boston_housing.ipynb

{
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    "# Machine Learning Engineer Nanodegree\n",
    "## Model Evaluation & Validation\n",
    "## Project: Predicting Boston Housing Prices\n",
    "\n",
    "Welcome to the first project of the Machine Learning Engineer Nanodegree! In this notebook, some template code has already been provided for you, and you will need to implement additional functionality to successfully complete this project. You will not need to modify the included code beyond what is requested. Sections that begin with **'Implementation'** in the header indicate that the following block of code will require additional functionality which you must provide. Instructions will be provided for each section and the specifics of the implementation are marked in the code block with a 'TODO' statement. Please be sure to read the instructions carefully!\n",
    "\n",
    "In addition to implementing code, there will be questions that you must answer which relate to the project and your implementation. Each section where you will answer a question is preceded by a **'Question X'** header. Carefully read each question and provide thorough answers in the following text boxes that begin with **'Answer:'**. Your project submission will be evaluated based on your answers to each of the questions and the implementation you provide.  \n",
    "\n",
    ">**Note:** Code and Markdown cells can be executed using the **Shift + Enter** keyboard shortcut. In addition, Markdown cells can be edited by typically double-clicking the cell to enter edit mode."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Getting Started\n",
    "In this project, you will evaluate the performance and predictive power of a model that has been trained and tested on data collected from homes in suburbs of Boston, Massachusetts. A model trained on this data that is seen as a *good fit* could then be used to make certain predictions about a home — in particular, its monetary value. This model would prove to be invaluable for someone like a real estate agent who could make use of such information on a daily basis.\n",
    "\n",
    "The dataset for this project originates from the [UCI Machine Learning Repository](https://archive.ics.uci.edu/ml/datasets/Housing). The Boston housing data was collected in 1978 and each of the 506 entries represent aggregated data about 14 features for homes from various suburbs in Boston, Massachusetts. For the purposes of this project, the following preprocessing steps have been made to the dataset:\n",
    "- 16 data points have an `'MEDV'` value of 50.0. These data points likely contain **missing or censored values** and have been removed.\n",
    "- 1 data point has an `'RM'` value of 8.78. This data point can be considered an **outlier** and has been removed.\n",
    "- The features `'RM'`, `'LSTAT'`, `'PTRATIO'`, and `'MEDV'` are essential. The remaining **non-relevant features** have been excluded.\n",
    "- The feature `'MEDV'` has been **multiplicatively scaled** to account for 35 years of market inflation.\n",
    "\n",
    "Run the code cell below to load the Boston housing dataset, along with a few of the necessary Python libraries required for this project. You will know the dataset loaded successfully if the size of the dataset is reported."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Boston housing dataset has 489 data points with 4 variables each.\n"
     ]
    }
   ],
   "source": [
    "# Import libraries necessary for this project\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.cross_validation import ShuffleSplit\n",
    "\n",
    "# Import supplementary visualizations code visuals.py\n",
    "import visuals as vs\n",
    "\n",
    "# Pretty display for notebooks\n",
    "%matplotlib inline\n",
    "\n",
    "# Load the Boston housing dataset\n",
    "data = pd.read_csv('housing.csv')\n",
    "prices = data['MEDV']\n",
    "features = data.drop('MEDV', axis = 1)\n",
    "    \n",
    "# Success\n",
    "print \"Boston housing dataset has {} data points with {} variables each.\".format(*data.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Exploration\n",
    "In this first section of this project, you will make a cursory investigation about the Boston housing data and provide your observations. Familiarizing yourself with the data through an explorative process is a fundamental practice to help you better understand and justify your results.\n",
    "\n",
    "Since the main goal of this project is to construct a working model which has the capability of predicting the value of houses, we will need to separate the dataset into **features** and the **target variable**. The **features**, `'RM'`, `'LSTAT'`, and `'PTRATIO'`, give us quantitative information about each data point. The **target variable**, `'MEDV'`, will be the variable we seek to predict. These are stored in `features` and `prices`, respectively."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation: Calculate Statistics\n",
