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<!DOCTYPE html>
<html>
<head><meta charset="utf-8" />
<title>boston_housing</title>
<script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/2.0.3/jquery.min.js"></script>
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<h1 id="Machine-Learning-Engineer-Nanodegree">Machine Learning Engineer Nanodegree<a class="anchor-link" href="#Machine-Learning-Engineer-Nanodegree">¶</a></h1><h2 id="Model-Evaluation-&-Validation">Model Evaluation & Validation<a class="anchor-link" href="#Model-Evaluation-&-Validation">¶</a></h2><h2 id="Project-1:-Predicting-Boston-Housing-Prices">Project 1: Predicting Boston Housing Prices<a class="anchor-link" href="#Project-1:-Predicting-Boston-Housing-Prices">¶</a></h2><p>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 <strong>'Implementation'</strong> 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!</p>
<p>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 <strong>'Question X'</strong> header. Carefully read each question and provide thorough answers in the following text boxes that begin with <strong>'Answer:'</strong>. Your project submission will be evaluated based on your answers to each of the questions and the implementation you provide.</p>
<blockquote><p><strong>Note:</strong> Code and Markdown cells can be executed using the <strong>Shift + Enter</strong> keyboard shortcut. In addition, Markdown cells can be edited by typically double-clicking the cell to enter edit mode.</p>
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<h2 id="Getting-Started">Getting Started<a class="anchor-link" href="#Getting-Started">¶</a></h2><p>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 <em>good fit</em> 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.</p>
<p>The dataset for this project originates from the <a href="https://archive.ics.uci.edu/ml/datasets/Housing">UCI Machine Learning Repository</a>. 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:</p>
<ul>
<li>16 data points have an <code>'MEDV'</code> value of 50.0. These data points likely contain <strong>missing or censored values</strong> and have been removed.</li>
<li>1 data point has an <code>'RM'</code> value of 8.78. This data point can be considered an <strong>outlier</strong> and has been removed.</li>
<li>The features <code>'RM'</code>, <code>'LSTAT'</code>, <code>'PTRATIO'</code>, and <code>'MEDV'</code> are essential. The remaining <strong>non-relevant features</strong> have been excluded.</li>
<li>The feature <code>'MEDV'</code> has been <strong>multiplicatively scaled</strong> to account for 35 years of market inflation.</li>
</ul>
<p>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.</p>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="c1"># Import libraries necessary for this project</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="kn">as</span> <span class="nn">pd</span>
<span class="kn">import</span> <span class="nn">visuals</span> <span class="kn">as</span> <span class="nn">vs</span> <span class="c1"># Supplementary code</span>
<span class="kn">from</span> <span class="nn">sklearn.cross_validation</span> <span class="kn">import</span> <span class="n">ShuffleSplit</span>
<span class="c1"># Pretty display for notebooks</span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="c1"># Load the Boston housing dataset</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="s1">'housing.csv'</span><span class="p">)</span>
<span class="n">prices</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="s1">'MEDV'</span><span class="p">]</span>
<span class="n">features</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">drop</span><span class="p">(</span><span class="s1">'MEDV'</span><span class="p">,</span> <span class="n">axis</span> <span class="o">=</span> <span class="mi">1</span><span class="p">)</span>
<span class="c1"># Success</span>
<span class="k">print</span> <span class="s2">"Boston housing dataset has {} data points with {} variables each."</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="o">*</span><span class="n">data</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
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<pre>Boston housing dataset has 489 data points with 4 variables each.
