Linear Regression with stats model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## importing libraries  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reading and understanding data from the file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv(r'C:\\Users\\Sayantan\\ML in python/real_estate_price_size.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>price</th>\n",
       "      <th>size</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>234314.144</td>\n",
       "      <td>643.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>228581.528</td>\n",
       "      <td>656.22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>281626.336</td>\n",
       "      <td>487.29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>401255.608</td>\n",
       "      <td>1504.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>458674.256</td>\n",
       "      <td>1275.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>252460.400</td>\n",
       "      <td>549.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>310522.592</td>\n",
       "      <td>1037.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>383635.568</td>\n",
       "      <td>1504.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>225145.248</td>\n",
       "      <td>648.29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>274922.856</td>\n",
       "      <td>705.29</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         price     size\n",
       "0   234314.144   643.09\n",
       "1   228581.528   656.22\n",
       "2   281626.336   487.29\n",
       "3   401255.608  1504.75\n",
       "4   458674.256  1275.46\n",
       "..         ...      ...\n",
       "95  252460.400   549.80\n",
       "96  310522.592  1037.44\n",
       "97  383635.568  1504.75\n",
       "98  225145.248   648.29\n",
       "99  274922.856   705.29\n",
       "\n",
       "[100 rows x 2 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>price</th>\n",
       "      <th>size</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>292289.470160</td>\n",
       "      <td>853.024200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>77051.727525</td>\n",
       "      <td>297.941951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>154282.128000</td>\n",
       "      <td>479.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>234280.148000</td>\n",
       "      <td>643.330000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>280590.716000</td>\n",
       "      <td>696.405000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>335723.696000</td>\n",
       "      <td>1029.322500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>500681.128000</td>\n",
       "      <td>1842.510000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               price         size\n",
       "count     100.000000   100.000000\n",
       "mean   292289.470160   853.024200\n",
       "std     77051.727525   297.941951\n",
       "min    154282.128000   479.750000\n",
       "25%    234280.148000   643.330000\n",
       "50%    280590.716000   696.405000\n",
       "75%    335723.696000  1029.322500\n",
       "max    500681.128000  1842.510000"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## creating and visualizing the regression model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = data['price']\n",
    "x1 = data['size']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'price')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x1,y)\n",
    "plt.xlabel('size',fontsize = 20)\n",
    "plt.ylabel('price',fontsize = 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>price</td>      <th>  R-squared:         </th> <td>   0.745</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.742</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   285.9</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 16 May 2020</td> <th>  Prob (F-statistic):</th> <td>8.13e-31</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:37:47</td>     <th>  Log-Likelihood:    </th> <td> -1198.3</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   100</td>      <th>  AIC:               </th> <td>   2401.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    98</td>      <th>  BIC:               </th> <td>   2406.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td> 1.019e+05</td> <td> 1.19e+04</td> <td>    8.550</td> <td> 0.000</td> <td> 7.83e+04</td> <td> 1.26e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>size</th>  <td>  223.1787</td> <td>   13.199</td> <td>   16.909</td> <td> 0.000</td> <td>  196.986</td> <td>  249.371</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 6.262</td> <th>  Durbin-Watson:     </th> <td>   2.267</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.044</td> <th>  Jarque-Bera (JB):  </th> <td>   2.938</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.117</td> <th>  Prob(JB):          </th> <td>   0.230</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.194</td> <th>  Cond. No.          </th> <td>2.75e+03</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 2.75e+03. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  price   R-squared:                       0.745\n",
       "Model:                            OLS   Adj. R-squared:                  0.742\n",
       "Method:                 Least Squares   F-statistic:                     285.9\n",
       "Date:                Sat, 16 May 2020   Prob (F-statistic):           8.13e-31\n",
       "Time:                        11:37:47   Log-Likelihood:                -1198.3\n",
       "No. Observations:                 100   AIC:                             2401.\n",
       "Df Residuals:                      98   BIC:                             2406.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const       1.019e+05   1.19e+04      8.550      0.000    7.83e+04    1.26e+05\n",
       "size         223.1787     13.199     16.909      0.000     196.986     249.371\n",
       "==============================================================================\n",
       "Omnibus:                        6.262   Durbin-Watson:                   2.267\n",
       "Prob(Omnibus):                  0.044   Jarque-Bera (JB):                2.938\n",
       "Skew:                           0.117   Prob(JB):                        0.230\n",
       "Kurtosis:                       2.194   Cond. No.                     2.75e+03\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 2.75e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = sm.add_constant(x1)\n",
    "results = sm.OLS(y,x).fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x1,y)\n",
    "yhat = x1*223.1787 + 1.019e+05\n",
    "fig = plt.plot(x1,yhat, lw = 2,c='Red' )\n",
    "plt.xlabel('size',fontsize = 20)\n",
    "plt.ylabel('price',fontsize = 20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}