weather_project.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analyzing Subway Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Exploratory Data Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this project I am using data from https://s3.amazonaws.com/content.udacity-data.com/courses/ud359/turnstile_data_master_with_weather.csv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>UNIT</th>\n",
       "      <th>DATEn</th>\n",
       "      <th>TIMEn</th>\n",
       "      <th>Hour</th>\n",
       "      <th>DESCn</th>\n",
       "      <th>ENTRIESn_hourly</th>\n",
       "      <th>EXITSn_hourly</th>\n",
       "      <th>maxpressurei</th>\n",
       "      <th>maxdewpti</th>\n",
       "      <th>...</th>\n",
       "      <th>meandewpti</th>\n",
       "      <th>meanpressurei</th>\n",
       "      <th>fog</th>\n",
       "      <th>rain</th>\n",
       "      <th>meanwindspdi</th>\n",
       "      <th>mintempi</th>\n",
       "      <th>meantempi</th>\n",
       "      <th>maxtempi</th>\n",
       "      <th>precipi</th>\n",
       "      <th>thunder</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>R001</td>\n",
       "      <td>2011-05-01</td>\n",
       "      <td>01:00:00</td>\n",
       "      <td>1</td>\n",
       "      <td>REGULAR</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>30.31</td>\n",
       "      <td>42.0</td>\n",
       "      <td>...</td>\n",
       "      <td>39.0</td>\n",
       "      <td>30.27</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>69.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>R001</td>\n",
       "      <td>2011-05-01</td>\n",
       "      <td>05:00:00</td>\n",
       "      <td>5</td>\n",
       "      <td>REGULAR</td>\n",
       "      <td>217.0</td>\n",
       "      <td>553.0</td>\n",
       "      <td>30.31</td>\n",
       "      <td>42.0</td>\n",
       "      <td>...</td>\n",
       "      <td>39.0</td>\n",
       "      <td>30.27</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>69.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>R001</td>\n",
       "      <td>2011-05-01</td>\n",
       "      <td>09:00:00</td>\n",
       "      <td>9</td>\n",
       "      <td>REGULAR</td>\n",
       "      <td>890.0</td>\n",
       "      <td>1262.0</td>\n",
       "      <td>30.31</td>\n",
       "      <td>42.0</td>\n",
       "      <td>...</td>\n",
       "      <td>39.0</td>\n",
       "      <td>30.27</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>69.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>R001</td>\n",
       "      <td>2011-05-01</td>\n",
       "      <td>13:00:00</td>\n",
       "      <td>13</td>\n",
       "      <td>REGULAR</td>\n",
       "      <td>2451.0</td>\n",
       "      <td>3708.0</td>\n",
       "      <td>30.31</td>\n",
       "      <td>42.0</td>\n",
       "      <td>...</td>\n",
       "      <td>39.0</td>\n",
       "      <td>30.27</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>69.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>R001</td>\n",
       "      <td>2011-05-01</td>\n",
       "      <td>17:00:00</td>\n",
       "      <td>17</td>\n",
       "      <td>REGULAR</td>\n",
       "      <td>4400.0</td>\n",
       "      <td>2501.0</td>\n",
       "      <td>30.31</td>\n",
       "      <td>42.0</td>\n",
       "      <td>...</td>\n",
       "      <td>39.0</td>\n",
       "      <td>30.27</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>69.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 22 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0  UNIT       DATEn     TIMEn  Hour    DESCn  ENTRIESn_hourly  \\\n",
       "0           0  R001  2011-05-01  01:00:00     1  REGULAR              0.0   \n",
       "1           1  R001  2011-05-01  05:00:00     5  REGULAR            217.0   \n",
       "2           2  R001  2011-05-01  09:00:00     9  REGULAR            890.0   \n",
       "3           3  R001  2011-05-01  13:00:00    13  REGULAR           2451.0   \n",
       "4           4  R001  2011-05-01  17:00:00    17  REGULAR           4400.0   \n",
       "\n",
       "   EXITSn_hourly  maxpressurei  maxdewpti   ...     meandewpti  meanpressurei  \\\n",
       "0            0.0         30.31       42.0   ...           39.0          30.27   \n",
       "1          553.0         30.31       42.0   ...           39.0          30.27   \n",
       "2         1262.0         30.31       42.0   ...           39.0          30.27   \n",
       "3         3708.0         30.31       42.0   ...           39.0          30.27   \n",
       "4         2501.0         30.31       42.0   ...           39.0          30.27   \n",
       "\n",
       "   fog  rain  meanwindspdi  mintempi  meantempi  maxtempi  precipi  thunder  \n",
       "0  0.0   0.0           5.0      50.0       60.0      69.0      0.0      0.0  \n",
       "1  0.0   0.0           5.0      50.0       60.0      69.0      0.0      0.0  \n",
       "2  0.0   0.0           5.0      50.0       60.0      69.0      0.0      0.0  \n",
       "3  0.0   0.0           5.0      50.0       60.0      69.0      0.0      0.0  \n",
       "4  0.0   0.0           5.0      50.0       60.0      69.0      0.0      0.0  \n",
       "\n",
       "[5 rows x 22 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas\n",
