " 419 │   0.275409  0.14002   0.455078\n",
       " 420 │   0.270205  0.13581   0.450245\n",
       " 421 │   0.265032  0.131668  0.445407\n",
       "\u001b[36m                      400 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probit_pred = predict(probit, df_pred, interval=:confidence)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d9707b5",
   "metadata": {},
   "source": [
    "Now we plot it. Note that we use `Matrix` constructor to create a matrix out of the data frame easily:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "eaf313c0",
   "metadata": {},
   "outputs": [
    {
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       "  1957.03,429.223 1961.82,434.432 1966.61,439.69 1971.4,444.997 1976.19,450.354 1980.99,455.759 1985.78,461.212 1990.57,466.714 1995.36,472.265 2000.15,477.863 \n",
       "  2004.94,483.509 2009.73,489.203 2014.52,494.944 2019.31,500.733 2024.1,506.568 2028.89,512.45 2033.68,518.378 2038.48,524.353 2043.27,530.373 2048.06,536.438 \n",
       "  2052.85,542.549 2057.64,548.704 2062.43,554.903 2067.22,561.147 2072.01,567.434 2076.8,573.764 2081.59,580.137 2086.38,586.552 2091.18,593.008 2095.97,599.506 \n",
       "  2100.76,606.045 2105.55,612.624 2110.34,619.243 2115.13,625.901 2119.92,632.597 2124.71,639.332 2129.5,646.104 2134.29,652.913 2139.08,659.758 2143.87,666.638 \n",
       "  2148.67,673.554 2153.46,680.503 2158.25,687.486 2163.04,694.502 2167.83,701.55 2172.62,708.629 2177.41,715.739 2182.2,722.879 2186.99,730.047 2191.78,737.244 \n",
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      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(df_pred.age, Matrix(probit_pred), labels=[\"lfp\" \"lower\" \"upper\"],\n",
    "     xlabel=\"age\", ylabel=\"Pr(lfp=1)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "763c00bc",
   "metadata": {},
   "source": [
    "## Advanced DataFrames.jl functionalities: bootstrapping example"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0a15dad",
   "metadata": {},
   "source": [
    "Let us investigate the `probit` object again:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "904c1d36",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "StatsModels.TableRegressionModel{GeneralizedLinearModel{GLM.GlmResp{Vector{Float64}, Binomial{Float64}, ProbitLink}, GLM.DensePredChol{Float64, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}}}, Matrix{Float64}}\n",
       "\n",
       "lfp ~ 1 + lnnlinc + age + :(age ^ 2) + educ + nyc + noc + foreign\n",
       "\n",
       "Coefficients:\n",
       "────────────────────────────────────────────────────────────────────────────\n",
       "                   Coef.  Std. Error      z  Pr(>|z|)  Lower 95%   Upper 95%\n",
       "────────────────────────────────────────────────────────────────────────────\n",
       "(Intercept)    3.74896     1.40663     2.67    0.0077   0.992006   6.50591\n",
       "lnnlinc       -0.666932    0.13192    -5.06    <1e-06  -0.92549   -0.408374\n",
       "age            2.07531     0.405407    5.12    <1e-06   1.28073    2.86989\n",
       "age ^ 2       -0.294345    0.0499446  -5.89    <1e-08  -0.392235  -0.196456\n",
       "educ           0.0191963   0.0179255   1.07    0.2842  -0.015937   0.0543295\n",
       "nyc           -0.714465    0.100397   -7.12    <1e-11  -0.911238  -0.517691\n",
       "noc           -0.146985    0.0508854  -2.89    0.0039  -0.246718  -0.0472509\n",
       "foreign: yes   0.71438     0.121324    5.89    <1e-08   0.476589   0.95217\n",
       "────────────────────────────────────────────────────────────────────────────"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "506f4ef0",
   "metadata": {},
   "source": [
    "We can see that we obtained parametric confidence intervals for the parameters. However, our sample was not very big, so we want to verify them using bootstrapping.\n",
    "\n",
    "First we will do bootstrapping by hand, and next we will compare the results with what the [Bootstrap.jl](https://github.com/juliangehring/Bootstrap.jl) package produces.\n",
    "\n",
    "As usual we will try to learn some new features of DataFrames.jl along the way."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "299dc82d",
   "metadata": {},
   "source": [
    "We start with a function that takes a data frame and:\n",
    "1. creates one bootstrap sample of its contents\n",
    "2. fits the probit model to the bootstrapped data\n",
    "3. returns a `NamedTuple` with the computed coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "df1877a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "boot_sample (generic function with 1 method)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function boot_sample(df)\n",
    "    df_boot = df[rand(1:nrow(df), nrow(df)), :]\n",
    "    probit_boot = glm(@formula(lfp ~ lnnlinc + age + age^2 + educ + nyc + noc + foreign),\n",
    "                      df_boot, Binomial(), ProbitLink())\n",
    "    return (; (Symbol.(coefnames(probit_boot)) .=> coef(probit_boot))...)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "884c0b4e",
   "metadata": {},
   "source": [
    "We need to run the `boot_sample` function multiple times. Note that we store the results in the `coef_boot` data frame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "ce6e33cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "run_boot (generic function with 1 method)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function run_boot(df, reps)\n",
    "    coef_boot = DataFrame()\n",
    "    for _ in 1:reps\n",
    "        push!(coef_boot, boot_sample(df))\n",
    "    end\n",
    "    return coef_boot\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a199747b",
   "metadata": {},
   "source": [
    "We seed the random number generator as we want comparable results to what Bootstrap.jl produces (I have made sure to sample rows for bootstrapping in the same way in our manual code)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "98bce91a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  2.207886 seconds (4.49 M allocations: 817.114 MiB, 7.05% gc time, 67.31% compilation time)\n"
     ]
    },
    {
     "data": {
      "text/html": [
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text-align: right;\">1</td><td style = \"text-align: right;\">3.89753</td><td style = \"text-align: right;\">-0.683644</td><td style = \"text-align: right;\">2.19622</td><td style = \"text-align: right;\">-0.315711</td><td style = \"text-align: right;\">0.00184476</td><td style = \"text-align: right;\">-0.759661</td><td style = \"text-align: right;\">-0.116304</td><td style = \"text-align: right;\">0.59132</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">6.03733</td><td style = \"text-align: right;\">-0.808077</td><td style = \"text-align: right;\">1.85422</td><td style = \"text-align: right;\">-0.277391</td><td style = \"text-align: right;\">0.00815517</td><td style = \"text-align: right;\">-0.817424</td><td style = \"text-align: right;\">-0.196143</td><td style = \"text-align: right;\">0.556323</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">3.78851</td><td style = \"text-align: right;\">-0.702459</td><td style = \"text-align: right;\">2.09578</td><td style = \"text-align: right;\">-0.289319</td><td style = \"text-align: right;\">0.0274796</td><td style = \"text-align: right;\">-0.560228</td><td style = \"text-align: right;\">-0.131949</td><td style = \"text-align: right;\">0.728109</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">3.84855</td><td style = \"text-align: right;\">-0.673669</td><td style = \"text-align: right;\">2.20824</td><td style = \"text-align: right;\">-0.30794</td><td style = \"text-align: right;\">-0.00995106</td><td style = \"text-align: right;\">-0.817733</td><td style = \"text-align: right;\">-0.199632</td><td style = \"text-align: right;\">0.612467</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">3.86901</td><td style = \"text-align: right;\">-0.677679</td><td style = \"text-align: right;\">2.07178</td><td style = \"text-align: right;\">-0.285416</td><td style = \"text-align: right;\">0.00782889</td><td style = \"text-align: right;\">-0.610081</td><td style = \"text-align: right;\">-0.173919</td><td style = \"text-align: right;\">0.607915</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">4.24138</td><td style = \"text-align: right;\">-0.678265</td><td style = \"text-align: right;\">2.28935</td><td style = \"text-align: right;\">-0.338982</td><td style = \"text-align: right;\">0.0034059</td><td style = \"text-align: right;\">-0.926661</td><td style = \"text-align: right;\">-0.350053</td><td style = \"text-align: right;\">0.654847</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">3.76902</td><td style = \"text-align: right;\">-0.64247</td><td style = \"text-align: right;\">1.91971</td><td style = \"text-align: right;\">-0.278204</td><td style = \"text-align: right;\">0.0287484</td><td style = \"text-align: right;\">-0.727808</td><td style = \"text-align: right;\">-0.201696</td><td style = \"text-align: right;\">0.868374</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">5.15023</td><td style = \"text-align: right;\">-0.798031</td><td style = \"text-align: right;\">1.90498</td><td style = \"text-align: right;\">-0.26878</td><td style = \"text-align: right;\">0.0373576</td><td style = \"text-align: right;\">-0.800226</td><td style = \"text-align: right;\">-0.111041</td><td style = \"text-align: right;\">0.883274</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">3.12347</td><td style = \"text-align: right;\">-0.650024</td><td style = \"text-align: right;\">2.37745</td><td style = \"text-align: right;\">-0.335066</td><td style = \"text-align: right;\">0.00352704</td><td style = \"text-align: right;\">-0.768625</td><td style = \"text-align: right;\">-0.101193</td><td style = \"text-align: right;\">0.692148</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">2.4329</td><td style = \"text-align: right;\">-0.62523</td><td style = \"text-align: right;\">2.32566</td><td style = \"text-align: right;\">-0.321631</td><td style = \"text-align: right;\">0.0426932</td><td style = \"text-align: right;\">-0.541257</td><td style = \"text-align: right;\">-0.0643429</td><td style = \"text-align: right;\">0.787447</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">3.06523</td><td style = \"text-align: right;\">-0.625967</td><td style = \"text-align: right;\">2.12135</td><td style = \"text-align: right;\">-0.298013</td><td style = \"text-align: right;\">0.0336568</td><td style = \"text-align: right;\">-0.723162</td><td style = \"text-align: right;\">-0.061559</td><td style = \"text-align: right;\">0.672631</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: right;\">4.60502</td><td style = \"text-align: right;\">-0.85555</td><td style = \"text-align: right;\">2.72291</td><td style = \"text-align: right;\">-0.365987</td><td style = \"text-align: right;\">0.00235041</td><td style = \"text-align: right;\">-0.600223</td><td style = \"text-align: right;\">-0.198477</td><td style = \"text-align: right;\">0.478912</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: right;\">6.53008</td><td style = \"text-align: right;\">-0.797675</td><td style = \"text-align: right;\">1.40956</td><td style = \"text-align: right;\">-0.221066</td><td style = \"text-align: right;\">0.0365393</td><td style = \"text-align: right;\">-0.885277</td><td style = \"text-align: right;\">-0.220697</td><td style = \"text-align: right;\">0.512136</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">989</td><td style = \"text-align: right;\">0.893652</td><td style = \"text-align: right;\">-0.443215</td><td style = \"text-align: right;\">2.32991</td><td style = \"text-align: right;\">-0.326623</td><td style = \"text-align: right;\">0.0275311</td><td style = \"text-align: right;\">-0.733449</td><td style = \"text-align: right;\">-0.214092</td><td style = \"text-align: