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<!DOCTYPE html>
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<meta charset="utf-8" />
<title>Data_Analyst_ND_Project2</title>
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<h1 id="P2:-Analyzing-the-NYC-Subway-Dataset">P2: Analyzing the NYC Subway Dataset<a class="anchor-link" href="#P2:-Analyzing-the-NYC-Subway-Dataset">¶</a></h1><h2 id="Overview">Overview<a class="anchor-link" href="#Overview">¶</a></h2><p>This project consists of two parts. In Part 1 of the project, you should have completed the questions in Problem Sets 2, 3, and 4 in the Introduction to Data Science course.</p>
<p>This document addresses part 2 of the project. Please use this document as a template and answer the following questions to explain your reasoning and conclusion behind your work in the problem sets. You will attach a document with your answers to these questions as part of your final project submission.</p>
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<h3 id="Section-0.-References">Section 0. References<a class="anchor-link" href="#Section-0.-References">¶</a></h3><p><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.mannwhitneyu.html">http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.mannwhitneyu.html</a></p>
<p><a href="https://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test#Assumptions_and_formal_statement_of_hypotheses">https://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test#Assumptions_and_formal_statement_of_hypotheses</a></p>
<p><a href="http://stackoverflow.com/questions/6986986/bin-size-in-matplotlib-histogram">http://stackoverflow.com/questions/6986986/bin-size-in-matplotlib-histogram</a></p>
<p><a href="https://discussions.udacity.com/t/ggplot-has-blank-space-on-right/37448">https://discussions.udacity.com/t/ggplot-has-blank-space-on-right/37448</a></p>
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<div class=" highlight hl-ipython2"><pre><span class="o">%</span><span class="k">matplotlib</span> inline
<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">scipy</span>
<span class="kn">import</span> <span class="nn">scipy.stats</span>
<span class="kn">import</span> <span class="nn">pandas</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">statsmodels.api</span> <span class="kn">as</span> <span class="nn">sm</span>
<span class="kn">from</span> <span class="nn">datetime</span> <span class="kn">import</span> <span class="n">datetime</span>
<span class="kn">from</span> <span class="nn">ggplot</span> <span class="kn">import</span> <span class="o">*</span>
<span class="n">turnstile_weather</span> <span class="o">=</span> <span class="n">pandas</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="s">"./turnstile_data_master_with_weather.csv"</span><span class="p">)</span>
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<h3 id="Section-1.-Statistical-Test">Section 1. Statistical Test<a class="anchor-link" href="#Section-1.-Statistical-Test">¶</a></h3>
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<div class=" highlight hl-ipython2"><pre><span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">turnstile_weather</span><span class="p">[</span><span class="s">'ENTRIESn_hourly'</span><span class="p">][</span><span class="n">turnstile_weather</span><span class="o">.</span><span class="n">rain</span> <span class="o">==</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">bins</span><span class="o">=</span><span class="mi">25</span><span class="p">,</span> <span class="nb">range</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">6000</span><span class="p">),</span> <span class="n">label</span><span class="o">=</span><span class="s">"No Rain"</span><span class="p">)</span>
<span class="n">turnstile_weather</span><span class="p">[</span><span class="s">'ENTRIESn_hourly'</span><span class="p">][</span><span class="n">turnstile_weather</span><span class="o">.</span><span class="n">rain</span> <span class="o">==</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">bins</span><span class="o">=</span><span class="mi">25</span><span class="p">,</span> <span class="nb">range</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">6000</span><span class="p">),</span> <span class="n">label</span><span class="o">=</span><span class="s">"Rain"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">"Histogram of ENTRIESn_hourly"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
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<pre><matplotlib.legend.Legend at 0x7fd50300be50></pre>
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<div class="prompt input_prompt">In [7]:</div>