    "data = pandas.read_csv(\"turnstile_data_master_with_weather.csv\")\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>Hour</th>\n",
       "      <th>ENTRIESn_hourly</th>\n",
       "      <th>EXITSn_hourly</th>\n",
       "      <th>maxpressurei</th>\n",
       "      <th>maxdewpti</th>\n",
       "      <th>mindewpti</th>\n",
       "      <th>minpressurei</th>\n",
       "      <th>meandewpti</th>\n",
       "      <th>meanpressurei</th>\n",
       "      <th>fog</th>\n",
       "      <th>rain</th>\n",
       "      <th>meanwindspdi</th>\n",
       "      <th>mintempi</th>\n",
       "      <th>meantempi</th>\n",
       "      <th>maxtempi</th>\n",
       "      <th>precipi</th>\n",
       "      <th>thunder</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>131951.000000</td>\n",
       "      <td>131951.000000</td>\n",
       "      <td>131951.000000</td>\n",
       "      <td>131951.000000</td>\n",
       "      <td>131951.000000</td>\n",
       "      <td>131951.000000</td>\n",
       "      <td>131951.000000</td>\n",
       "      <td>131951.000000</td>\n",
       "      <td>131951.000000</td>\n",
       "      <td>131951.000000</td>\n",
       "      <td>131951.000000</td>\n",
       "      <td>131951.000000</td>\n",
       "      <td>131951.000000</td>\n",
       "      <td>131951.000000</td>\n",
       "      <td>131951.000000</td>\n",
       "      <td>131951.000000</td>\n",
       "      <td>131951.000000</td>\n",
       "      <td>131951.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>65975.000000</td>\n",
       "      <td>10.896158</td>\n",
       "      <td>1095.348478</td>\n",
       "      <td>886.890838</td>\n",
       "      <td>30.031894</td>\n",
       "      <td>57.241302</td>\n",
       "      <td>48.259013</td>\n",
       "      <td>29.892714</td>\n",
       "      <td>52.703526</td>\n",
       "      <td>29.965077</td>\n",
       "      <td>0.167100</td>\n",
       "      <td>0.334245</td>\n",
       "      <td>5.543065</td>\n",
       "      <td>56.169775</td>\n",
       "      <td>64.269729</td>\n",
       "      <td>71.769968</td>\n",
       "      <td>0.172276</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>38091.117022</td>\n",
       "      <td>6.892084</td>\n",
       "      <td>2337.015421</td>\n",
       "      <td>2008.604886</td>\n",
       "      <td>0.125689</td>\n",
       "      <td>8.770891</td>\n",
       "      <td>11.305312</td>\n",
       "      <td>0.146384</td>\n",
       "      <td>9.943590</td>\n",
       "      <td>0.130461</td>\n",
       "      <td>0.373066</td>\n",
       "      <td>0.471728</td>\n",
       "      <td>1.982441</td>\n",
       "      <td>6.338875</td>\n",
       "      <td>6.568289</td>\n",
       "      <td>7.627218</td>\n",
       "      <td>0.429005</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>29.740000</td>\n",
       "      <td>39.000000</td>\n",
       "      <td>22.000000</td>\n",
       "      <td>29.540000</td>\n",
       "      <td>31.000000</td>\n",
       "      <td>29.640000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>46.000000</td>\n",
       "      <td>55.000000</td>\n",
       "      <td>58.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>32987.500000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>39.000000</td>\n",
       "      <td>32.000000</td>\n",
       "      <td>29.960000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>38.000000</td>\n",
       "      <td>29.840000</td>\n",
       "      <td>45.000000</td>\n",
       "      <td>29.910000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>52.000000</td>\n",
       "      <td>60.000000</td>\n",
       "      <td>65.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>65975.000000</td>\n",
       "      <td>12.000000</td>\n",
       "      <td>279.000000</td>\n",
       "      <td>232.000000</td>\n",
       "      <td>30.030000</td>\n",
       "      <td>57.000000</td>\n",
       "      <td>51.000000</td>\n",
       "      <td>29.910000</td>\n",
       "      <td>54.000000</td>\n",
       "      <td>29.960000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>54.000000</td>\n",
       "      <td>63.000000</td>\n",
       "      <td>71.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>98962.500000</td>\n",
       "      <td>17.000000</td>\n",
       "      <td>1109.000000</td>\n",
       "      <td>847.000000</td>\n",
       "      <td>30.100000</td>\n",
       "      <td>64.000000</td>\n",
       "      <td>55.000000</td>\n",
       "      <td>29.970000</td>\n",
       "      <td>60.000000</td>\n",
       "      <td>30.050000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>60.000000</td>\n",
       "      <td>68.000000</td>\n",
       "      <td>78.000000</td>\n",
       "      <td>0.100000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>131950.000000</td>\n",
       "      <td>23.000000</td>\n",
       "      <td>51839.000000</td>\n",
       "      <td>45249.000000</td>\n",
       "      <td>30.310000</td>\n",
       "      <td>70.000000</td>\n",
       "      <td>66.000000</td>\n",
       "      <td>30.230000</td>\n",
       "      <td>68.000000</td>\n",
       "      <td>30.270000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>12.000000</td>\n",