    "For your very first coding implementation, you will calculate descriptive statistics about the Boston housing prices. Since `numpy` has already been imported for you, use this library to perform the necessary calculations. These statistics will be extremely important later on to analyze various prediction results from the constructed model.\n",
    "\n",
    "In the code cell below, you will need to implement the following:\n",
    "- Calculate the minimum, maximum, mean, median, and standard deviation of `'MEDV'`, which is stored in `prices`.\n",
    "  - Store each calculation in their respective variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistics for Boston housing dataset:\n",
      "\n",
      "Minimum price: $105,000.00\n",
      "Maximum price: $1,024,800.00\n",
      "Mean price: $454,342.94\n",
      "Median price $438,900.00\n",
      "Standard deviation of prices: $165,171.13\n"
     ]
    }
   ],
   "source": [
    "# Minimum price of the data\n",
    "minimum_price = np.min(prices)\n",
    "\n",
    "# Maximum price of the data\n",
    "maximum_price = np.max(prices)\n",
    "\n",
    "# Mean price of the data\n",
    "mean_price = np.mean(prices)\n",
    "\n",
    "# Median price of the data\n",
    "median_price = np.median(prices)\n",
    "\n",
    "# Standard deviation of prices of the data\n",
    "std_price = np.std(prices)\n",
    "\n",
    "# Show the calculated statistics\n",
    "print \"Statistics for Boston housing dataset:\\n\"\n",
    "print \"Minimum price: ${:,.2f}\".format(minimum_price)\n",
    "print \"Maximum price: ${:,.2f}\".format(maximum_price)\n",
    "print \"Mean price: ${:,.2f}\".format(mean_price)\n",
    "print \"Median price ${:,.2f}\".format(median_price)\n",
    "print \"Standard deviation of prices: ${:,.2f}\".format(std_price)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 1 - Feature Observation\n",
    "As a reminder, we are using three features from the Boston housing dataset: `'RM'`, `'LSTAT'`, and `'PTRATIO'`. For each data point (neighborhood):\n",
    "- `'RM'` is the average number of rooms among homes in the neighborhood.\n",
    "- `'LSTAT'` is the percentage of homeowners in the neighborhood considered \"lower class\" (working poor).\n",
    "- `'PTRATIO'` is the ratio of students to teachers in primary and secondary schools in the neighborhood.\n",
    "\n",
    "\n",
    "** Using your intuition, for each of the three features above, do you think that an increase in the value of that feature would lead to an **increase** in the value of `'MEDV'` or a **decrease** in the value of `'MEDV'`? Justify your answer for each.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer: **\n",
    "\n",
    "* An increase in `'RM'` would **increase** `'MEDV'` since it means more rooms and consequently more valuable space for the buyer.\n",
    "* An increase in `'LSTAT'` would **decrease** `'MEDV'` because it says something about the average purchasing power of the neighborhood going down, or even criminality rates going up. Both of these situations tend to devalue a neighborhood.\n",
    "* An increase in  `'PTRATIO'` would **decrease** `'MEDV'` as it could mean that classes would be crowded and children not receiving the proper attention/education thus upsetting parents. Furthermore it can correlate with `'LSTAT'` as we can assume teachers are not \"lower class\" and that `'LSTAT'` could also be increasing."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "\n",
    "## Developing a Model\n",
    "In this second section of the project, you will develop the tools and techniques necessary for a model to make a prediction. Being able to make accurate evaluations of each model's performance through the use of these tools and techniques helps to greatly reinforce the confidence in your predictions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation: Define a Performance Metric\n",
    "It is difficult to measure the quality of a given model without quantifying its performance over training and testing. This is typically done using some type of performance metric, whether it is through calculating some type of error, the goodness of fit, or some other useful measurement. For this project, you will be calculating the [*coefficient of determination*](http://stattrek.com/statistics/dictionary.aspx?definition=coefficient_of_determination), R<sup>2</sup>, to quantify your model's performance. The coefficient of determination for a model is a useful statistic in regression analysis, as it often describes how \"good\" that model is at making predictions. \n",
    "\n",
    "The values for R<sup>2</sup> range from 0 to 1, which captures the percentage of squared correlation between the predicted and actual values of the **target variable**. A model with an R<sup>2</sup> of 0 is no better than a model that always predicts the *mean* of the target variable, whereas a model with an R<sup>2</sup> of 1 perfectly predicts the target variable. Any value between 0 and 1 indicates what percentage of the target variable, using this model, can be explained by the **features**. _A model can be given a negative R<sup>2</sup> as well, which indicates that the model is **arbitrarily worse** than one that always predicts the mean of the target variable._\n",