right;\">0.75764</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">990</td><td style = \"text-align: right;\">2.72127</td><td style = \"text-align: right;\">-0.595846</td><td style = \"text-align: right;\">2.47114</td><td style = \"text-align: right;\">-0.354721</td><td style = \"text-align: right;\">-0.00300546</td><td style = \"text-align: right;\">-0.847013</td><td style = \"text-align: right;\">-0.209531</td><td style = \"text-align: right;\">0.863269</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">991</td><td style = \"text-align: right;\">5.96651</td><td style = \"text-align: right;\">-0.801122</td><td style = \"text-align: right;\">1.67656</td><td style = \"text-align: right;\">-0.244864</td><td style = \"text-align: right;\">0.0157645</td><td style = \"text-align: right;\">-0.802483</td><td style = \"text-align: right;\">-0.126939</td><td style = \"text-align: right;\">0.795918</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">992</td><td style = \"text-align: right;\">1.9278</td><td style = \"text-align: right;\">-0.500438</td><td style = \"text-align: right;\">2.10367</td><td style = \"text-align: right;\">-0.300194</td><td style = \"text-align: right;\">0.0224147</td><td style = \"text-align: right;\">-0.750327</td><td style = \"text-align: right;\">-0.167591</td><td style = \"text-align: right;\">0.710357</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">993</td><td style = \"text-align: right;\">4.37019</td><td style = \"text-align: right;\">-0.750974</td><td style = \"text-align: right;\">2.06325</td><td style = \"text-align: right;\">-0.282058</td><td style = \"text-align: right;\">0.0264602</td><td style = \"text-align: right;\">-0.638799</td><td style = \"text-align: right;\">-0.136621</td><td style = \"text-align: right;\">0.815887</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">994</td><td style = \"text-align: right;\">2.1564</td><td style = \"text-align: right;\">-0.506433</td><td style = \"text-align: right;\">2.12799</td><td style = \"text-align: right;\">-0.299474</td><td style = \"text-align: right;\">-0.00236112</td><td style = \"text-align: right;\">-0.778277</td><td style = \"text-align: right;\">-0.192514</td><td style = \"text-align: right;\">0.619935</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">995</td><td style = \"text-align: right;\">4.50008</td><td style = \"text-align: right;\">-0.655927</td><td style = \"text-align: right;\">1.85878</td><td style = \"text-align: right;\">-0.270815</td><td style = \"text-align: right;\">-0.026267</td><td style = \"text-align: right;\">-0.595757</td><td style = \"text-align: right;\">-0.139348</td><td style = \"text-align: right;\">0.571691</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">996</td><td style = \"text-align: right;\">3.65681</td><td style = \"text-align: right;\">-0.631198</td><td style = \"text-align: right;\">1.91247</td><td style = \"text-align: right;\">-0.268847</td><td style = \"text-align: right;\">0.00620034</td><td style = \"text-align: right;\">-0.672621</td><td style = \"text-align: right;\">-0.0951452</td><td style = \"text-align: right;\">0.802052</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">997</td><td style = \"text-align: right;\">3.82428</td><td style = \"text-align: right;\">-0.583837</td><td style = \"text-align: right;\">1.75444</td><td style = \"text-align: right;\">-0.264595</td><td style = \"text-align: right;\">-0.00302802</td><td style = \"text-align: right;\">-0.737808</td><td style = \"text-align: right;\">-0.141895</td><td style = \"text-align: right;\">0.830021</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">998</td><td style = \"text-align: right;\">4.3505</td><td style = \"text-align: right;\">-0.707234</td><td style = \"text-align: right;\">2.17916</td><td style = \"text-align: right;\">-0.319459</td><td style = \"text-align: right;\">0.00677002</td><td style = \"text-align: right;\">-0.772209</td><td style = \"text-align: right;\">-0.19449</td><td style = \"text-align: right;\">0.688061</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">999</td><td style = \"text-align: right;\">2.37425</td><td style = \"text-align: right;\">-0.583229</td><td style = \"text-align: right;\">2.25732</td><td style = \"text-align: right;\">-0.315333</td><td style = \"text-align: right;\">0.0342427</td><td style = \"text-align: right;\">-0.846287</td><td style = \"text-align: right;\">-0.173309</td><td style = \"text-align: right;\">0.895702</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1000</td><td style = \"text-align: right;\">5.35087</td><td style = \"text-align: right;\">-0.843876</td><td style = \"text-align: right;\">2.16397</td><td style = \"text-align: right;\">-0.29809</td><td style = \"text-align: right;\">0.0140982</td><td style = \"text-align: right;\">-0.483684</td><td style = \"text-align: right;\">-0.120694</td><td style = \"text-align: right;\">0.700699</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& (Intercept) & lnnlinc & age & age \\^ 2 & educ & nyc & noc & \\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & \\\\\n",
       "\t\\hline\n",
       "\t1 & 3.89753 & -0.683644 & 2.19622 & -0.315711 & 0.00184476 & -0.759661 & -0.116304 & $\\dots$ \\\\\n",
       "\t2 & 6.03733 & -0.808077 & 1.85422 & -0.277391 & 0.00815517 & -0.817424 & -0.196143 & $\\dots$ \\\\\n",
       "\t3 & 3.78851 & -0.702459 & 2.09578 & -0.289319 & 0.0274796 & -0.560228 & -0.131949 & $\\dots$ \\\\\n",
       "\t4 & 3.84855 & -0.673669 & 2.20824 & -0.30794 & -0.00995106 & -0.817733 & -0.199632 & $\\dots$ \\\\\n",
       "\t5 & 3.86901 & -0.677679 & 2.07178 & -0.285416 & 0.00782889 & -0.610081 & -0.173919 & $\\dots$ \\\\\n",
       "\t6 & 4.24138 & -0.678265 & 2.28935 & -0.338982 & 0.0034059 & -0.926661 & -0.350053 & $\\dots$ \\\\\n",
       "\t7 & 3.76902 & -0.64247 & 1.91971 & -0.278204 & 0.0287484 & -0.727808 & -0.201696 & $\\dots$ \\\\\n",
       "\t8 & 5.15023 & -0.798031 & 1.90498 & -0.26878 & 0.0373576 & -0.800226 & -0.111041 & $\\dots$ \\\\\n",
       "\t9 & 3.12347 & -0.650024 & 2.37745 & -0.335066 & 0.00352704 & -0.768625 & -0.101193 & $\\dots$ \\\\\n",
       "\t10 & 2.4329 & -0.62523 & 2.32566 & -0.321631 & 0.0426932 & -0.541257 & -0.0643429 & $\\dots$ \\\\\n",
       "\t11 & 3.06523 & -0.625967 & 2.12135 & -0.298013 & 0.0336568 & -0.723162 & -0.061559 & $\\dots$ \\\\\n",
       "\t12 & 4.60502 & -0.85555 & 2.72291 & -0.365987 & 0.00235041 & -0.600223 & -0.198477 & $\\dots$ \\\\\n",
       "\t13 & 6.53008 & -0.797675 & 1.40956 & -0.221066 & 0.0365393 & -0.885277 & -0.220697 & $\\dots$ \\\\\n",
       "\t14 & 2.14633 & -0.540803 & 2.23767 & -0.315759 & 0.0151176 & -0.78152 & -0.174004 & $\\dots$ \\\\\n",
       "\t15 & 1.74928 & -0.481763 & 2.40743 & -0.347117 & -0.0157087 & -0.750511 & -0.157627 & $\\dots$ \\\\\n",
       "\t16 & 5.04343 & -0.772946 & 2.16923 & -0.309786 & 0.00697176 & -0.835845 & -0.220684 & $\\dots$ \\\\\n",
       "\t17 & 3.21179 & -0.537728 & 1.78635 & -0.262943 & -0.0090764 & -0.721048 & -0.188545 & $\\dots$ \\\\\n",
       "\t18 & 6.20101 & -0.996644 & 2.45431 & -0.342986 & 0.0651541 & -0.642571 & -0.227372 & $\\dots$ \\\\\n",
       "\t19 & 3.36975 & -0.623907 & 2.01254 & -0.294752 & 0.0376487 & -0.81264 & -0.149462 & $\\dots$ \\\\\n",
       "\t20 & 4.20439 & -0.739063 & 2.36511 & -0.333994 & 0.0170522 & -0.758426 & -0.224078 & $\\dots$ \\\\\n",
       "\t21 & 2.58454 & -0.541718 & 1.89479 & -0.270313 & 0.0234723 & -0.646551 & -0.127249 & $\\dots$ \\\\\n",
       "\t22 & 2.90434 & -0.536464 & 1.82871 & -0.272165 & 0.00331773 & -0.634511 & -0.00722016 & $\\dots$ \\\\\n",
       "\t23 & 5.49798 & -0.691475 & 1.35163 & -0.201982 & -0.00427995 & -0.689496 & -0.0837819 & $\\dots$ \\\\\n",
       "\t24 & 7.40983 & -0.885409 & 1.12672 & -0.175524 & 0.0467756 & -0.789496 & -0.0525805 & $\\dots$ \\\\\n",
       "\t25 & 4.68955 & -0.795269 & 2.05814 & -0.276166 & 0.0317646 & -0.670591 & -0.0921888 & $\\dots$ \\\\\n",
       "\t26 & 5.37405 & -0.822864 & 1.95716 & -0.268404 & 0.0325762 & -0.683122 & -0.123383 & $\\dots$ \\\\\n",
       "\t27 & 4.0729 & -0.803499 & 2.66621 & -0.368712 & 0.0338197 & -0.774696 & -0.237184 & $\\dots$ \\\\\n",
       "\t28 & 3.30481 & -0.598957 & 1.99496 & -0.280004 & 0.00112482 & -0.87051 & -0.190765 & $\\dots$ \\\\\n",
       "\t29 & 4.66477 & -0.684524 & 1.65512 & -0.242086 & 0.0164044 & -0.730929 & -0.0982033 & $\\dots$ \\\\\n",
       "\t30 & 0.768289 & -0.397229 & 2.30299 & -0.320106 & -0.0163254 & -0.694104 & -0.171745 & $\\dots$ \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ &  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m1000×8 DataFrame\u001b[0m\n",
       "\u001b[1m  Row \u001b[0m│\u001b[1m (Intercept) \u001b[0m\u001b[1m lnnlinc   \u001b[0m\u001b[1m age     \u001b[0m\u001b[1m age ^ 2   \u001b[0m\u001b[1m educ        \u001b[0m\u001b[1m nyc       \u001b[0m\u001b[1m no\u001b[0m ⋯\n",
       "      │\u001b[90m Float64     \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64     \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Fl\u001b[0m ⋯\n",
       "──────┼─────────────────────────────────────────────────────────────────────────\n",
       "    1 │    3.89753   -0.683644  2.19622  -0.315711   0.00184476  -0.759661  -0 ⋯\n",
       "    2 │    6.03733   -0.808077  1.85422  -0.277391   0.00815517  -0.817424  -0\n",
       "    3 │    3.78851   -0.702459  2.09578  -0.289319   0.0274796   -0.560228  -0\n",
       "    4 │    3.84855   -0.673669  2.20824  -0.30794   -0.00995106  -0.817733  -0\n",
       "    5 │    3.86901   -0.677679  2.07178  -0.285416   0.00782889  -0.610081  -0 ⋯\n",
       "    6 │    4.24138   -0.678265  2.28935  -0.338982   0.0034059   -0.926661  -0\n",
       "    7 │    3.76902   -0.64247   1.91971  -0.278204   0.0287484   -0.727808  -0\n",
       "    8 │    5.15023   -0.798031  1.90498  -0.26878    0.0373576   -0.800226  -0\n",
       "    9 │    3.12347   -0.650024  2.37745  -0.335066   0.00352704  -0.768625  -0 ⋯\n",
       "   10 │    2.4329    -0.62523   2.32566  -0.321631   0.0426932   -0.541257  -0\n",
       "   11 │    3.06523   -0.625967  2.12135  -0.298013   0.0336568   -0.723162  -0\n",
       "  ⋮   │      ⋮           ⋮         ⋮         ⋮           ⋮           ⋮         ⋱\n",
       "  991 │    5.96651   -0.801122  1.67656  -0.244864   0.0157645   -0.802483  -0\n",
       "  992 │    1.9278    -0.500438  2.10367  -0.300194   0.0224147   -0.750327  -0 ⋯\n",
       "  993 │    4.37019   -0.750974  2.06325  -0.282058   0.0264602   -0.638799  -0\n",
       "  994 │    2.1564    -0.506433  2.12799  -0.299474  -0.00236112  -0.778277  -0\n",
       "  995 │    4.50008   -0.655927  1.85878  -0.270815  -0.026267    -0.595757  -0\n",
       "  996 │    3.65681   -0.631198  1.91247  -0.268847   0.00620034  -0.672621  -0 ⋯\n",
       "  997 │    3.82428   -0.583837  1.75444  -0.264595  -0.00302802  -0.737808  -0\n",
       "  998 │    4.3505    -0.707234  2.17916  -0.319459   0.00677002  -0.772209  -0\n",
       "  999 │    2.37425   -0.583229  2.25732  -0.315333   0.0342427   -0.846287  -0\n",
       " 1000 │    5.35087   -0.843876  2.16397  -0.29809    0.0140982   -0.483684  -0 ⋯\n",
       "\u001b[36m                                                  2 columns and 979 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Random.seed!(1234)\n",
    "@time coef_boot = run_boot(df, 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3548bfa2",
   "metadata": {},
   "source": [