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<div class=" highlight hl-ipython2"><pre><span class="n">with_rain</span> <span class="o">=</span> <span class="n">turnstile_weather</span><span class="p">[</span><span class="s">'ENTRIESn_hourly'</span><span class="p">][</span><span class="n">turnstile_weather</span><span class="o">.</span><span class="n">rain</span> <span class="o">==</span> <span class="mi">1</span><span class="p">]</span>
<span class="n">without_rain</span> <span class="o">=</span> <span class="n">turnstile_weather</span><span class="p">[</span><span class="s">'ENTRIESn_hourly'</span><span class="p">][</span><span class="n">turnstile_weather</span><span class="o">.</span><span class="n">rain</span> <span class="o">==</span> <span class="mi">0</span><span class="p">]</span>
<span class="n">with_rain_mean</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">with_rain</span><span class="p">)</span>
<span class="n">without_rain_mean</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">without_rain</span><span class="p">)</span>
<span class="n">mwu</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">mannwhitneyu</span><span class="p">(</span><span class="n">with_rain</span><span class="p">,</span> <span class="n">without_rain</span><span class="p">)</span>
<span class="n">U</span> <span class="o">=</span> <span class="n">mwu</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">mwu</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="mi">2</span>
<span class="n">with_rain_mean</span><span class="p">,</span> <span class="n">without_rain_mean</span><span class="p">,</span> <span class="n">U</span><span class="p">,</span> <span class="n">p</span>
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<pre>(1105.4463767458733, 1090.278780151855, 1924409167.0, 0.049999825586979442)</pre>
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<h4 id="1.1-Which-statistical-test-did-you-use-to-analyze-the-NYC-subway-data?-Did-you-use-a-one-tail-or-a-two-tail-P-value?-What-is-the-null-hypothesis?-What-is-your-p-critical-value?">1.1 Which statistical test did you use to analyze the NYC subway data? Did you use a one-tail or a two-tail P value? What is the null hypothesis? What is your p-critical value?<a class="anchor-link" href="#1.1-Which-statistical-test-did-you-use-to-analyze-the-NYC-subway-data?-Did-you-use-a-one-tail-or-a-two-tail-P-value?-What-is-the-null-hypothesis?-What-is-your-p-critical-value?">¶</a></h4><p>I used a Mann-Whitney U-test with two-tailed P-value. The null hypothesis was that the distribution of hourly entries into subway stations in NYC were the same between rainy and non-rain conditions. The alternative hypothesis was that the probability of an hourly entry without rain being greater than an hourly entry with rain was not equal to the probability of an hourly entry with rain being greather than an hourly entry with without rain. We used a two-tailed p-value because we do not specify if the difference during rain is greater than or less than the entries during non-rain. A critical value of 0.05 was used.</p>
<h4 id="1.2-Why-is-this-statistical-test-applicable-to-the-dataset?-In-particular,-consider-the-assumptions-that-the-test-is-making-about-the-distribution-of-ridership-in-the-two-samples.">1.2 Why is this statistical test applicable to the dataset? In particular, consider the assumptions that the test is making about the distribution of ridership in the two samples.<a class="anchor-link" href="#1.2-Why-is-this-statistical-test-applicable-to-the-dataset?-In-particular,-consider-the-assumptions-that-the-test-is-making-about-the-distribution-of-ridership-in-the-two-samples.">¶</a></h4><p>We are using Mann-Whitney U-test because the data is non-normal (see histogram above).</p>
<h4 id="1.3-What-results-did-you-get-from-this-statistical-test?-These-should-include-the-following-numerical-values:-p-values,-as-well-as-the-means-for-each-of-the-two-samples-under-test.">1.3 What results did you get from this statistical test? These should include the following numerical values: p-values, as well as the means for each of the two samples under test.<a class="anchor-link" href="#1.3-What-results-did-you-get-from-this-statistical-test?-These-should-include-the-following-numerical-values:-p-values,-as-well-as-the-means-for-each-of-the-two-samples-under-test.">¶</a></h4><p>Mean hourly entries with rain: 1105</p>
<p>Mean hourly entries without rain: 1090</p>
<p>U-statistic: 1924409167</p>
<p>p-value: 0.0499998</p>
<h4 id="1.4-What-is-the-significance-and-interpretation-of-these-results?">1.4 What is the significance and interpretation of these results?<a class="anchor-link" href="#1.4-What-is-the-significance-and-interpretation-of-these-results?">¶</a></h4><p>We reject the null hypothesis since the p-value is under 0.05 and conclude that the distribution of hourly entries to NYC subway stations are not the same between rain and no-rain conditions. The mean entries are higher for rain suggesting that there is an increased in subway ridership when it is rainning.</p>