    "\n",
    "For the `performance_metric` function in the code cell below, you will need to implement the following:\n",
    "- Use `r2_score` from `sklearn.metrics` to perform a performance calculation between `y_true` and `y_predict`.\n",
    "- Assign the performance score to the `score` variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import 'r2_score'\n",
    "from sklearn.metrics import r2_score\n",
    "\n",
    "def performance_metric(y_true, y_predict):\n",
    "    \"\"\" Calculates and returns the performance score between \n",
    "        true and predicted values based on the metric chosen. \"\"\"\n",
    "    \n",
    "    # Calculate the performance score between 'y_true' and 'y_predict'\n",
    "    score = r2_score(y_true, y_predict)\n",
    "    \n",
    "    # Return the score\n",
    "    return score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 2 - Goodness of Fit\n",
    "Assume that a dataset contains five data points and a model made the following predictions for the target variable:\n",
    "\n",
    "| True Value | Prediction |\n",
    "| :-------------: | :--------: |\n",
    "| 3.0 | 2.5 |\n",
    "| -0.5 | 0.0 |\n",
    "| 2.0 | 2.1 |\n",
    "| 7.0 | 7.8 |\n",
    "| 4.2 | 5.3 |\n",
    "\n",
    "Run the code cell below to use the `performance_metric` function and calculate this model's coefficient of determination."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model has a coefficient of determination, R^2, of 0.923.\n"
     ]
    }
   ],
   "source": [
    "# Calculate the performance of this model\n",
    "score = performance_metric([3, -0.5, 2, 7, 4.2], [2.5, 0.0, 2.1, 7.8, 5.3])\n",
    "print \"Model has a coefficient of determination, R^2, of {:.3f}.\".format(score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Would you consider this model to have successfully captured the variation of the target variable? \n",
    "* Why or why not?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer:**\n",
    "\n",
    "R<sup>2</sup>Score = 1 - (SS<sub>res</sub>/SS<sub>total</sub>), being SS<sub>res</sub> the sum of squares of the errors of the predicted value to the true value, and SS<sub>total</sub> the total sum of squares (proportional to the variance of the data). The result means the proportion of the variance in the dependent variable that is predictable from the independent variable.\n",
    "\n",
    "A good model would have a small SS<sub>res</sub> and the R<sup>2</sup> score close to 1.\n",
    "Since our result is a score of **0.923**, 92.3% of the variance is predictable with this model. It is not perfect but it **successfully** captures the variation of the target variable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation: Shuffle and Split Data\n",
    "Your next implementation requires that you take the Boston housing dataset and split the data into training and testing subsets. Typically, the data is also shuffled into a random order when creating the training and testing subsets to remove any bias in the ordering of the dataset.\n",
    "\n",
    "For the code cell below, you will need to implement the following:\n",
    "- Use `train_test_split` from `sklearn.cross_validation` to shuffle and split the `features` and `prices` data into training and testing sets.\n",
    "  - Split the data into 80% training and 20% testing.\n",
    "  - Set the `random_state` for `train_test_split` to a value of your choice. This ensures results are consistent.\n",
    "- Assign the train and testing splits to `X_train`, `X_test`, `y_train`, and `y_test`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training and testing split was successful.\n"
     ]
    }
   ],
   "source": [
    "# Import 'train_test_split'\n",
    "from sklearn.cross_validation import train_test_split\n",
    "\n",
    "# Shuffle and split the data into training and testing subsets\n",
    "X_train, X_test, y_train, y_test = train_test_split(features, prices, test_size=0.20, random_state=0)\n",
    "\n",
    "# Success\n",
    "print \"Training and testing split was successful.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 3 - Training and Testing\n",
    "\n",
    "* What is the benefit to splitting a dataset into some ratio of training and testing subsets for a learning algorithm?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer: **\n",
    "\n",
    "We need to check if the model has a good performance and to do so we need a subset to perform a final evaluation of the model to check if it really maintains performance **with data that was not used for training**.\n",
    "\n",
    "If we don't separate training and testing sets(or even use the testing set to make decisions about our model) we are using the same data that the model used to be trained and using it to test our data, thus we are not measuring any actual performance as it will probably perform well on already seen data that it used to learn from."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "\n",