    "Using this data calculate the 95% confidence interval using the percentile bootstrap:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "513c4b2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>2×8 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">(Intercept)</th><th style = \"text-align: left;\">lnnlinc</th><th style = \"text-align: left;\">age</th><th style = \"text-align: left;\">age ^ 2</th><th style = \"text-align: left;\">educ</th><th style = \"text-align: left;\">nyc</th><th style = \"text-align: left;\">noc</th><th style = \"text-align: left;\">foreign: yes</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1.24129</td><td style = \"text-align: right;\">-0.947283</td><td style = \"text-align: right;\">1.29334</td><td style = \"text-align: right;\">-0.405375</td><td style = \"text-align: right;\">-0.015854</td><td style = \"text-align: right;\">-0.926779</td><td style = \"text-align: right;\">-0.259494</td><td style = \"text-align: right;\">0.478879</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">6.79873</td><td style = \"text-align: right;\">-0.443171</td><td style = \"text-align: right;\">2.98478</td><td style = \"text-align: right;\">-0.19818</td><td style = \"text-align: right;\">0.0565269</td><td style = \"text-align: right;\">-0.52503</td><td style = \"text-align: right;\">-0.0525333</td><td style = \"text-align: right;\">0.961622</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& (Intercept) & lnnlinc & age & age \\^ 2 & educ & nyc & noc & foreign: yes\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1.24129 & -0.947283 & 1.29334 & -0.405375 & -0.015854 & -0.926779 & -0.259494 & 0.478879 \\\\\n",
       "\t2 & 6.79873 & -0.443171 & 2.98478 & -0.19818 & 0.0565269 & -0.52503 & -0.0525333 & 0.961622 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×8 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m (Intercept) \u001b[0m\u001b[1m lnnlinc   \u001b[0m\u001b[1m age     \u001b[0m\u001b[1m age ^ 2   \u001b[0m\u001b[1m educ       \u001b[0m\u001b[1m nyc       \u001b[0m\u001b[1m noc \u001b[0m ⋯\n",
       "     │\u001b[90m Float64     \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64    \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Floa\u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │     1.24129  -0.947283  1.29334  -0.405375  -0.015854   -0.926779  -0.2 ⋯\n",
       "   2 │     6.79873  -0.443171  2.98478  -0.19818    0.0565269  -0.52503   -0.0\n",
       "\u001b[36m                                                               2 columns omitted\u001b[0m"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conf_boot = mapcols(x -> quantile(x, [0.025, 0.975]), coef_boot)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12e0e950",
   "metadata": {},
   "source": [
    "Here are the parametric confidence intervals computed by GLM.jl. We will want to compare them against bootstrapping results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "71669a67",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8×2 Matrix{Float64}:\n",
       "  0.992006   6.50591\n",
       " -0.92549   -0.408374\n",
       "  1.28073    2.86989\n",
       " -0.392235  -0.196456\n",
       " -0.015937   0.0543295\n",
       " -0.911238  -0.517691\n",
       " -0.246718  -0.0472509\n",
       "  0.476589   0.95217"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "confint(probit)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef5d962d",
   "metadata": {},
   "source": [
    "First we transform the above matrix and create a data frame using the same column names as in bootstrapping:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "63939c35",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>2×8 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">(Intercept)</th><th style = \"text-align: left;\">lnnlinc</th><th style = \"text-align: left;\">age</th><th style = \"text-align: left;\">age ^ 2</th><th style = \"text-align: left;\">educ</th><th style = \"text-align: left;\">nyc</th><th style = \"text-align: left;\">noc</th><th style = \"text-align: left;\">foreign: yes</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0.992006</td><td style = \"text-align: right;\">-0.92549</td><td style = \"text-align: right;\">1.28073</td><td style = \"text-align: right;\">-0.392235</td><td style = \"text-align: right;\">-0.015937</td><td style = \"text-align: right;\">-0.911238</td><td style = \"text-align: right;\">-0.246718</td><td style = \"text-align: right;\">0.476589</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">6.50591</td><td style = \"text-align: right;\">-0.408374</td><td style = \"text-align: right;\">2.86989</td><td style = \"text-align: right;\">-0.196456</td><td style = \"text-align: right;\">0.0543295</td><td style = \"text-align: right;\">-0.517691</td><td style = \"text-align: right;\">-0.0472509</td><td style = \"text-align: right;\">0.95217</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& (Intercept) & lnnlinc & age & age \\^ 2 & educ & nyc & noc & foreign: yes\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 0.992006 & -0.92549 & 1.28073 & -0.392235 & -0.015937 & -0.911238 & -0.246718 & 0.476589 \\\\\n",
       "\t2 & 6.50591 & -0.408374 & 2.86989 & -0.196456 & 0.0543295 & -0.517691 & -0.0472509 & 0.95217 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×8 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m (Intercept) \u001b[0m\u001b[1m lnnlinc   \u001b[0m\u001b[1m age     \u001b[0m\u001b[1m age ^ 2   \u001b[0m\u001b[1m educ       \u001b[0m\u001b[1m nyc       \u001b[0m\u001b[1m noc \u001b[0m ⋯\n",
       "     │\u001b[90m Float64     \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64    \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Floa\u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │    0.992006  -0.92549   1.28073  -0.392235  -0.015937   -0.911238  -0.2 ⋯\n",
       "   2 │    6.50591   -0.408374  2.86989  -0.196456   0.0543295  -0.517691  -0.0\n",
       "\u001b[36m                                                               2 columns omitted\u001b[0m"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conf_param = DataFrame(permutedims(confint(probit)), names(conf_boot))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c54f2dd",
   "metadata": {},
   "source": [
    "and we `append!` it to our `conf_boot` data frame:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "f5e4c5f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>4×8 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">(Intercept)</th><th style = \"text-align: left;\">lnnlinc</th><th style = \"text-align: left;\">age</th><th style = \"text-align: left;\">age ^ 2</th><th style = \"text-align: left;\">educ</th><th style = \"text-align: left;\">nyc</th><th style = \"text-align: left;\">noc</th><th style = \"text-align: left;\">foreign: yes</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1.24129</td><td style = \"text-align: right;\">-0.947283</td><td style = \"text-align: right;\">1.29334</td><td style = \"text-align: right;\">-0.405375</td><td style = \"text-align: right;\">-0.015854</td><td style = \"text-align: right;\">-0.926779</td><td style = \"text-align: right;\">-0.259494</td><td style = \"text-align: right;\">0.478879</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">6.79873</td><td style = \"text-align: right;\">-0.443171</td><td style = \"text-align: right;\">2.98478</td><td style = \"text-align: right;\">-0.19818</td><td style = \"text-align: right;\">0.0565269</td><td style = \"text-align: right;\">-0.52503</td><td style = \"text-align: right;\">-0.0525333</td><td style = \"text-align: right;\">0.961622</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">0.992006</td><td style = \"text-align: right;\">-0.92549</td><td style = \"text-align: right;\">1.28073</td><td style = \"text-align: right;\">-0.392235</td><td style = \"text-align: right;\">-0.015937</td><td style = \"text-align: right;\">-0.911238</td><td style = \"text-align: right;\">-0.246718</td><td style = \"text-align: right;\">0.476589</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">6.50591</td><td style = \"text-align: right;\">-0.408374</td><td style = \"text-align: right;\">2.86989</td><td style = \"text-align: right;\">-0.196456</td><td style = \"text-align: right;\">0.0543295</td><td style = \"text-align: right;\">-0.517691</td><td style = \"text-align: right;\">-0.0472509</td><td style = \"text-align: right;\">0.95217</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& (Intercept) & lnnlinc & age & age \\^ 2 & educ & nyc & noc & foreign: yes\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1.24129 & -0.947283 & 1.29334 & -0.405375 & -0.015854 & -0.926779 & -0.259494 & 0.478879 \\\\\n",
       "\t2 & 6.79873 & -0.443171 & 2.98478 & -0.19818 & 0.0565269 & -0.52503 & -0.0525333 & 0.961622 \\\\\n",
       "\t3 & 0.992006 & -0.92549 & 1.28073 & -0.392235 & -0.015937 & -0.911238 & -0.246718 & 0.476589 \\\\\n",
       "\t4 & 6.50591 & -0.408374 & 2.86989 & -0.196456 & 0.0543295 & -0.517691 & -0.0472509 & 0.95217 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m4×8 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m (Intercept) \u001b[0m\u001b[1m lnnlinc   \u001b[0m\u001b[1m age     \u001b[0m\u001b[1m age ^ 2   \u001b[0m\u001b[1m educ       \u001b[0m\u001b[1m nyc       \u001b[0m\u001b[1m noc \u001b[0m ⋯\n",
       "     │\u001b[90m Float64     \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64    \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Floa\u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │    1.24129   -0.947283  1.29334  -0.405375  -0.015854   -0.926779  -0.2 ⋯\n",
       "   2 │    6.79873   -0.443171  2.98478  -0.19818    0.0565269  -0.52503   -0.0\n",
       "   3 │    0.992006  -0.92549   1.28073  -0.392235  -0.015937   -0.911238  -0.2\n",
       "   4 │    6.50591   -0.408374  2.86989  -0.196456   0.0543295  -0.517691  -0.0\n",
       "\u001b[36m                                                               2 columns omitted\u001b[0m"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "append!(conf_boot, conf_param)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5134d48",
   "metadata": {},
   "source": [
    "It is good to keep track of what each row of our data holds. Therefore we insert a new column to our data farme. As we want to put it in front we use the `insertcols!` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "dd8ab64d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>4×9 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">statistic</th><th style = \"text-align: left;\">(Intercept)</th><th style = \"text-align: left;\">lnnlinc</th><th style = \"text-align: left;\">age</th><th style = \"text-align: left;\">age ^ 2</th><th style = \"text-align: left;\">educ</th><th style = \"text-align: left;\">nyc</th><th style = \"text-align: left;\">noc</th><th style = \"text-align: left;\">foreign: yes</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"String\" style = \"text-align: left;\">String</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">boot lo</td><td style = \"text-align: right;\">1.24129</td><td style = \"text-align: right;\">-0.947283</td><td style = \"text-align: right;\">1.29334</td><td style = \"text-align: right;\">-0.405375</td><td style = \"text-align: right;\">-0.015854</td><td style = \"text-align: right;\">-0.926779</td><td style = \"text-align: right;\">-0.259494</td><td style = \"text-align: right;\">0.478879</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">boot hi</td><td style = \"text-align: right;\">6.79873</td><td style = \"text-align: right;\">-0.443171</td><td style = \"text-align: right;\">2.98478</td><td style = \"text-align: right;\">-0.19818</td><td style = \"text-align: right;\">0.0565269</td><td style = \"text-align: right;\">-0.52503</td><td style = \"text-align: right;\">-0.0525333</td><td style = \"text-align: right;\">0.961622</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">parametric lo</td><td style = \"text-align: right;\">0.992006</td><td style = \"text-align: right;\">-0.92549</td><td style = \"text-align: right;\">1.28073</td><td style = \"text-align: right;\">-0.392235</td><td style = \"text-align: right;\">-0.015937</td><td style = \"text-align: right;\">-0.911238</td><td style = \"text-align: right;\">-0.246718</td><td style = \"text-align: right;\">0.476589</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">parametric hi</td><td style = \"text-align: right;\">6.50591</td><td style = \"text-align: right;\">-0.408374</td><td style = \"text-align: right;\">2.86989</td><td style = \"text-align: right;\">-0.196456</td><td style = \"text-align: right;\">0.0543295</td><td style = \"text-align: right;\">-0.517691</td><td style = \"text-align: right;\">-0.0472509</td><td style = \"text-align: right;\">0.95217</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& statistic & (Intercept) & lnnlinc & age & age \\^ 2 & educ & nyc & \\\\\n",