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<h2 id="Data-Exploration">Data Exploration<a class="anchor-link" href="#Data-Exploration">¶</a></h2><p>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.</p>
<p>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 <strong>features</strong> and the <strong>target variable</strong>. The <strong>features</strong>, <code>'RM'</code>, <code>'LSTAT'</code>, and <code>'PTRATIO'</code>, give us quantitative information about each data point. The <strong>target variable</strong>, <code>'MEDV'</code>, will be the variable we seek to predict. These are stored in <code>features</code> and <code>prices</code>, respectively.</p>
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<h3 id="Implementation:-Calculate-Statistics">Implementation: Calculate Statistics<a class="anchor-link" href="#Implementation:-Calculate-Statistics">¶</a></h3><p>For your very first coding implementation, you will calculate descriptive statistics about the Boston housing prices. Since <code>numpy</code> 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.</p>
<p>In the code cell below, you will need to implement the following:</p>
<ul>
<li>Calculate the minimum, maximum, mean, median, and standard deviation of <code>'MEDV'</code>, which is stored in <code>prices</code>.<ul>
<li>Store each calculation in their respective variable.</li>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="c1"># TODO: Minimum price of the data</span>
<span class="n">minimum_price</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">amin</span><span class="p">(</span><span class="n">prices</span><span class="p">)</span>
<span class="c1"># TODO: Maximum price of the data</span>
<span class="n">maximum_price</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">amax</span><span class="p">(</span><span class="n">prices</span><span class="p">)</span>
<span class="c1"># TODO: Mean price of the data</span>
<span class="n">mean_price</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">prices</span><span class="p">)</span>
<span class="c1"># TODO: Median price of the data</span>
<span class="n">median_price</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">median</span><span class="p">(</span><span class="n">prices</span><span class="p">)</span>
<span class="c1"># TODO: Standard deviation of prices of the data</span>
<span class="n">std_price</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">prices</span><span class="p">)</span>
<span class="c1"># Show the calculated statistics</span>
<span class="k">print</span> <span class="s2">"Statistics for Boston housing dataset:</span><span class="se">\n</span><span class="s2">"</span>
<span class="k">print</span> <span class="s2">"Minimum price: ${:,.2f}"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">minimum_price</span><span class="p">)</span>
<span class="k">print</span> <span class="s2">"Maximum price: ${:,.2f}"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">maximum_price</span><span class="p">)</span>
<span class="k">print</span> <span class="s2">"Mean price: ${:,.2f}"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">mean_price</span><span class="p">)</span>
<span class="k">print</span> <span class="s2">"Median price ${:,.2f}"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">median_price</span><span class="p">)</span>
<span class="k">print</span> <span class="s2">"Standard deviation of prices: ${:,.2f}"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">std_price</span><span class="p">)</span>
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<pre>Statistics for Boston housing dataset:
Minimum price: $105,000.00
Maximum price: $1,024,800.00
Mean price: $454,342.94
Median price $438,900.00
Standard deviation of prices: $165,171.13
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<h3 id="Question-1---Feature-Observation">Question 1 - Feature Observation<a class="anchor-link" href="#Question-1---Feature-Observation">¶</a></h3><p>As a reminder, we are using three features from the Boston housing dataset: <code>'RM'</code>, <code>'LSTAT'</code>, and <code>'PTRATIO'</code>. For each data point (neighborhood):</p>
<ul>
<li><code>'RM'</code> is the average number of rooms among homes in the neighborhood.</li>
<li><code>'LSTAT'</code> is the percentage of homeowners in the neighborhood considered "lower class" (working poor).</li>
<li><code>'PTRATIO'</code> is the ratio of students to teachers in primary and secondary schools in the neighborhood.</li>
</ul>
<p><em>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 <strong>increase</strong> in the value of <code>'MEDV'</code> or a <strong>decrease</strong> in the value of <code>'MEDV'</code>? Justify your answer for each.</em><br>
<strong>Hint:</strong> Would you expect a home that has an <code>'RM'</code> value of 6 be worth more or less than a home that has an <code>'RM'</code> value of 7?</p>
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<p><strong>Answer</strong>: <em>The target 'MDEV' (or is it 'MEDV' for "median value"?) will increase as 'RM' increases. More rooms equals more square feet of property, hence a larger property value. 'MDEV' would rise as 'LSTAT' decreases, and we can see this using an extreme case: consider a house with an 'LSTAT' of 0. This means no one else in Boston is wealthier than the homeowner, so this house is probably very snazzy. 'PTRATIO' will be inversely related to 'MDEV'. More teachers generally means better schools, which bolsters house prices in a given area.</em></p>
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<hr>
<h2 id="Developing-a-Model">Developing a Model<a class="anchor-link" href="#Developing-a-Model">¶</a></h2><p>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.</p>
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<h3 id="Implementation:-Define-a-Performance-Metric">Implementation: Define a Performance Metric<a class="anchor-link" href="#Implementation:-Define-a-Performance-Metric">¶</a></h3><p>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 <a href="http://stattrek.com/statistics/dictionary.aspx?definition=coefficient_of_determination"><em>coefficient of determination</em></a>, 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.</p>
<p>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 <strong>target variable</strong>. A model with an R<sup>2</sup> of 0 always fails to predict 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 <strong>features</strong>. <em>A model can be given a negative R<sup>2</sup> as well, which indicates that the model is no better than one that naively predicts the mean of the target variable.</em></p>
<p>For the <code>performance_metric</code> function in the code cell below, you will need to implement the following:</p>
<ul>
<li>Use <code>r2_score</code> from <code>sklearn.metrics</code> to perform a performance calculation between <code>y_true</code> and <code>y_predict</code>.</li>