    "## Analyzing Model Performance\n",
    "In this third section of the project, you'll take a look at several models' learning and testing performances on various subsets of training data. Additionally, you'll investigate one particular algorithm with an increasing `'max_depth'` parameter on the full training set to observe how model complexity affects performance. Graphing your model's performance based on varying criteria can be beneficial in the analysis process, such as visualizing behavior that may not have been apparent from the results alone."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Learning Curves\n",
    "The following code cell produces four graphs for a decision tree model with different maximum depths. Each graph visualizes the learning curves of the model for both training and testing as the size of the training set is increased. Note that the shaded region of a learning curve denotes the uncertainty of that curve (measured as the standard deviation). The model is scored on both the training and testing sets using R<sup>2</sup>, the coefficient of determination.  \n",
    "\n",
    "Run the code cell below and use these graphs to answer the following question."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f51f0132150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Produce learning curves for varying training set sizes and maximum depths\n",
    "vs.ModelLearning(features, prices)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 4 - Learning the Data\n",
    "* Choose one of the graphs above and state the maximum depth for the model. \n",
    "* What happens to the score of the training curve as more training points are added? What about the testing curve? \n",
    "* Would having more training points benefit the model? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer: **\n",
    "\n",
    "Choosing **max_depth=10** we can observe that:\n",
    "* Training scores starts close to 1.0 at 50 training points and as the number of training points increases the curve slightly decreases but still maintain a high score of almost 1.0, meaning that it fits the training set way too much, hence the small variation and high scores.\n",
    "\n",
    "* Validation scores starts with 0.6 score at 50 training points and as the number of training points increases it  slightly increases, peaking ~0.7 score at 200 training points and stays around this value with a slight decrease as more training points are added.\n",
    "\n",
    "In summary, training scores stays high with a small difference as more training points are added and validation scores stays low with a small difference as more training points are added, thus these curves get closer as more points are added(since they have more information as more training points are used), but they never converge, keeping a great distance between each other.\n",
    "\n",
    "This distance shows a a scenario of Overfitting(High Variance) since it does too well on training but it memorizes and doesn't perform well on validation. \n",
    "\n",
    "* So adding more training points would not benefit the model as it already overfits the training data and the distance between the scores will not decrease. We need to decrease the model's complexity instead."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Complexity Curves\n",
    "The following code cell produces a graph for a decision tree model that has been trained and validated on the training data using different maximum depths. The graph produces two complexity curves — one for training and one for validation. Similar to the **learning curves**, the shaded regions of both the complexity curves denote the uncertainty in those curves, and the model is scored on both the training and validation sets using the `performance_metric` function.  \n",
    "\n",
    "** Run the code cell below and use this graph to answer the following two questions Q5 and Q6. **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f51ba1a3b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vs.ModelComplexity(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 5 - Bias-Variance Tradeoff\n",
    "* When the model is trained with a maximum depth of 1, does the model suffer from high bias or from high variance? \n",
    "* How about when the model is trained with a maximum depth of 10? What visual cues in the graph justify your conclusions?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer: **\n",
    "\n",
    "* When the **maximum depth is 1** it suffers from **high bias** as the training and validation scores are close but with low values. This means that the model is not fitting neither generalizing the dataset well enough, thus giving poor scores both on training and validation.\n",
    "\n",