       "\t\\hline\n",
       "\t& String & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & \\\\\n",
       "\t\\hline\n",
       "\t1 & boot lo & 1.24129 & -0.947283 & 1.29334 & -0.405375 & -0.015854 & -0.926779 & $\\dots$ \\\\\n",
       "\t2 & boot hi & 6.79873 & -0.443171 & 2.98478 & -0.19818 & 0.0565269 & -0.52503 & $\\dots$ \\\\\n",
       "\t3 & parametric lo & 0.992006 & -0.92549 & 1.28073 & -0.392235 & -0.015937 & -0.911238 & $\\dots$ \\\\\n",
       "\t4 & parametric hi & 6.50591 & -0.408374 & 2.86989 & -0.196456 & 0.0543295 & -0.517691 & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m4×9 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m statistic     \u001b[0m\u001b[1m (Intercept) \u001b[0m\u001b[1m lnnlinc   \u001b[0m\u001b[1m age     \u001b[0m\u001b[1m age ^ 2   \u001b[0m\u001b[1m educ       \u001b[0m\u001b[1m \u001b[0m ⋯\n",
       "     │\u001b[90m String        \u001b[0m\u001b[90m Float64     \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64    \u001b[0m\u001b[90m \u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │ boot lo           1.24129   -0.947283  1.29334  -0.405375  -0.015854    ⋯\n",
       "   2 │ boot hi           6.79873   -0.443171  2.98478  -0.19818    0.0565269\n",
       "   3 │ parametric lo     0.992006  -0.92549   1.28073  -0.392235  -0.015937\n",
       "   4 │ parametric hi     6.50591   -0.408374  2.86989  -0.196456   0.0543295\n",
       "\u001b[36m                                                               3 columns omitted\u001b[0m"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "insertcols!(conf_boot, 1, :statistic => [\"boot lo\", \"boot hi\", \"parametric lo\", \"parametric hi\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6aef4daa",
   "metadata": {},
   "source": [
    "Notice that data frame also can be transposed. However, we need to provide a column that we will use as column names in the target data frame (data frame objects must have column names):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "f190f135",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>8×5 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">statistic</th><th style = \"text-align: left;\">boot lo</th><th style = \"text-align: left;\">boot hi</th><th style = \"text-align: left;\">parametric lo</th><th style = \"text-align: left;\">parametric hi</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"String\" style = \"text-align: left;\">String</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">(Intercept)</td><td style = \"text-align: right;\">1.24129</td><td style = \"text-align: right;\">6.79873</td><td style = \"text-align: right;\">0.992006</td><td style = \"text-align: right;\">6.50591</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">lnnlinc</td><td style = \"text-align: right;\">-0.947283</td><td style = \"text-align: right;\">-0.443171</td><td style = \"text-align: right;\">-0.92549</td><td style = \"text-align: right;\">-0.408374</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">age</td><td style = \"text-align: right;\">1.29334</td><td style = \"text-align: right;\">2.98478</td><td style = \"text-align: right;\">1.28073</td><td style = \"text-align: right;\">2.86989</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">age ^ 2</td><td style = \"text-align: right;\">-0.405375</td><td style = \"text-align: right;\">-0.19818</td><td style = \"text-align: right;\">-0.392235</td><td style = \"text-align: right;\">-0.196456</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">educ</td><td style = \"text-align: right;\">-0.015854</td><td style = \"text-align: right;\">0.0565269</td><td style = \"text-align: right;\">-0.015937</td><td style = \"text-align: right;\">0.0543295</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: left;\">nyc</td><td style = \"text-align: right;\">-0.926779</td><td style = \"text-align: right;\">-0.52503</td><td style = \"text-align: right;\">-0.911238</td><td style = \"text-align: right;\">-0.517691</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: left;\">noc</td><td style = \"text-align: right;\">-0.259494</td><td style = \"text-align: right;\">-0.0525333</td><td style = \"text-align: right;\">-0.246718</td><td style = \"text-align: right;\">-0.0472509</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: left;\">foreign: yes</td><td style = \"text-align: right;\">0.478879</td><td style = \"text-align: right;\">0.961622</td><td style = \"text-align: right;\">0.476589</td><td style = \"text-align: right;\">0.95217</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccc}\n",
       "\t& statistic & boot lo & boot hi & parametric lo & parametric hi\\\\\n",
       "\t\\hline\n",
       "\t& String & Float64 & Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & (Intercept) & 1.24129 & 6.79873 & 0.992006 & 6.50591 \\\\\n",
       "\t2 & lnnlinc & -0.947283 & -0.443171 & -0.92549 & -0.408374 \\\\\n",
       "\t3 & age & 1.29334 & 2.98478 & 1.28073 & 2.86989 \\\\\n",
       "\t4 & age \\^ 2 & -0.405375 & -0.19818 & -0.392235 & -0.196456 \\\\\n",
       "\t5 & educ & -0.015854 & 0.0565269 & -0.015937 & 0.0543295 \\\\\n",
       "\t6 & nyc & -0.926779 & -0.52503 & -0.911238 & -0.517691 \\\\\n",
       "\t7 & noc & -0.259494 & -0.0525333 & -0.246718 & -0.0472509 \\\\\n",
       "\t8 & foreign: yes & 0.478879 & 0.961622 & 0.476589 & 0.95217 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m8×5 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m statistic    \u001b[0m\u001b[1m boot lo   \u001b[0m\u001b[1m boot hi    \u001b[0m\u001b[1m parametric lo \u001b[0m\u001b[1m parametric hi \u001b[0m\n",
       "     │\u001b[90m String       \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64    \u001b[0m\u001b[90m Float64       \u001b[0m\u001b[90m Float64       \u001b[0m\n",
       "─────┼───────────────────────────────────────────────────────────────────\n",
       "   1 │ (Intercept)    1.24129    6.79873         0.992006      6.50591\n",
       "   2 │ lnnlinc       -0.947283  -0.443171       -0.92549      -0.408374\n",
       "   3 │ age            1.29334    2.98478         1.28073       2.86989\n",
       "   4 │ age ^ 2       -0.405375  -0.19818        -0.392235     -0.196456\n",
       "   5 │ educ          -0.015854   0.0565269      -0.015937      0.0543295\n",
       "   6 │ nyc           -0.926779  -0.52503        -0.911238     -0.517691\n",
       "   7 │ noc           -0.259494  -0.0525333      -0.246718     -0.0472509\n",
       "   8 │ foreign: yes   0.478879   0.961622        0.476589      0.95217"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conf_boot_t = permutedims(conf_boot, :statistic)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e83705f0",
   "metadata": {},
   "source": [
    "Let us also add the estimates of the coefficients to the table:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "574a4c53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>8×6 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">statistic</th><th style = \"text-align: left;\">estimate</th><th style = \"text-align: left;\">boot lo</th><th style = \"text-align: left;\">boot hi</th><th style = \"text-align: left;\">parametric lo</th><th style = \"text-align: left;\">parametric hi</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"String\" style = \"text-align: left;\">String</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">(Intercept)</td><td style = \"text-align: right;\">3.74896</td><td style = \"text-align: right;\">1.24129</td><td style = \"text-align: right;\">6.79873</td><td style = \"text-align: right;\">0.992006</td><td style = \"text-align: right;\">6.50591</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">lnnlinc</td><td style = \"text-align: right;\">-0.666932</td><td style = \"text-align: right;\">-0.947283</td><td style = \"text-align: right;\">-0.443171</td><td style = \"text-align: right;\">-0.92549</td><td style = \"text-align: right;\">-0.408374</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">age</td><td style = \"text-align: right;\">2.07531</td><td style = \"text-align: right;\">1.29334</td><td style = \"text-align: right;\">2.98478</td><td style = \"text-align: right;\">1.28073</td><td style = \"text-align: right;\">2.86989</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">age ^ 2</td><td style = \"text-align: right;\">-0.294345</td><td style = \"text-align: right;\">-0.405375</td><td style = \"text-align: right;\">-0.19818</td><td style = \"text-align: right;\">-0.392235</td><td style = \"text-align: right;\">-0.196456</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">educ</td><td style = \"text-align: right;\">0.0191963</td><td style = \"text-align: right;\">-0.015854</td><td style = \"text-align: right;\">0.0565269</td><td style = \"text-align: right;\">-0.015937</td><td style = \"text-align: right;\">0.0543295</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: left;\">nyc</td><td style = \"text-align: right;\">-0.714465</td><td style = \"text-align: right;\">-0.926779</td><td style = \"text-align: right;\">-0.52503</td><td style = \"text-align: right;\">-0.911238</td><td style = \"text-align: right;\">-0.517691</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: left;\">noc</td><td style = \"text-align: right;\">-0.146985</td><td style = \"text-align: right;\">-0.259494</td><td style = \"text-align: right;\">-0.0525333</td><td style = \"text-align: right;\">-0.246718</td><td style = \"text-align: right;\">-0.0472509</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: left;\">foreign: yes</td><td style = \"text-align: right;\">0.71438</td><td style = \"text-align: right;\">0.478879</td><td style = \"text-align: right;\">0.961622</td><td style = \"text-align: right;\">0.476589</td><td style = \"text-align: right;\">0.95217</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccc}\n",
       "\t& statistic & estimate & boot lo & boot hi & parametric lo & parametric hi\\\\\n",
       "\t\\hline\n",
       "\t& String & Float64 & Float64 & Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & (Intercept) & 3.74896 & 1.24129 & 6.79873 & 0.992006 & 6.50591 \\\\\n",
       "\t2 & lnnlinc & -0.666932 & -0.947283 & -0.443171 & -0.92549 & -0.408374 \\\\\n",
       "\t3 & age & 2.07531 & 1.29334 & 2.98478 & 1.28073 & 2.86989 \\\\\n",
       "\t4 & age \\^ 2 & -0.294345 & -0.405375 & -0.19818 & -0.392235 & -0.196456 \\\\\n",
       "\t5 & educ & 0.0191963 & -0.015854 & 0.0565269 & -0.015937 & 0.0543295 \\\\\n",
       "\t6 & nyc & -0.714465 & -0.926779 & -0.52503 & -0.911238 & -0.517691 \\\\\n",
       "\t7 & noc & -0.146985 & -0.259494 & -0.0525333 & -0.246718 & -0.0472509 \\\\\n",
       "\t8 & foreign: yes & 0.71438 & 0.478879 & 0.961622 & 0.476589 & 0.95217 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m8×6 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m statistic    \u001b[0m\u001b[1m estimate   \u001b[0m\u001b[1m boot lo   \u001b[0m\u001b[1m boot hi    \u001b[0m\u001b[1m parametric lo \u001b[0m\u001b[1m paramet\u001b[0m ⋯\n",
       "     │\u001b[90m String       \u001b[0m\u001b[90m Float64    \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64    \u001b[0m\u001b[90m Float64       \u001b[0m\u001b[90m Float64\u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │ (Intercept)    3.74896     1.24129    6.79873         0.992006      6.5 ⋯\n",
       "   2 │ lnnlinc       -0.666932   -0.947283  -0.443171       -0.92549      -0.4\n",