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<h3 id="Section-2.-Linear-Regression">Section 2. Linear Regression<a class="anchor-link" href="#Section-2.-Linear-Regression">¶</a></h3>
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<div class=" highlight hl-ipython2"><pre><span class="k">def</span> <span class="nf">linear_regression</span><span class="p">(</span><span class="n">features</span><span class="p">,</span> <span class="n">values</span><span class="p">):</span>
<span class="n">features</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">add_constant</span><span class="p">(</span><span class="n">features</span><span class="p">)</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">OLS</span><span class="p">(</span><span class="n">values</span><span class="p">,</span> <span class="n">features</span><span class="p">)</span>
<span class="n">results</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">fit</span><span class="p">()</span>
<span class="n">intercept</span> <span class="o">=</span> <span class="n">results</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">params</span> <span class="o">=</span> <span class="n">results</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span>
<span class="k">return</span> <span class="n">intercept</span><span class="p">,</span> <span class="n">params</span>
<span class="k">def</span> <span class="nf">predictions</span><span class="p">(</span><span class="n">dataframe</span><span class="p">):</span>
<span class="n">features</span> <span class="o">=</span> <span class="n">dataframe</span><span class="p">[[</span><span class="s">'precipi'</span><span class="p">,</span> <span class="s">'Hour'</span><span class="p">,</span> <span class="s">'meandewpti'</span><span class="p">]]</span>
<span class="n">dummy_units</span> <span class="o">=</span> <span class="n">pandas</span><span class="o">.</span><span class="n">get_dummies</span><span class="p">(</span><span class="n">dataframe</span><span class="p">[</span><span class="s">'UNIT'</span><span class="p">],</span> <span class="n">prefix</span><span class="o">=</span><span class="s">'unit'</span><span class="p">)</span>
<span class="n">features</span> <span class="o">=</span> <span class="n">features</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">dummy_units</span><span class="p">)</span>
<span class="c"># Values</span>
<span class="n">values</span> <span class="o">=</span> <span class="n">dataframe</span><span class="p">[</span><span class="s">'ENTRIESn_hourly'</span><span class="p">]</span>
<span class="c"># Perform linear regression</span>
<span class="n">intercept</span><span class="p">,</span> <span class="n">params</span> <span class="o">=</span> <span class="n">linear_regression</span><span class="p">(</span><span class="n">features</span><span class="p">,</span> <span class="n">values</span><span class="p">)</span>
<span class="n">predictions</span> <span class="o">=</span> <span class="n">intercept</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">features</span><span class="p">,</span> <span class="n">params</span><span class="p">)</span>
<span class="k">return</span> <span class="n">intercept</span><span class="p">,</span> <span class="n">params</span><span class="p">,</span> <span class="n">predictions</span>
<span class="p">[</span><span class="n">model_intercept</span><span class="p">,</span> <span class="n">model_param</span><span class="p">,</span> <span class="n">model_predictions</span><span class="p">]</span> <span class="o">=</span> <span class="n">predictions</span><span class="p">(</span><span class="n">turnstile_weather</span><span class="p">)</span>
<span class="p">[</span><span class="n">model_intercept</span><span class="p">,</span> <span class="n">model_param</span><span class="p">,</span> <span class="n">model_predictions</span><span class="p">]</span>
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<pre>[1067.8853402933114, precipi 71.007407
Hour 67.404459
meandewpti -4.305779
unit_R001 2429.643537
unit_R002 -633.258716
unit_R003 -1331.370915
unit_R004 -1005.772236
unit_R005 -1019.721870
unit_R006 -948.229638
unit_R007 -1167.834450
unit_R008 -1134.788593
unit_R009 -1206.303993
unit_R010 3030.572162
unit_R011 6515.154760
unit_R012 5952.924292
unit_R013 964.613397
unit_R014 2486.856108
unit_R015 625.558242
unit_R016 -566.458675
unit_R017 2709.515977
unit_R018 4422.736911
unit_R019 1376.875155
unit_R020 4982.433186
unit_R021 2947.088351
unit_R022 7104.429397
unit_R023 5027.022404
unit_R024 1506.794471
unit_R025 3513.349584
unit_R027 1430.501172
unit_R028 768.809505
...