    "* When the **maximum depth is 10** it suffers from **high variance** as the training score is high and the testing score is low. There is a high gap between these scores and this indicates that the model is overfitting the training dataset but not generalizing well enough for the validation set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 6 - Best-Guess Optimal Model\n",
    "* Which maximum depth do you think results in a model that best generalizes to unseen data? \n",
    "* What intuition lead you to this answer?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer: **\n",
    "\n",
    "Observing the graph I would pick **maximum depth of 4** because it peaks the validation score while maintaining a reasonable gap between validation and training scores in comparison to maximum depth of 3. If we go higher on the complexity the gap tends to increase while the validation score tends to decrease, so depth 4 seems the right choice.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-----\n",
    "\n",
    "## Evaluating Model Performance\n",
    "In this final section of the project, you will construct a model and make a prediction on the client's feature set using an optimized model from `fit_model`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 7 - Grid Search\n",
    "* What is the grid search technique?\n",
    "* How it can be applied to optimize a learning algorithm?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer: **\n",
    "\n",
    "The grid search technique is a way to lay combinations of hyper-parameters of a model in a grid. Each combination generates parameters using the training set and then are scored by cross-validation, giving the opportunity to optimize a learning algorithm by picking the combination of hyper-parameters that generated the best score."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 8 - Cross-Validation\n",
    "\n",
    "* What is the k-fold cross-validation training technique? \n",
    "\n",
    "* What benefit does this technique provide for grid search when optimizing a model?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer: **\n",
    "\n",
    "K-Fold cross-validation is a technique that splits the training set into K subsets of equal size on which each subset is used as the validation set once, and as the training set K-1 times. Then the K performances are averaged to estimate the general model performance on those hyper-parameters.\n",
    "\n",
    "The best benefit offered by this technique is to reuse our data without biasing the model, generating a lower variance than a single train/test split that could be performing well(or poorly) in just one specific split of the data. This particular benefit is what makes it great for the grid search once it will reduce the chance of picking up hyper-parameters that only function well on a determinate split."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation: Fitting a Model\n",
    "Your final implementation requires that you bring everything together and train a model using the **decision tree algorithm**. To ensure that you are producing an optimized model, you will train the model using the grid search technique to optimize the `'max_depth'` parameter for the decision tree. The `'max_depth'` parameter can be thought of as how many questions the decision tree algorithm is allowed to ask about the data before making a prediction. Decision trees are part of a class of algorithms called *supervised learning algorithms*.\n",
    "\n",
    "In addition, you will find your implementation is using `ShuffleSplit()` for an alternative form of cross-validation (see the `'cv_sets'` variable). While it is not the K-Fold cross-validation technique you describe in **Question 8**, this type of cross-validation technique is just as useful!. The `ShuffleSplit()` implementation below will create 10 (`'n_splits'`) shuffled sets, and for each shuffle, 20% (`'test_size'`) of the data will be used as the *validation set*. While you're working on your implementation, think about the contrasts and similarities it has to the K-fold cross-validation technique.\n",
    "\n",
    "Please note that ShuffleSplit has different parameters in scikit-learn versions 0.17 and 0.18.\n",
    "For the `fit_model` function in the code cell below, you will need to implement the following:\n",
    "- Use [`DecisionTreeRegressor`](http://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeRegressor.html) from `sklearn.tree` to create a decision tree regressor object.\n",
    "  - Assign this object to the `'regressor'` variable.\n",
    "- Create a dictionary for `'max_depth'` with the values from 1 to 10, and assign this to the `'params'` variable.\n",
    "- Use [`make_scorer`](http://scikit-learn.org/stable/modules/generated/sklearn.metrics.make_scorer.html) from `sklearn.metrics` to create a scoring function object.\n",
    "  - Pass the `performance_metric` function as a parameter to the object.\n",
    "  - Assign this scoring function to the `'scoring_fnc'` variable.\n",
    "- Use [`GridSearchCV`](http://scikit-learn.org/0.17/modules/generated/sklearn.grid_search.GridSearchCV.html) from `sklearn.grid_search` to create a grid search object.\n",