       "   3 │ age            2.07531     1.29334    2.98478         1.28073       2.8\n",
       "   4 │ age ^ 2       -0.294345   -0.405375  -0.19818        -0.392235     -0.1\n",
       "   5 │ educ           0.0191963  -0.015854   0.0565269      -0.015937      0.0 ⋯\n",
       "   6 │ nyc           -0.714465   -0.926779  -0.52503        -0.911238     -0.5\n",
       "   7 │ noc           -0.146985   -0.259494  -0.0525333      -0.246718     -0.0\n",
       "   8 │ foreign: yes   0.71438     0.478879   0.961622        0.476589      0.9\n",
       "\u001b[36m                                                                1 column omitted\u001b[0m"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "insertcols!(conf_boot_t, 2, :estimate => coef(probit))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cfc47a9",
   "metadata": {},
   "source": [
    "Now it is time for some more advanced stuff. We want to transform columns holding the ends of the confidence intervals (which are columns from 3 to 6) into absolute deviations from the estimate. Such a transformation will be useful for plotting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "55ae9719",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>8×6 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">statistic</th><th style = \"text-align: left;\">estimate</th><th style = \"text-align: left;\">boot lo</th><th style = \"text-align: left;\">boot hi</th><th style = \"text-align: left;\">parametric lo</th><th style = \"text-align: left;\">parametric hi</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"String\" style = \"text-align: left;\">String</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">(Intercept)</td><td style = \"text-align: right;\">3.74896</td><td style = \"text-align: right;\">2.50766</td><td style = \"text-align: right;\">3.04977</td><td style = \"text-align: right;\">2.75695</td><td style = \"text-align: right;\">2.75695</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">lnnlinc</td><td style = \"text-align: right;\">-0.666932</td><td style = \"text-align: right;\">0.280351</td><td style = \"text-align: right;\">0.223761</td><td style = \"text-align: right;\">0.258558</td><td style = \"text-align: right;\">0.258558</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">age</td><td style = \"text-align: right;\">2.07531</td><td style = \"text-align: right;\">0.78197</td><td style = \"text-align: right;\">0.909466</td><td style = \"text-align: right;\">0.794584</td><td style = \"text-align: right;\">0.794584</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">age ^ 2</td><td style = \"text-align: right;\">-0.294345</td><td style = \"text-align: right;\">0.11103</td><td style = \"text-align: right;\">0.0961656</td><td style = \"text-align: right;\">0.0978895</td><td style = \"text-align: right;\">0.0978895</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">educ</td><td style = \"text-align: right;\">0.0191963</td><td style = \"text-align: right;\">0.0350502</td><td style = \"text-align: right;\">0.0373307</td><td style = \"text-align: right;\">0.0351333</td><td style = \"text-align: right;\">0.0351333</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: left;\">nyc</td><td style = \"text-align: right;\">-0.714465</td><td style = \"text-align: right;\">0.212315</td><td style = \"text-align: right;\">0.189435</td><td style = \"text-align: right;\">0.196774</td><td style = \"text-align: right;\">0.196774</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: left;\">noc</td><td style = \"text-align: right;\">-0.146985</td><td style = \"text-align: right;\">0.112509</td><td style = \"text-align: right;\">0.0944512</td><td style = \"text-align: right;\">0.0997336</td><td style = \"text-align: right;\">0.0997336</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: left;\">foreign: yes</td><td style = \"text-align: right;\">0.71438</td><td style = \"text-align: right;\">0.235501</td><td style = \"text-align: right;\">0.247242</td><td style = \"text-align: right;\">0.23779</td><td style = \"text-align: right;\">0.23779</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccc}\n",
       "\t& statistic & estimate & boot lo & boot hi & parametric lo & parametric hi\\\\\n",
       "\t\\hline\n",
       "\t& String & Float64 & Float64 & Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & (Intercept) & 3.74896 & 2.50766 & 3.04977 & 2.75695 & 2.75695 \\\\\n",
       "\t2 & lnnlinc & -0.666932 & 0.280351 & 0.223761 & 0.258558 & 0.258558 \\\\\n",
       "\t3 & age & 2.07531 & 0.78197 & 0.909466 & 0.794584 & 0.794584 \\\\\n",
       "\t4 & age \\^ 2 & -0.294345 & 0.11103 & 0.0961656 & 0.0978895 & 0.0978895 \\\\\n",
       "\t5 & educ & 0.0191963 & 0.0350502 & 0.0373307 & 0.0351333 & 0.0351333 \\\\\n",
       "\t6 & nyc & -0.714465 & 0.212315 & 0.189435 & 0.196774 & 0.196774 \\\\\n",
       "\t7 & noc & -0.146985 & 0.112509 & 0.0944512 & 0.0997336 & 0.0997336 \\\\\n",
       "\t8 & foreign: yes & 0.71438 & 0.235501 & 0.247242 & 0.23779 & 0.23779 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m8×6 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m statistic    \u001b[0m\u001b[1m estimate   \u001b[0m\u001b[1m boot lo   \u001b[0m\u001b[1m boot hi   \u001b[0m\u001b[1m parametric lo \u001b[0m\u001b[1m parametr\u001b[0m ⋯\n",
       "     │\u001b[90m String       \u001b[0m\u001b[90m Float64    \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64       \u001b[0m\u001b[90m Float64 \u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │ (Intercept)    3.74896    2.50766    3.04977        2.75695        2.75 ⋯\n",
       "   2 │ lnnlinc       -0.666932   0.280351   0.223761       0.258558       0.25\n",
       "   3 │ age            2.07531    0.78197    0.909466       0.794584       0.79\n",
       "   4 │ age ^ 2       -0.294345   0.11103    0.0961656      0.0978895      0.09\n",
       "   5 │ educ           0.0191963  0.0350502  0.0373307      0.0351333      0.03 ⋯\n",
       "   6 │ nyc           -0.714465   0.212315   0.189435       0.196774       0.19\n",
       "   7 │ noc           -0.146985   0.112509   0.0944512      0.0997336      0.09\n",
       "   8 │ foreign: yes   0.71438    0.235501   0.247242       0.23779        0.23\n",
       "\u001b[36m                                                                1 column omitted\u001b[0m"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "select!(conf_boot_t, :statistic, :estimate, 3:6 .=> x -> abs.(x .- conf_boot_t.estimate), renamecols=false)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6c40ddd",
   "metadata": {},
   "source": [
    "I have promised you a plot, so let us not hesitate producing it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "1fa4b3c3",
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scatter(0.05 .+ (1:8), conf_boot_t.estimate,\n",
    "        yerror=(conf_boot_t.\"boot lo\", conf_boot_t.\"boot hi\"),\n",
    "        label=\"bootstrap\",\n",
    "        xticks=(1:8, conf_boot_t.statistic), xrotation=45)\n",
    "scatter!(-0.05 .+ (1:8), conf_boot_t.estimate,\n",
    "         yerror=(conf_boot_t.\"parametric lo\", conf_boot_t.\"parametric hi\"),\n",
    "         label=\"parametric\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "886241ab",
   "metadata": {},
   "source": [
    "As you can see both types of intervals are quite close in this case."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9174206",
   "metadata": {},
   "source": [
    "Before we finish let us get a sample of how the same task could have been done using the Bootstrap.jl package."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7a48f62",
   "metadata": {},
   "source": [
    "This time the function compiting the statistics does not have to perform sampling as this is handled by the Bootstrap.jl package:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "4e742fa8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "boot_probit (generic function with 1 method)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function boot_probit(df_boot)\n",
    "    probit_boot = glm(@formula(lfp ~ lnnlinc + age + age^2 + educ + nyc + noc + foreign),\n",
    "                      df_boot, Binomial(), ProbitLink())\n",
    "    return (; (Symbol.(coefnames(probit_boot)) .=> coef(probit_boot))...)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38a10aeb",
   "metadata": {},
   "source": [
    "First we create a bootstrap sample:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "72676d1a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  2.040960 seconds (3.30 M allocations: 747.538 MiB, 6.53% gc time, 67.43% compilation time)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Bootstrap Sampling\n",
       "  Estimates:\n",
       "     Var │ Estimate    Bias         StdError\n",
       "         │ Float64     Float64      Float64\n",
       "    ─────┼────────────────────────────────────\n",
       "       1 │  3.74896     0.140457    1.40631\n",
       "       2 │ -0.666932   -0.0153319   0.129736\n",
       "       3 │  2.07531     0.0181637   0.425717\n",
       "       4 │ -0.294345   -0.00301596  0.0527653\n",
       "       5 │  0.0191963   0.00079884  0.0181964\n",
       "       6 │ -0.714465   -0.0113149   0.103201\n",
       "       7 │ -0.146985   -0.00136068  0.0522856\n",
       "       8 │  0.71438     0.00181945  0.12334\n",
       "  Sampling: BasicSampling\n",
       "  Samples:  1000\n",
       "  Data:     DataFrame: { 872 × 8 }\n"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Random.seed!(1234)\n",
    "@time bs = bootstrap(boot_probit, df, BasicSampling(1000))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5cc5d5a3",
   "metadata": {},
   "source": [
    "and next we compute 95% percentile confidence intervals:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "fb116658",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((3.748955649227034, 1.2412907300091973, 6.798729981241066), (-0.666931846730154, -0.9472825354846413, -0.4431707323683799), (2.075310025309972, 1.2933397235684967, 2.984776234514467), (-0.29434520313638085, -0.40537532831790735, -0.19817960501825893), (0.019196260085104954, -0.01585397748961663, 0.056526936720340114), (-0.7144647481686721, -0.9267794739575893, -0.5250296490239624), (-0.14698450450783618, -0.25949386579672723, -0.0525332765735234), (0.7143798526957522, 0.4788791797099514, 0.9616215302542083))"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bs_ci = confint(bs, PercentileConfInt(0.95))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a097882f",
   "metadata": {},
   "source": [
    "Let us chceck if the result matches our manual invervals. First create a new column in our data frame containing tuples. This is a typical example of *nested* data structure, that is handled by DataFrames.jl without any problems.\n",
    "\n",
    "Notice that I compute the deviations of lower and upper ends of confidence intervals from the estimate to match our earlier computations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "9dfbef2b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8-element Vector{Tuple{Float64, Float64, Float64}}:\n",
       " (3.748955649227034, 2.5076649192178366, 3.049774332014032)\n",
       " (-0.666931846730154, 0.2803506887544872, 0.22376111436177415)\n",
       " (2.075310025309972, 0.7819703017414752, 0.9094662092044952)\n",
       " (-0.29434520313638085, 0.1110301251815265, 0.09616559811812192)\n",
       " (0.019196260085104954, 0.03505023757472159, 0.03733067663523516)\n",
       " (-0.7144647481686721, 0.2123147257889172, 0.18943509914470968)\n",
       " (-0.14698450450783618, 0.11250936128889105, 0.09445122793431278)\n",
       " (0.7143798526957522, 0.2355006729858008, 0.24724167755845605)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conf_boot_t.bootstrap = [(ci[1], ci[1] - ci[2], ci[3] - ci[1]) for ci in bs_ci]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09660eeb",