unit_R450 -1031.322375
unit_R451 -605.484763
unit_R452 4214.154051
unit_R453 314.802860
unit_R454 -1342.371685
unit_R455 -1396.035416
unit_R456 -1268.747590
unit_R459 -1419.432810
unit_R460 15.771944
unit_R461 1564.606913
unit_R462 497.468509
unit_R463 1580.191813
unit_R464 -1538.832289
unit_R468 -1079.202679
unit_R469 -1075.948027
unit_R535 -1084.212893
unit_R536 -1070.596746
unit_R540 -1368.620878
unit_R541 -1475.370359
unit_R542 -1495.262626
unit_R543 -1532.082922
unit_R544 -1545.657044
unit_R545 -1495.933645
unit_R546 -1357.000541
unit_R547 -1463.083726
unit_R548 -1428.608026
unit_R549 -1569.125713
unit_R550 -1530.927278
unit_R551 -1504.352286
unit_R552 -1439.311437
dtype: float64, array([ 3397.00794908, 3666.62578583, 3936.24362259, ..., 906.67562972,
906.67562972, 906.67562972])]</pre>
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<div class=" highlight hl-ipython2"><pre><span class="n">r_data</span> <span class="o">=</span> <span class="n">turnstile_weather</span><span class="p">[</span><span class="s">'ENTRIESn_hourly'</span><span class="p">]</span>
<span class="n">r_squared</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">r_data</span><span class="o">-</span><span class="n">model_predictions</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="nb">sum</span><span class="p">((</span><span class="n">r_data</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">r_data</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
<span class="n">r_squared</span>
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<pre>0.45795994209043134</pre>
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<div class=" highlight hl-ipython2"><pre><span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">resid</span> <span class="o">=</span> <span class="n">turnstile_weather</span><span class="p">[</span><span class="s">'ENTRIESn_hourly'</span><span class="p">]</span> <span class="o">-</span> <span class="n">model_predictions</span>
<span class="p">(</span><span class="n">resid</span><span class="p">)</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">bins</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="nb">min</span><span class="p">(</span><span class="n">resid</span><span class="p">)),</span> <span class="nb">int</span><span class="p">(</span><span class="nb">max</span><span class="p">(</span><span class="n">resid</span><span class="p">))</span> <span class="o">+</span> <span class="mi">100</span><span class="p">,</span> <span class="mi">100</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">'Histogram residuals'</span><span class="p">)</span>
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<pre><matplotlib.text.Text at 0x7fd5027f0f90></pre>
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<h4 id="2.1-What-approach-did-you-use-to-compute-the-coefficients-theta-and-produce-prediction-for-ENTRIESn_hourly-in-your-regression-model:">2.1 What approach did you use to compute the coefficients theta and produce prediction for ENTRIESn_hourly in your regression model:<a class="anchor-link" href="#2.1-What-approach-did-you-use-to-compute-the-coefficients-theta-and-produce-prediction-for-ENTRIESn_hourly-in-your-regression-model:">¶</a></h4><p>a. OLS using Statsmodels</p>
<h4 id="2.2-What-features-(input-variables)-did-you-use-in-your-model?-Did-you-use-any-dummy-variables-as-part-of-your-features?">2.2 What features (input variables) did you use in your model? Did you use any dummy variables as part of your features?<a class="anchor-link" href="#2.2-What-features-(input-variables)-did-you-use-in-your-model?-Did-you-use-any-dummy-variables-as-part-of-your-features?">¶</a></h4><p>I used precipitation, hour, mean dew point station. Station was a dummy variable.</p>
<h4 id="2.3-Why-did-you-select-these-features-in-your-model?-We-are-looking-for-specific-reasons-that-lead-you-to-believe-that">2.3 Why did you select these features in your model? We are looking for specific reasons that lead you to believe that<a class="anchor-link" href="#2.3-Why-did-you-select-these-features-in-your-model?-We-are-looking-for-specific-reasons-that-lead-you-to-believe-that">¶</a></h4><p>I used intuition for this model. I thought including station information was very important since different stations have vastly different number of riders. I included precipitation instead of rain because it is a quantitative matric (rain is boolean).</p>
<h4 id="2.4-What-are-the-parameters-(also-known-as-"coefficients"-or-"weights")-of-the-non-dummy-features-in-your-linear-regression-model?">2.4 What are the parameters (also known as "coefficients" or "weights") of the non-dummy features in your linear regression model?<a class="anchor-link" href="#2.4-What-are-the-parameters-(also-known-as-"coefficients"-or-"weights")-of-the-non-dummy-features-in-your-linear-regression-model?">¶</a></h4><p>`
precipi 71.007407
Hour 67.404459
meandewpti -4.305779
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<h4 id="2.5-What-is-your-model’s-R^2-(coefficients-of-determination)-value?">2.5 What is your model’s R^2 (coefficients of determination) value?<a class="anchor-link" href="#2.5-What-is-your-model’s-R^2-(coefficients-of-determination)-value?">¶</a></h4><p>0.458</p>