    "  - Pass the variables `'regressor'`, `'params'`, `'scoring_fnc'`, and `'cv_sets'` as parameters to the object. \n",
    "  - Assign the `GridSearchCV` object to the `'grid'` variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import 'make_scorer', 'DecisionTreeRegressor', and 'GridSearchCV'\n",
    "from sklearn.metrics import make_scorer\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "from sklearn.grid_search import GridSearchCV\n",
    "\n",
    "def fit_model(X, y):\n",
    "    \"\"\" Performs grid search over the 'max_depth' parameter for a \n",
    "        decision tree regressor trained on the input data [X, y]. \"\"\"\n",
    "    \n",
    "    # Create cross-validation sets from the training data\n",
    "    # sklearn version 0.18: ShuffleSplit(n_splits=10, test_size=0.1, train_size=None, random_state=None)\n",
    "    # sklearn versiin 0.17: ShuffleSplit(n, n_iter=10, test_size=0.1, train_size=None, random_state=None)\n",
    "    cv_sets = ShuffleSplit(X.shape[0], n_iter = 10, test_size = 0.20, random_state = 0)\n",
    "\n",
    "    # Create a decision tree regressor object\n",
    "    regressor = DecisionTreeRegressor(random_state=0)\n",
    "\n",
    "    # Create a dictionary for the parameter 'max_depth' with a range from 1 to 10\n",
    "    params = {'max_depth': range(1, 11)}\n",
    "\n",
    "    # Transform 'performance_metric' into a scoring function using 'make_scorer' \n",
    "    scoring_fnc = make_scorer(performance_metric)\n",
    "\n",
    "    # Create the grid search cv object --> GridSearchCV()\n",
    "    grid = GridSearchCV(regressor, params, scoring=scoring_fnc, cv=cv_sets)\n",
    "\n",
    "    # Fit the grid search object to the data to compute the optimal model\n",
    "    grid = grid.fit(X, y)\n",
    "\n",
    "    # Return the optimal model after fitting the data\n",
    "    return grid.best_estimator_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Making Predictions\n",
    "Once a model has been trained on a given set of data, it can now be used to make predictions on new sets of input data. In the case of a *decision tree regressor*, the model has learned *what the best questions to ask about the input data are*, and can respond with a prediction for the **target variable**. You can use these predictions to gain information about data where the value of the target variable is unknown — such as data the model was not trained on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 9 - Optimal Model\n",
    "\n",
    "* What maximum depth does the optimal model have? How does this result compare to your guess in **Question 6**?  \n",
    "\n",
    "Run the code block below to fit the decision tree regressor to the training data and produce an optimal model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter 'max_depth' is 4 for the optimal model.\n"
     ]
    }
   ],
   "source": [
    "# Fit the training data to the model using grid search\n",
    "reg = fit_model(X_train, y_train)\n",
    "\n",
    "# Produce the value for 'max_depth'\n",
    "print \"Parameter 'max_depth' is {} for the optimal model.\".format(reg.get_params()['max_depth'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer: **\n",
    "\n",
    "The output for the max_depth param using fit_model was **4**, just as predicted in Question 6 by analyzing the Complexity Curves."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 10 - Predicting Selling Prices\n",
    "Imagine that you were a real estate agent in the Boston area looking to use this model to help price homes owned by your clients that they wish to sell. You have collected the following information from three of your clients:\n",
    "\n",
    "| Feature | Client 1 | Client 2 | Client 3 |\n",
    "| :---: | :---: | :---: | :---: |\n",
    "| Total number of rooms in home | 5 rooms | 4 rooms | 8 rooms |\n",
    "| Neighborhood poverty level (as %) | 17% | 32% | 3% |\n",
    "| Student-teacher ratio of nearby schools | 15-to-1 | 22-to-1 | 12-to-1 |\n",
    "\n",
    "* What price would you recommend each client sell his/her home at? \n",
    "* Do these prices seem reasonable given the values for the respective features? \n",
    "\n",
    "Run the code block below to have your optimized model make predictions for each client's home."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted selling price for Client 1's home: $391,183.33\n",
      "Predicted selling price for Client 2's home: $189,123.53\n",
      "Predicted selling price for Client 3's home: $942,666.67\n"
     ]
    }
   ],
   "source": [
    "# Produce a matrix for client data\n",
    "client_data = [[5, 17, 15], # Client 1\n",
    "               [4, 32, 22], # Client 2\n",
    "               [8, 3, 12]]  # Client 3\n",
    "\n",
    "# Show predictions\n",
    "for i, price in enumerate(reg.predict(client_data)):\n",
    "    print \"Predicted selling price for Client {}'s home: ${:,.2f}\".format(i+1, price)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer: **\n",
    "\n",
    "The output of the predicted selling price is what I would recommend for each client:\n",