   "metadata": {},
   "source": [
    "We could have inspected our data frame now:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "e5f7090a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>8×7 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">statistic</th><th style = \"text-align: left;\">estimate</th><th style = \"text-align: left;\">boot lo</th><th style = \"text-align: left;\">boot hi</th><th style = \"text-align: left;\">parametric lo</th><th style = \"text-align: left;\">parametric hi</th><th style = \"text-align: left;\">bootstrap</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"String\" style = \"text-align: left;\">String</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Tuple{Float64, Float64, Float64}\" style = \"text-align: left;\">Tuple…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">(Intercept)</td><td style = \"text-align: right;\">3.74896</td><td style = \"text-align: right;\">2.50766</td><td style = \"text-align: right;\">3.04977</td><td style = \"text-align: right;\">2.75695</td><td style = \"text-align: right;\">2.75695</td><td style = \"text-align: left;\">(3.74896, 2.50766, 3.04977)</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">lnnlinc</td><td style = \"text-align: right;\">-0.666932</td><td style = \"text-align: right;\">0.280351</td><td style = \"text-align: right;\">0.223761</td><td style = \"text-align: right;\">0.258558</td><td style = \"text-align: right;\">0.258558</td><td style = \"text-align: left;\">(-0.666932, 0.280351, 0.223761)</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">age</td><td style = \"text-align: right;\">2.07531</td><td style = \"text-align: right;\">0.78197</td><td style = \"text-align: right;\">0.909466</td><td style = \"text-align: right;\">0.794584</td><td style = \"text-align: right;\">0.794584</td><td style = \"text-align: left;\">(2.07531, 0.78197, 0.909466)</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">age ^ 2</td><td style = \"text-align: right;\">-0.294345</td><td style = \"text-align: right;\">0.11103</td><td style = \"text-align: right;\">0.0961656</td><td style = \"text-align: right;\">0.0978895</td><td style = \"text-align: right;\">0.0978895</td><td style = \"text-align: left;\">(-0.294345, 0.11103, 0.0961656)</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">educ</td><td style = \"text-align: right;\">0.0191963</td><td style = \"text-align: right;\">0.0350502</td><td style = \"text-align: right;\">0.0373307</td><td style = \"text-align: right;\">0.0351333</td><td style = \"text-align: right;\">0.0351333</td><td style = \"text-align: left;\">(0.0191963, 0.0350502, 0.0373307)</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: left;\">nyc</td><td style = \"text-align: right;\">-0.714465</td><td style = \"text-align: right;\">0.212315</td><td style = \"text-align: right;\">0.189435</td><td style = \"text-align: right;\">0.196774</td><td style = \"text-align: right;\">0.196774</td><td style = \"text-align: left;\">(-0.714465, 0.212315, 0.189435)</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: left;\">noc</td><td style = \"text-align: right;\">-0.146985</td><td style = \"text-align: right;\">0.112509</td><td style = \"text-align: right;\">0.0944512</td><td style = \"text-align: right;\">0.0997336</td><td style = \"text-align: right;\">0.0997336</td><td style = \"text-align: left;\">(-0.146985, 0.112509, 0.0944512)</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: left;\">foreign: yes</td><td style = \"text-align: right;\">0.71438</td><td style = \"text-align: right;\">0.235501</td><td style = \"text-align: right;\">0.247242</td><td style = \"text-align: right;\">0.23779</td><td style = \"text-align: right;\">0.23779</td><td style = \"text-align: left;\">(0.71438, 0.235501, 0.247242)</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccccc}\n",
       "\t& statistic & estimate & boot lo & boot hi & parametric lo & parametric hi & bootstrap\\\\\n",
       "\t\\hline\n",
       "\t& String & Float64 & Float64 & Float64 & Float64 & Float64 & Tuple…\\\\\n",
       "\t\\hline\n",
       "\t1 & (Intercept) & 3.74896 & 2.50766 & 3.04977 & 2.75695 & 2.75695 & (3.74896, 2.50766, 3.04977) \\\\\n",
       "\t2 & lnnlinc & -0.666932 & 0.280351 & 0.223761 & 0.258558 & 0.258558 & (-0.666932, 0.280351, 0.223761) \\\\\n",
       "\t3 & age & 2.07531 & 0.78197 & 0.909466 & 0.794584 & 0.794584 & (2.07531, 0.78197, 0.909466) \\\\\n",
       "\t4 & age \\^ 2 & -0.294345 & 0.11103 & 0.0961656 & 0.0978895 & 0.0978895 & (-0.294345, 0.11103, 0.0961656) \\\\\n",
       "\t5 & educ & 0.0191963 & 0.0350502 & 0.0373307 & 0.0351333 & 0.0351333 & (0.0191963, 0.0350502, 0.0373307) \\\\\n",
       "\t6 & nyc & -0.714465 & 0.212315 & 0.189435 & 0.196774 & 0.196774 & (-0.714465, 0.212315, 0.189435) \\\\\n",
       "\t7 & noc & -0.146985 & 0.112509 & 0.0944512 & 0.0997336 & 0.0997336 & (-0.146985, 0.112509, 0.0944512) \\\\\n",
       "\t8 & foreign: yes & 0.71438 & 0.235501 & 0.247242 & 0.23779 & 0.23779 & (0.71438, 0.235501, 0.247242) \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m8×7 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m statistic    \u001b[0m\u001b[1m estimate   \u001b[0m\u001b[1m boot lo   \u001b[0m\u001b[1m boot hi   \u001b[0m\u001b[1m parametric lo \u001b[0m\u001b[1m parametr\u001b[0m ⋯\n",
       "     │\u001b[90m String       \u001b[0m\u001b[90m Float64    \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64       \u001b[0m\u001b[90m Float64 \u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │ (Intercept)    3.74896    2.50766    3.04977        2.75695        2.75 ⋯\n",
       "   2 │ lnnlinc       -0.666932   0.280351   0.223761       0.258558       0.25\n",
       "   3 │ age            2.07531    0.78197    0.909466       0.794584       0.79\n",
       "   4 │ age ^ 2       -0.294345   0.11103    0.0961656      0.0978895      0.09\n",
       "   5 │ educ           0.0191963  0.0350502  0.0373307      0.0351333      0.03 ⋯\n",
       "   6 │ nyc           -0.714465   0.212315   0.189435       0.196774       0.19\n",
       "   7 │ noc           -0.146985   0.112509   0.0944512      0.0997336      0.09\n",
       "   8 │ foreign: yes   0.71438    0.235501   0.247242       0.23779        0.23\n",
       "\u001b[36m                                                               2 columns omitted\u001b[0m"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conf_boot_t"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c048b6f1",
   "metadata": {},
   "source": [
    "But it is a bit inconvenient."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1552992b",
   "metadata": {},
   "source": [
    "First un-nest the `:bootstrap` column into three columns:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "6b606849",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>8×9 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">statistic</th><th style = \"text-align: left;\">estimate</th><th style = \"text-align: left;\">boot lo</th><th style = \"text-align: left;\">boot hi</th><th style = \"text-align: left;\">parametric lo</th><th style = \"text-align: left;\">parametric hi</th><th style = \"text-align: left;\">estimate 2</th><th style = \"text-align: left;\">boot lo 2</th><th style = \"text-align: left;\">boot hi 2</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"String\" style = \"text-align: left;\">String</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">(Intercept)</td><td style = \"text-align: right;\">3.74896</td><td style = \"text-align: right;\">2.50766</td><td style = \"text-align: right;\">3.04977</td><td style = \"text-align: right;\">2.75695</td><td style = \"text-align: right;\">2.75695</td><td style = \"text-align: right;\">3.74896</td><td style = \"text-align: right;\">2.50766</td><td style = \"text-align: right;\">3.04977</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">lnnlinc</td><td style = \"text-align: right;\">-0.666932</td><td style = \"text-align: right;\">0.280351</td><td style = \"text-align: right;\">0.223761</td><td style = \"text-align: right;\">0.258558</td><td style = \"text-align: right;\">0.258558</td><td style = \"text-align: right;\">-0.666932</td><td style = \"text-align: right;\">0.280351</td><td style = \"text-align: right;\">0.223761</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">age</td><td style = \"text-align: right;\">2.07531</td><td style = \"text-align: right;\">0.78197</td><td style = \"text-align: right;\">0.909466</td><td style = \"text-align: right;\">0.794584</td><td style = \"text-align: right;\">0.794584</td><td style = \"text-align: right;\">2.07531</td><td style = \"text-align: right;\">0.78197</td><td style = \"text-align: right;\">0.909466</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">age ^ 2</td><td style = \"text-align: right;\">-0.294345</td><td style = \"text-align: right;\">0.11103</td><td style = \"text-align: right;\">0.0961656</td><td style = \"text-align: right;\">0.0978895</td><td style = \"text-align: right;\">0.0978895</td><td style = \"text-align: right;\">-0.294345</td><td style = \"text-align: right;\">0.11103</td><td style = \"text-align: right;\">0.0961656</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">educ</td><td style = \"text-align: right;\">0.0191963</td><td style = \"text-align: right;\">0.0350502</td><td style = \"text-align: right;\">0.0373307</td><td style = \"text-align: right;\">0.0351333</td><td style = \"text-align: right;\">0.0351333</td><td style = \"text-align: right;\">0.0191963</td><td style = \"text-align: right;\">0.0350502</td><td style = \"text-align: right;\">0.0373307</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: left;\">nyc</td><td style = \"text-align: right;\">-0.714465</td><td style = \"text-align: right;\">0.212315</td><td style = \"text-align: right;\">0.189435</td><td style = \"text-align: right;\">0.196774</td><td style = \"text-align: right;\">0.196774</td><td style = \"text-align: right;\">-0.714465</td><td style = \"text-align: right;\">0.212315</td><td style = \"text-align: right;\">0.189435</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: left;\">noc</td><td style = \"text-align: right;\">-0.146985</td><td style = \"text-align: right;\">0.112509</td><td style = \"text-align: right;\">0.0944512</td><td style = \"text-align: right;\">0.0997336</td><td style = \"text-align: right;\">0.0997336</td><td style = \"text-align: right;\">-0.146985</td><td style = \"text-align: right;\">0.112509</td><td style = \"text-align: right;\">0.0944512</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: left;\">foreign: yes</td><td style = \"text-align: right;\">0.71438</td><td style = \"text-align: right;\">0.235501</td><td style = \"text-align: right;\">0.247242</td><td style = \"text-align: right;\">0.23779</td><td style = \"text-align: right;\">0.23779</td><td style = \"text-align: right;\">0.71438</td><td style = \"text-align: right;\">0.235501</td><td style = \"text-align: right;\">0.247242</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& statistic & estimate & boot lo & boot hi & parametric lo & parametric hi & estimate 2 & \\\\\n",
       "\t\\hline\n",
       "\t& String & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & \\\\\n",
       "\t\\hline\n",
       "\t1 & (Intercept) & 3.74896 & 2.50766 & 3.04977 & 2.75695 & 2.75695 & 3.74896 & $\\dots$ \\\\\n",
       "\t2 & lnnlinc & -0.666932 & 0.280351 & 0.223761 & 0.258558 & 0.258558 & -0.666932 & $\\dots$ \\\\\n",
       "\t3 & age & 2.07531 & 0.78197 & 0.909466 & 0.794584 & 0.794584 & 2.07531 & $\\dots$ \\\\\n",
       "\t4 & age \\^ 2 & -0.294345 & 0.11103 & 0.0961656 & 0.0978895 & 0.0978895 & -0.294345 & $\\dots$ \\\\\n",
       "\t5 & educ & 0.0191963 & 0.0350502 & 0.0373307 & 0.0351333 & 0.0351333 & 0.0191963 & $\\dots$ \\\\\n",
       "\t6 & nyc & -0.714465 & 0.212315 & 0.189435 & 0.196774 & 0.196774 & -0.714465 & $\\dots$ \\\\\n",