<h4 id="2.6-What-does-this-R^2-value-mean-for-the-goodness-of-fit-for-your-regression-model?-Do-you-think-this-linear-model-to-predict-ridership-is-appropriate-for-this-dataset,-given-this-R^2-value?">2.6 What does this R^2 value mean for the goodness of fit for your regression model? Do you think this linear model to predict ridership is appropriate for this dataset, given this R^2 value?<a class="anchor-link" href="#2.6-What-does-this-R^2-value-mean-for-the-goodness-of-fit-for-your-regression-model?-Do-you-think-this-linear-model-to-predict-ridership-is-appropriate-for-this-dataset,-given-this-R^2-value?">¶</a></h4><p>45.8% of the variation of hourly entries of NYC subway stations is explained by the selected features. The residuals are normally distributed around 0 which is a good sign, however, the range is quite large especially compared to the mean hourly entries is only around 1000.</p>
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<h3 id="Section-3.-Visualization">Section 3. Visualization<a class="anchor-link" href="#Section-3.-Visualization">¶</a></h3><p>Please include two visualizations that show the relationships between two or more variables in the NYC subway data.</p>
<p>Remember to add appropriate titles and axes labels to your plots. Also, please add a short description below each figure commenting on the key insights depicted in the figure.</p>
<h4 id="3.1-One-visualization-should-contain-two-histograms:-one-of--ENTRIESn_hourly-for-rainy-days-and-one-of-ENTRIESn_hourly-for-non-rainy-days.">3.1 One visualization should contain two histograms: one of ENTRIESn_hourly for rainy days and one of ENTRIESn_hourly for non-rainy days.<a class="anchor-link" href="#3.1-One-visualization-should-contain-two-histograms:-one-of--ENTRIESn_hourly-for-rainy-days-and-one-of-ENTRIESn_hourly-for-non-rainy-days.">¶</a></h4><ul>
<li>You can combine the two histograms in a single plot or you can use two separate plots.</li>
<li>If you decide to use to two separate plots for the two histograms, please ensure that the x-axis limits for both of the plots are identical. It is much easier to compare the two in that case.</li>
<li>For the histograms, you should have intervals representing the volume of ridership (value of ENTRIESn_hourly) on the x-axis and the frequency of occurrence on the y-axis. For example, each interval (along the x-axis), the height of the bar for this interval will represent the number of records (rows in our data) that have ENTRIESn_hourly that falls in this interval.</li>
<li>Remember to increase the number of bins in the histogram (by having larger number of bars). The default bin width is not sufficient to capture the variability in the two samples. </li>
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<div class=" highlight hl-ipython2"><pre><span class="p">[</span><span class="nb">max</span><span class="p">(</span><span class="n">turnstile_weather</span><span class="p">[</span><span class="s">'ENTRIESn_hourly'</span><span class="p">]),</span> <span class="nb">min</span><span class="p">(</span><span class="n">turnstile_weather</span><span class="p">[</span><span class="s">'ENTRIESn_hourly'</span><span class="p">])]</span>
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<pre>[51839.0, 0.0]</pre>
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<div class=" highlight hl-ipython2"><pre><span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">turnstile_weather</span><span class="p">[</span><span class="s">'ENTRIESn_hourly'</span><span class="p">][</span><span class="n">turnstile_weather</span><span class="o">.</span><span class="n">rain</span> <span class="o">==</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">bins</span><span class="o">=</span><span class="mi">200</span><span class="p">,</span> <span class="nb">range</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">51839</span><span class="p">),</span> <span class="n">label</span><span class="o">=</span><span class="s">"No Rain"</span><span class="p">)</span>
<span class="n">turnstile_weather</span><span class="p">[</span><span class="s">'ENTRIESn_hourly'</span><span class="p">][</span><span class="n">turnstile_weather</span><span class="o">.</span><span class="n">rain</span> <span class="o">==</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">bins</span><span class="o">=</span><span class="mi">200</span><span class="p">,</span> <span class="nb">range</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">51839</span><span class="p">),</span> <span class="n">label</span><span class="o">=</span><span class="s">"Rain"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">"Histogram of ENTRIESn_hourly"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s">'Number of entries per hour'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
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<pre><matplotlib.legend.Legend at 0x7f32db246e90></pre>
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