<li>Assign the performance score to the <code>score</code> variable.</li>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="c1"># TODO: Import 'r2_score'</span>
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">r2_score</span>
<span class="k">def</span> <span class="nf">performance_metric</span><span class="p">(</span><span class="n">y_true</span><span class="p">,</span> <span class="n">y_predict</span><span class="p">):</span>
<span class="sd">""" Calculates and returns the performance score between </span>
<span class="sd"> true and predicted values based on the metric chosen. """</span>
<span class="c1"># TODO: Calculate the performance score between 'y_true' and 'y_predict'</span>
<span class="n">score</span> <span class="o">=</span> <span class="n">r2_score</span><span class="p">(</span><span class="n">y_true</span><span class="p">,</span> <span class="n">y_predict</span><span class="p">)</span>
<span class="c1"># Return the score</span>
<span class="k">return</span> <span class="n">score</span>
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<h3 id="Question-2---Goodness-of-Fit">Question 2 - Goodness of Fit<a class="anchor-link" href="#Question-2---Goodness-of-Fit">¶</a></h3><p>Assume that a dataset contains five data points and a model made the following predictions for the target variable:</p>
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<thead><tr>
<th style="text-align:center">True Value</th>
<th style="text-align:center">Prediction</th>
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<td style="text-align:center">3.0</td>
<td style="text-align:center">2.5</td>
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<td style="text-align:center">-0.5</td>
<td style="text-align:center">0.0</td>
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<td style="text-align:center">2.0</td>
<td style="text-align:center">2.1</td>
</tr>
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<td style="text-align:center">7.0</td>
<td style="text-align:center">7.8</td>
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<td style="text-align:center">4.2</td>
<td style="text-align:center">5.3</td>
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</tbody>
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<p><em>Would you consider this model to have successfully captured the variation of the target variable? Why or why not?</em></p>
<p>Run the code cell below to use the <code>performance_metric</code> function and calculate this model's coefficient of determination.</p>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="c1"># Calculate the performance of this model</span>
<span class="n">score</span> <span class="o">=</span> <span class="n">performance_metric</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mf">4.2</span><span class="p">],</span> <span class="p">[</span><span class="mf">2.5</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">2.1</span><span class="p">,</span> <span class="mf">7.8</span><span class="p">,</span> <span class="mf">5.3</span><span class="p">])</span>
<span class="k">print</span> <span class="s2">"Model has a coefficient of determination, R^2, of {:.3f}."</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">score</span><span class="p">)</span>
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<pre>Model has a coefficient of determination, R^2, of 0.923.
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<p><strong>Answer</strong>:<em>Model has a coefficient of determination, R^2, of 0.923.</em></p>
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<h3 id="Implementation:-Shuffle-and-Split-Data">Implementation: Shuffle and Split Data<a class="anchor-link" href="#Implementation:-Shuffle-and-Split-Data">¶</a></h3><p>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.</p>
<p>For the code cell below, you will need to implement the following:</p>
<ul>
<li>Use <code>train_test_split</code> from <code>sklearn.cross_validation</code> to shuffle and split the <code>features</code> and <code>prices</code> data into training and testing sets.<ul>
<li>Split the data into 80% training and 20% testing.</li>
<li>Set the <code>random_state</code> for <code>train_test_split</code> to a value of your choice. This ensures results are consistent.</li>
</ul>
</li>
<li>Assign the train and testing splits to <code>X_train</code>, <code>X_test</code>, <code>y_train</code>, and <code>y_test</code>.</li>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="c1"># TODO: Import 'train_test_split'</span>
<span class="kn">from</span> <span class="nn">sklearn.cross_validation</span> <span class="kn">import</span> <span class="n">train_test_split</span>
<span class="c1"># TODO: Shuffle and split the data into training and testing subsets</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span><span class="n">train_test_split</span><span class="p">(</span><span class="n">features</span><span class="p">,</span> <span class="n">prices</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">,</span> <span class="n">test_size</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span>
<span class="c1"># Success</span>
<span class="k">print</span> <span class="s2">"Training and testing split was successful."</span>
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<pre>Training and testing split was successful.
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<h3 id="Question-3---Training-and-Testing">Question 3 - Training and Testing<a class="anchor-link" href="#Question-3---Training-and-Testing">¶</a></h3><p><em>What is the benefit to splitting a dataset into some ratio of training and testing subsets for a learning algorithm?</em><br>
<strong>Hint:</strong> What could go wrong with not having a way to test your model?</p>
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<p><strong>Answer</strong>: <em> No test data leads to a model with high variance. If you let it loose in the world without testing, it won't generalize well and thus have high prediction error. Simple as that.</em></p>
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<h2 id="Analyzing-Model-Performance">Analyzing Model Performance<a class="anchor-link" href="#Analyzing-Model-Performance">¶</a></h2><p>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 <code>'max_depth'</code> 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.</p>
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<h3 id="Learning-Curves">Learning Curves<a class="anchor-link" href="#Learning-Curves">¶</a></h3><p>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.</p>
<p>Run the code cell below and use these graphs to answer the following question.</p>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="c1"># Produce learning curves for varying training set sizes and maximum depths</span>
<span class="n">vs</span><span class="o">.</span><span class="n">ModelLearning</span><span class="p">(</span><span class="n">features</span><span class="p">,</span> <span class="n">prices</span><span class="p">)</span>
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