       "\t7 & noc & -0.146985 & 0.112509 & 0.0944512 & 0.0997336 & 0.0997336 & -0.146985 & $\\dots$ \\\\\n",
       "\t8 & foreign: yes & 0.71438 & 0.235501 & 0.247242 & 0.23779 & 0.23779 & 0.71438 & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m8×9 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m statistic    \u001b[0m\u001b[1m estimate   \u001b[0m\u001b[1m boot lo   \u001b[0m\u001b[1m boot hi   \u001b[0m\u001b[1m parametric lo \u001b[0m\u001b[1m parametr\u001b[0m ⋯\n",
       "     │\u001b[90m String       \u001b[0m\u001b[90m Float64    \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64       \u001b[0m\u001b[90m Float64 \u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │ (Intercept)    3.74896    2.50766    3.04977        2.75695        2.75 ⋯\n",
       "   2 │ lnnlinc       -0.666932   0.280351   0.223761       0.258558       0.25\n",
       "   3 │ age            2.07531    0.78197    0.909466       0.794584       0.79\n",
       "   4 │ age ^ 2       -0.294345   0.11103    0.0961656      0.0978895      0.09\n",
       "   5 │ educ           0.0191963  0.0350502  0.0373307      0.0351333      0.03 ⋯\n",
       "   6 │ nyc           -0.714465   0.212315   0.189435       0.196774       0.19\n",
       "   7 │ noc           -0.146985   0.112509   0.0944512      0.0997336      0.09\n",
       "   8 │ foreign: yes   0.71438    0.235501   0.247242       0.23779        0.23\n",
       "\u001b[36m                                                               4 columns omitted\u001b[0m"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "select!(conf_boot_t, Not(:bootstrap), :bootstrap => [\"estimate 2\", \"boot lo 2\", \"boot hi 2\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "210860c5",
   "metadata": {},
   "source": [
    "Next reorder the columns using regular expressions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "ff8bda17",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>8×9 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">statistic</th><th style = \"text-align: left;\">estimate</th><th style = \"text-align: left;\">estimate 2</th><th style = \"text-align: left;\">boot lo</th><th style = \"text-align: left;\">parametric lo</th><th style = \"text-align: left;\">boot lo 2</th><th style = \"text-align: left;\">boot hi</th><th style = \"text-align: left;\">parametric hi</th><th style = \"text-align: left;\">boot hi 2</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"String\" style = \"text-align: left;\">String</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">(Intercept)</td><td style = \"text-align: right;\">3.74896</td><td style = \"text-align: right;\">3.74896</td><td style = \"text-align: right;\">2.50766</td><td style = \"text-align: right;\">2.75695</td><td style = \"text-align: right;\">2.50766</td><td style = \"text-align: right;\">3.04977</td><td style = \"text-align: right;\">2.75695</td><td style = \"text-align: right;\">3.04977</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">lnnlinc</td><td style = \"text-align: right;\">-0.666932</td><td style = \"text-align: right;\">-0.666932</td><td style = \"text-align: right;\">0.280351</td><td style = \"text-align: right;\">0.258558</td><td style = \"text-align: right;\">0.280351</td><td style = \"text-align: right;\">0.223761</td><td style = \"text-align: right;\">0.258558</td><td style = \"text-align: right;\">0.223761</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">age</td><td style = \"text-align: right;\">2.07531</td><td style = \"text-align: right;\">2.07531</td><td style = \"text-align: right;\">0.78197</td><td style = \"text-align: right;\">0.794584</td><td style = \"text-align: right;\">0.78197</td><td style = \"text-align: right;\">0.909466</td><td style = \"text-align: right;\">0.794584</td><td style = \"text-align: right;\">0.909466</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">age ^ 2</td><td style = \"text-align: right;\">-0.294345</td><td style = \"text-align: right;\">-0.294345</td><td style = \"text-align: right;\">0.11103</td><td style = \"text-align: right;\">0.0978895</td><td style = \"text-align: right;\">0.11103</td><td style = \"text-align: right;\">0.0961656</td><td style = \"text-align: right;\">0.0978895</td><td style = \"text-align: right;\">0.0961656</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">educ</td><td style = \"text-align: right;\">0.0191963</td><td style = \"text-align: right;\">0.0191963</td><td style = \"text-align: right;\">0.0350502</td><td style = \"text-align: right;\">0.0351333</td><td style = \"text-align: right;\">0.0350502</td><td style = \"text-align: right;\">0.0373307</td><td style = \"text-align: right;\">0.0351333</td><td style = \"text-align: right;\">0.0373307</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: left;\">nyc</td><td style = \"text-align: right;\">-0.714465</td><td style = \"text-align: right;\">-0.714465</td><td style = \"text-align: right;\">0.212315</td><td style = \"text-align: right;\">0.196774</td><td style = \"text-align: right;\">0.212315</td><td style = \"text-align: right;\">0.189435</td><td style = \"text-align: right;\">0.196774</td><td style = \"text-align: right;\">0.189435</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: left;\">noc</td><td style = \"text-align: right;\">-0.146985</td><td style = \"text-align: right;\">-0.146985</td><td style = \"text-align: right;\">0.112509</td><td style = \"text-align: right;\">0.0997336</td><td style = \"text-align: right;\">0.112509</td><td style = \"text-align: right;\">0.0944512</td><td style = \"text-align: right;\">0.0997336</td><td style = \"text-align: right;\">0.0944512</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: left;\">foreign: yes</td><td style = \"text-align: right;\">0.71438</td><td style = \"text-align: right;\">0.71438</td><td style = \"text-align: right;\">0.235501</td><td style = \"text-align: right;\">0.23779</td><td style = \"text-align: right;\">0.235501</td><td style = \"text-align: right;\">0.247242</td><td style = \"text-align: right;\">0.23779</td><td style = \"text-align: right;\">0.247242</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& statistic & estimate & estimate 2 & boot lo & parametric lo & boot lo 2 & boot hi & \\\\\n",
       "\t\\hline\n",
       "\t& String & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & \\\\\n",
       "\t\\hline\n",
       "\t1 & (Intercept) & 3.74896 & 3.74896 & 2.50766 & 2.75695 & 2.50766 & 3.04977 & $\\dots$ \\\\\n",
       "\t2 & lnnlinc & -0.666932 & -0.666932 & 0.280351 & 0.258558 & 0.280351 & 0.223761 & $\\dots$ \\\\\n",
       "\t3 & age & 2.07531 & 2.07531 & 0.78197 & 0.794584 & 0.78197 & 0.909466 & $\\dots$ \\\\\n",
       "\t4 & age \\^ 2 & -0.294345 & -0.294345 & 0.11103 & 0.0978895 & 0.11103 & 0.0961656 & $\\dots$ \\\\\n",
       "\t5 & educ & 0.0191963 & 0.0191963 & 0.0350502 & 0.0351333 & 0.0350502 & 0.0373307 & $\\dots$ \\\\\n",
       "\t6 & nyc & -0.714465 & -0.714465 & 0.212315 & 0.196774 & 0.212315 & 0.189435 & $\\dots$ \\\\\n",
       "\t7 & noc & -0.146985 & -0.146985 & 0.112509 & 0.0997336 & 0.112509 & 0.0944512 & $\\dots$ \\\\\n",
       "\t8 & foreign: yes & 0.71438 & 0.71438 & 0.235501 & 0.23779 & 0.235501 & 0.247242 & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m8×9 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m statistic    \u001b[0m\u001b[1m estimate   \u001b[0m\u001b[1m estimate 2 \u001b[0m\u001b[1m boot lo   \u001b[0m\u001b[1m parametric lo \u001b[0m\u001b[1m boot lo\u001b[0m ⋯\n",
       "     │\u001b[90m String       \u001b[0m\u001b[90m Float64    \u001b[0m\u001b[90m Float64    \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64       \u001b[0m\u001b[90m Float64\u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │ (Intercept)    3.74896     3.74896    2.50766        2.75695    2.50766 ⋯\n",
       "   2 │ lnnlinc       -0.666932   -0.666932   0.280351       0.258558   0.28035\n",
       "   3 │ age            2.07531     2.07531    0.78197        0.794584   0.78197\n",
       "   4 │ age ^ 2       -0.294345   -0.294345   0.11103        0.0978895  0.11103\n",
       "   5 │ educ           0.0191963   0.0191963  0.0350502      0.0351333  0.03505 ⋯\n",
       "   6 │ nyc           -0.714465   -0.714465   0.212315       0.196774   0.21231\n",
       "   7 │ noc           -0.146985   -0.146985   0.112509       0.0997336  0.11250\n",
       "   8 │ foreign: yes   0.71438     0.71438    0.235501       0.23779    0.23550\n",
       "\u001b[36m                                                               4 columns omitted\u001b[0m"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "select(conf_boot_t, :statistic, r\"estimate\", r\"lo\", r\"hi\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6105ee8",
   "metadata": {},
   "source": [
    "More discussion of various column selectors supported can be found [here](https://bkamins.github.io/julialang/2021/02/06/colsel.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f118c31",
   "metadata": {},
   "source": [
    "Now we can more easily see that our manual computations produce exactly the same results as the Bootstrap.jl package."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49d7372a",
   "metadata": {},
   "source": [
    "Before we finish sort our data frame by the `:estimate`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "d2352f4c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>8×9 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">statistic</th><th style = \"text-align: left;\">estimate</th><th style = \"text-align: left;\">boot lo</th><th style = \"text-align: left;\">boot hi</th><th style = \"text-align: left;\">parametric lo</th><th style = \"text-align: left;\">parametric hi</th><th style = \"text-align: left;\">estimate 2</th><th style = \"text-align: left;\">boot lo 2</th><th style = \"text-align: left;\">boot hi 2</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"String\" style = \"text-align: left;\">String</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">nyc</td><td style = \"text-align: right;\">-0.714465</td><td style = \"text-align: right;\">0.212315</td><td style = \"text-align: right;\">0.189435</td><td style = \"text-align: right;\">0.196774</td><td style = \"text-align: right;\">0.196774</td><td style = \"text-align: right;\">-0.714465</td><td style = \"text-align: right;\">0.212315</td><td style = \"text-align: right;\">0.189435</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">lnnlinc</td><td style = \"text-align: right;\">-0.666932</td><td style = \"text-align: right;\">0.280351</td><td style = \"text-align: right;\">0.223761</td><td style = \"text-align: right;\">0.258558</td><td style = \"text-align: right;\">0.258558</td><td style = \"text-align: right;\">-0.666932</td><td style = \"text-align: right;\">0.280351</td><td style = \"text-align: right;\">0.223761</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">age ^ 2</td><td style = \"text-align: right;\">-0.294345</td><td style = \"text-align: right;\">0.11103</td><td style = \"text-align: right;\">0.0961656</td><td style = \"text-align: right;\">0.0978895</td><td style = \"text-align: right;\">0.0978895</td><td style = \"text-align: right;\">-0.294345</td><td style = \"text-align: right;\">0.11103</td><td style = \"text-align: right;\">0.0961656</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">noc</td><td style = \"text-align: right;\">-0.146985</td><td style = \"text-align: right;\">0.112509</td><td style = \"text-align: right;\">0.0944512</td><td style = \"text-align: right;\">0.0997336</td><td style = \"text-align: right;\">0.0997336</td><td style = \"text-align: right;\">-0.146985</td><td style = \"text-align: right;\">0.112509</td><td style = \"text-align: right;\">0.0944512</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">educ</td><td style = \"text-align: right;\">0.0191963</td><td style = \"text-align: right;\">0.0350502</td><td style = \"text-align: right;\">0.0373307</td><td style = \"text-align: right;\">0.0351333</td><td style = \"text-align: right;\">0.0351333</td><td style = \"text-align: right;\">0.0191963</td><td style = \"text-align: right;\">0.0350502</td><td style = \"text-align: right;\">0.0373307</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: left;\">foreign: yes</td><td style = \"text-align: right;\">0.71438</td><td style = \"text-align: right;\">0.235501</td><td style = \"text-align: right;\">0.247242</td><td style = \"text-align: right;\">0.23779</td><td style = \"text-align: right;\">0.23779</td><td style = \"text-align: right;\">0.71438</td><td style = \"text-align: right;\">0.235501</td><td style = \"text-align: right;\">0.247242</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: left;\">age</td><td style = \"text-align: right;\">2.07531</td><td style = \"text-align: right;\">0.78197</td><td style = \"text-align: right;\">0.909466</td><td style = \"text-align: right;\">0.794584</td><td style = \"text-align: right;\">0.794584</td><td style = \"text-align: right;\">2.07531</td><td style = \"text-align: right;\">0.78197</td><td style = \"text-align: right;\">0.909466</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: left;\">(Intercept)</td><td style = \"text-align: right;\">3.74896</td><td style = \"text-align: right;\">2.50766</td><td style = \"text-align: right;\">3.04977</td><td style = \"text-align: right;\">2.75695</td><td style = \"text-align: right;\">2.75695</td><td style = \"text-align: right;\">3.74896</td><td style = \"text-align: right;\">2.50766</td><td style = \"text-align: right;\">3.04977</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& statistic & estimate & boot lo & boot hi & parametric lo & parametric hi & estimate 2 & \\\\\n",