    "- Client 1: \\$391,183.33\n",
    "- Client 2: \\$189,123.53\n",
    "- Client 3: \\$942,666.67\n",
    "\n",
    "Using the **Data Exploration** section we can check that **Client 1** and **Client 2** values are bellow the mean(\\$454,342.94) and the median(\\$438,900.00), but this is reasonable since:\n",
    "- Client 2 has few rooms with a high neighborhood poverty level and student-teacher ratio, hence the lowest of the 3 prices and the closest to the minimum price of the dataset(\\$105,000.00).\n",
    "- Client 1 has one more room in comparison to Client 2 and although the student-teacher ratio and poverty level are bellow Client 2, they are still high(poverty level mainly).\n",
    "\n",
    "**Client 3** on other hand has a low neighborhood poverty level, high number of rooms and a small student-teacher ratio, justifying the high price that is close to the maximum price of the dataset(\\$1,024,800.00)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sensitivity\n",
    "An optimal model is not necessarily a robust model. Sometimes, a model is either too complex or too simple to sufficiently generalize to new data. Sometimes, a model could use a learning algorithm that is not appropriate for the structure of the data given. Other times, the data itself could be too noisy or contain too few samples to allow a model to adequately capture the target variable — i.e., the model is underfitted. \n",
    "\n",
    "**Run the code cell below to run the `fit_model` function ten times with different training and testing sets to see how the prediction for a specific client changes with respect to the data it's trained on.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trial 1: $391,183.33\n",
      "Trial 2: $424,935.00\n",
      "Trial 3: $415,800.00\n",
      "Trial 4: $420,622.22\n",
      "Trial 5: $418,377.27\n",
      "Trial 6: $411,931.58\n",
      "Trial 7: $399,663.16\n",
      "Trial 8: $407,232.00\n",
      "Trial 9: $351,577.61\n",
      "Trial 10: $413,700.00\n",
      "\n",
      "Range in prices: $73,357.39\n"
     ]
    }
   ],
   "source": [
    "vs.PredictTrials(features, prices, fit_model, client_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 11 - Applicability\n",
    "\n",
    "* In a few sentences, discuss whether the constructed model should or should not be used in a real-world setting.  \n",
    "\n",
    "**Hint:** Take a look at the range in prices as calculated in the code snippet above. Some questions to answering:\n",
    "- How relevant today is data that was collected from 1978? How important is inflation?\n",
    "- Are the features present in the data sufficient to describe a home? Do you think factors like quality of apppliances in the home, square feet of the plot area, presence of pool or not etc should factor in?\n",
    "- Is the model robust enough to make consistent predictions?\n",
    "- Would data collected in an urban city like Boston be applicable in a rural city?\n",
    "- Is it fair to judge the price of an individual home based on the characteristics of the entire neighborhood?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer: **\n",
    "\n",
    "Although the prices were multiplicatively scaled to account for 35 years of market inflation, the features of the dataset might only have been relevant to 1978 reality, meaning that demographics and other deciding factors have changed a lot since. So I would say this dataset collected from 1978 is not relevant to today market reality.\n",
    "\n",
    "The dataset is only using 3 features that barely describes a house and 2 of those are neighborhood characteristics, focusing the price on the neighborhood and not the house alone, which is not fair. Neighborhood should be factored in but the majority of features should be towards the house: Quality of appliances in the home, square feet of the plot area, presence of pool or not, public transportation, distance from commerce, proximity of parks and many other indicators of life quality are just a few examples of house features that can be influencing the final price.\n",
    "\n",
    "This simplicity negatively reflects on the robustness of this model, since there is a high range in prices(\\$73,357.39) from different splits of the data. Also is important to say that this model came from a urban dataset so it cannot generalize to a rural city since the features that are important to one are way different to another. This model might only be reused to some urban city similar in features to Boston in 1978."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> **Note**: Once you have completed all of the code implementations and successfully answered each question above, you may finalize your work by exporting the iPython Notebook as an HTML document. You can do this by using the menu above and navigating to  \n",
    "**File -> Download as -> HTML (.html)**. Include the finished document along with this notebook as your submission."
   ]
  }
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