       "\t\\hline\n",
       "\t& String & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & \\\\\n",
       "\t\\hline\n",
       "\t1 & nyc & -0.714465 & 0.212315 & 0.189435 & 0.196774 & 0.196774 & -0.714465 & $\\dots$ \\\\\n",
       "\t2 & lnnlinc & -0.666932 & 0.280351 & 0.223761 & 0.258558 & 0.258558 & -0.666932 & $\\dots$ \\\\\n",
       "\t3 & age \\^ 2 & -0.294345 & 0.11103 & 0.0961656 & 0.0978895 & 0.0978895 & -0.294345 & $\\dots$ \\\\\n",
       "\t4 & noc & -0.146985 & 0.112509 & 0.0944512 & 0.0997336 & 0.0997336 & -0.146985 & $\\dots$ \\\\\n",
       "\t5 & educ & 0.0191963 & 0.0350502 & 0.0373307 & 0.0351333 & 0.0351333 & 0.0191963 & $\\dots$ \\\\\n",
       "\t6 & foreign: yes & 0.71438 & 0.235501 & 0.247242 & 0.23779 & 0.23779 & 0.71438 & $\\dots$ \\\\\n",
       "\t7 & age & 2.07531 & 0.78197 & 0.909466 & 0.794584 & 0.794584 & 2.07531 & $\\dots$ \\\\\n",
       "\t8 & (Intercept) & 3.74896 & 2.50766 & 3.04977 & 2.75695 & 2.75695 & 3.74896 & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m8×9 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m statistic    \u001b[0m\u001b[1m estimate   \u001b[0m\u001b[1m boot lo   \u001b[0m\u001b[1m boot hi   \u001b[0m\u001b[1m parametric lo \u001b[0m\u001b[1m parametr\u001b[0m ⋯\n",
       "     │\u001b[90m String       \u001b[0m\u001b[90m Float64    \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64       \u001b[0m\u001b[90m Float64 \u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │ nyc           -0.714465   0.212315   0.189435       0.196774       0.19 ⋯\n",
       "   2 │ lnnlinc       -0.666932   0.280351   0.223761       0.258558       0.25\n",
       "   3 │ age ^ 2       -0.294345   0.11103    0.0961656      0.0978895      0.09\n",
       "   4 │ noc           -0.146985   0.112509   0.0944512      0.0997336      0.09\n",
       "   5 │ educ           0.0191963  0.0350502  0.0373307      0.0351333      0.03 ⋯\n",
       "   6 │ foreign: yes   0.71438    0.235501   0.247242       0.23779        0.23\n",
       "   7 │ age            2.07531    0.78197    0.909466       0.794584       0.79\n",
       "   8 │ (Intercept)    3.74896    2.50766    3.04977        2.75695        2.75\n",
       "\u001b[36m                                                               4 columns omitted\u001b[0m"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sort(conf_boot_t, :estimate)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a71d91f3",
   "metadata": {},
   "source": [
    "Here is some more advanced example, where we sort the rows by the width of the confidence interval:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "b7d1d9ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>8×9 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">statistic</th><th style = \"text-align: left;\">estimate</th><th style = \"text-align: left;\">boot lo</th><th style = \"text-align: left;\">boot hi</th><th style = \"text-align: left;\">parametric lo</th><th style = \"text-align: left;\">parametric hi</th><th style = \"text-align: left;\">estimate 2</th><th style = \"text-align: left;\">boot lo 2</th><th style = \"text-align: left;\">boot hi 2</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"String\" style = \"text-align: left;\">String</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">educ</td><td style = \"text-align: right;\">0.0191963</td><td style = \"text-align: right;\">0.0350502</td><td style = \"text-align: right;\">0.0373307</td><td style = \"text-align: right;\">0.0351333</td><td style = \"text-align: right;\">0.0351333</td><td style = \"text-align: right;\">0.0191963</td><td style = \"text-align: right;\">0.0350502</td><td style = \"text-align: right;\">0.0373307</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">noc</td><td style = \"text-align: right;\">-0.146985</td><td style = \"text-align: right;\">0.112509</td><td style = \"text-align: right;\">0.0944512</td><td style = \"text-align: right;\">0.0997336</td><td style = \"text-align: right;\">0.0997336</td><td style = \"text-align: right;\">-0.146985</td><td style = \"text-align: right;\">0.112509</td><td style = \"text-align: right;\">0.0944512</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">age ^ 2</td><td style = \"text-align: right;\">-0.294345</td><td style = \"text-align: right;\">0.11103</td><td style = \"text-align: right;\">0.0961656</td><td style = \"text-align: right;\">0.0978895</td><td style = \"text-align: right;\">0.0978895</td><td style = \"text-align: right;\">-0.294345</td><td style = \"text-align: right;\">0.11103</td><td style = \"text-align: right;\">0.0961656</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">nyc</td><td style = \"text-align: right;\">-0.714465</td><td style = \"text-align: right;\">0.212315</td><td style = \"text-align: right;\">0.189435</td><td style = \"text-align: right;\">0.196774</td><td style = \"text-align: right;\">0.196774</td><td style = \"text-align: right;\">-0.714465</td><td style = \"text-align: right;\">0.212315</td><td style = \"text-align: right;\">0.189435</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">foreign: yes</td><td style = \"text-align: right;\">0.71438</td><td style = \"text-align: right;\">0.235501</td><td style = \"text-align: right;\">0.247242</td><td style = \"text-align: right;\">0.23779</td><td style = \"text-align: right;\">0.23779</td><td style = \"text-align: right;\">0.71438</td><td style = \"text-align: right;\">0.235501</td><td style = \"text-align: right;\">0.247242</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: left;\">lnnlinc</td><td style = \"text-align: right;\">-0.666932</td><td style = \"text-align: right;\">0.280351</td><td style = \"text-align: right;\">0.223761</td><td style = \"text-align: right;\">0.258558</td><td style = \"text-align: right;\">0.258558</td><td style = \"text-align: right;\">-0.666932</td><td style = \"text-align: right;\">0.280351</td><td style = \"text-align: right;\">0.223761</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: left;\">age</td><td style = \"text-align: right;\">2.07531</td><td style = \"text-align: right;\">0.78197</td><td style = \"text-align: right;\">0.909466</td><td style = \"text-align: right;\">0.794584</td><td style = \"text-align: right;\">0.794584</td><td style = \"text-align: right;\">2.07531</td><td style = \"text-align: right;\">0.78197</td><td style = \"text-align: right;\">0.909466</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: left;\">(Intercept)</td><td style = \"text-align: right;\">3.74896</td><td style = \"text-align: right;\">2.50766</td><td style = \"text-align: right;\">3.04977</td><td style = \"text-align: right;\">2.75695</td><td style = \"text-align: right;\">2.75695</td><td style = \"text-align: right;\">3.74896</td><td style = \"text-align: right;\">2.50766</td><td style = \"text-align: right;\">3.04977</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& statistic & estimate & boot lo & boot hi & parametric lo & parametric hi & estimate 2 & \\\\\n",
       "\t\\hline\n",
       "\t& String & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & \\\\\n",
       "\t\\hline\n",
       "\t1 & educ & 0.0191963 & 0.0350502 & 0.0373307 & 0.0351333 & 0.0351333 & 0.0191963 & $\\dots$ \\\\\n",
       "\t2 & noc & -0.146985 & 0.112509 & 0.0944512 & 0.0997336 & 0.0997336 & -0.146985 & $\\dots$ \\\\\n",
       "\t3 & age \\^ 2 & -0.294345 & 0.11103 & 0.0961656 & 0.0978895 & 0.0978895 & -0.294345 & $\\dots$ \\\\\n",
       "\t4 & nyc & -0.714465 & 0.212315 & 0.189435 & 0.196774 & 0.196774 & -0.714465 & $\\dots$ \\\\\n",
       "\t5 & foreign: yes & 0.71438 & 0.235501 & 0.247242 & 0.23779 & 0.23779 & 0.71438 & $\\dots$ \\\\\n",
       "\t6 & lnnlinc & -0.666932 & 0.280351 & 0.223761 & 0.258558 & 0.258558 & -0.666932 & $\\dots$ \\\\\n",
       "\t7 & age & 2.07531 & 0.78197 & 0.909466 & 0.794584 & 0.794584 & 2.07531 & $\\dots$ \\\\\n",
       "\t8 & (Intercept) & 3.74896 & 2.50766 & 3.04977 & 2.75695 & 2.75695 & 3.74896 & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m8×9 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m statistic    \u001b[0m\u001b[1m estimate   \u001b[0m\u001b[1m boot lo   \u001b[0m\u001b[1m boot hi   \u001b[0m\u001b[1m parametric lo \u001b[0m\u001b[1m parametr\u001b[0m ⋯\n",
       "     │\u001b[90m String       \u001b[0m\u001b[90m Float64    \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64       \u001b[0m\u001b[90m Float64 \u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │ educ           0.0191963  0.0350502  0.0373307      0.0351333      0.03 ⋯\n",
       "   2 │ noc           -0.146985   0.112509   0.0944512      0.0997336      0.09\n",
       "   3 │ age ^ 2       -0.294345   0.11103    0.0961656      0.0978895      0.09\n",
       "   4 │ nyc           -0.714465   0.212315   0.189435       0.196774       0.19\n",
       "   5 │ foreign: yes   0.71438    0.235501   0.247242       0.23779        0.23 ⋯\n",
       "   6 │ lnnlinc       -0.666932   0.280351   0.223761       0.258558       0.25\n",
       "   7 │ age            2.07531    0.78197    0.909466       0.794584       0.79\n",
       "   8 │ (Intercept)    3.74896    2.50766    3.04977        2.75695        2.75\n",
       "\u001b[36m                                                               4 columns omitted\u001b[0m"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conf_boot_t[sortperm(conf_boot_t.\"boot hi\" + conf_boot_t.\"boot lo\"), :]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f76e6583",
   "metadata": {},
   "source": [
    "More examples of sorting data frames can be found [here](https://bkamins.github.io/julialang/2021/03/12/sorting.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c8bae3c",
   "metadata": {},
   "source": [
    "## That is all for today"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e43d40c1",
   "metadata": {},
   "source": [
    "I hope you enjoyed the tutorial.\n",
    "\n",
    "If you would like to learn more about [DataFrames.jl](https://github.com/JuliaData/DataFrames.jl) please do not hesitate to visit its documentation [here](https://dataframes.juliadata.org/stable/)."
   ]
  }
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