       "      <td>70.000000</td>\n",
       "      <td>78.000000</td>\n",
       "      <td>86.000000</td>\n",
       "      <td>2.180000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Unnamed: 0           Hour  ENTRIESn_hourly  EXITSn_hourly  \\\n",
       "count  131951.000000  131951.000000    131951.000000  131951.000000   \n",
       "mean    65975.000000      10.896158      1095.348478     886.890838   \n",
       "std     38091.117022       6.892084      2337.015421    2008.604886   \n",
       "min         0.000000       0.000000         0.000000       0.000000   \n",
       "25%     32987.500000       5.000000        39.000000      32.000000   \n",
       "50%     65975.000000      12.000000       279.000000     232.000000   \n",
       "75%     98962.500000      17.000000      1109.000000     847.000000   \n",
       "max    131950.000000      23.000000     51839.000000   45249.000000   \n",
       "\n",
       "        maxpressurei      maxdewpti      mindewpti   minpressurei  \\\n",
       "count  131951.000000  131951.000000  131951.000000  131951.000000   \n",
       "mean       30.031894      57.241302      48.259013      29.892714   \n",
       "std         0.125689       8.770891      11.305312       0.146384   \n",
       "min        29.740000      39.000000      22.000000      29.540000   \n",
       "25%        29.960000      50.000000      38.000000      29.840000   \n",
       "50%        30.030000      57.000000      51.000000      29.910000   \n",
       "75%        30.100000      64.000000      55.000000      29.970000   \n",
       "max        30.310000      70.000000      66.000000      30.230000   \n",
       "\n",
       "          meandewpti  meanpressurei            fog           rain  \\\n",
       "count  131951.000000  131951.000000  131951.000000  131951.000000   \n",
       "mean       52.703526      29.965077       0.167100       0.334245   \n",
       "std         9.943590       0.130461       0.373066       0.471728   \n",
       "min        31.000000      29.640000       0.000000       0.000000   \n",
       "25%        45.000000      29.910000       0.000000       0.000000   \n",
       "50%        54.000000      29.960000       0.000000       0.000000   \n",
       "75%        60.000000      30.050000       0.000000       1.000000   \n",
       "max        68.000000      30.270000       1.000000       1.000000   \n",
       "\n",
       "        meanwindspdi       mintempi      meantempi       maxtempi  \\\n",
       "count  131951.000000  131951.000000  131951.000000  131951.000000   \n",
       "mean        5.543065      56.169775      64.269729      71.769968   \n",
       "std         1.982441       6.338875       6.568289       7.627218   \n",
       "min         1.000000      46.000000      55.000000      58.000000   \n",
       "25%         5.000000      52.000000      60.000000      65.000000   \n",
       "50%         5.000000      54.000000      63.000000      71.000000   \n",
       "75%         6.000000      60.000000      68.000000      78.000000   \n",
       "max        12.000000      70.000000      78.000000      86.000000   \n",
       "\n",
       "             precipi   thunder  \n",
       "count  131951.000000  131951.0  \n",
       "mean        0.172276       0.0  \n",
       "std         0.429005       0.0  \n",
       "min         0.000000       0.0  \n",
       "25%         0.000000       0.0  \n",
       "50%         0.000000       0.0  \n",
       "75%         0.100000       0.0  \n",
       "max         2.180000       0.0  "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have 131951 rows."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we perform any analysis, it might be useful to take a look at the data we're hoping to analyze. More specifically, let's examine the hourly entries in our NYC subway data and determine what distribution the data follows. .\n",
    "    \n",
    "Let's plot two histograms on the same axes to show hourly entries when raining vs. when not raining. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1177ab6d8>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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tybmV58yqcW7lObPW56LHatHR0VF3F9qScyvPmVXj3MpzZq3Pt6EYIt+GwszM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\n1+/y1M7GOG7FOWaNcdyKc8w6X1ckPRHxgTrKnEu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pu9IjtRKenK8BcyV9kpRUfoDNe8TM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\nmVlPcNJjZmZmPcFJj5mZmfWE/wejsrhqckZdDAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11762ecc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "plt.figure()\n",
    "plt.xlim(0, 6000)\n",
    "\n",
    "data[data['rain'] == 0.0]['ENTRIESn_hourly'].hist(bins=200)\n",
    "data[data['rain'] == 1.0]['ENTRIESn_hourly'].hist(bins=200)\n",
    "plt.title(\"'ENTRIESn_hourly' Rainy Days vs. Nonrainy Days\")\n",
    "plt.xlabel(\"Entries Hourly\")\n",
    "plt.ylabel(\"Frequency\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Statistical Tests"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our data is not normally distributed. Thus, we cannot run Welch's test. \n",
    "\n",
    "Let's take the means and run the Mann Whitney U-test on the ENTRIESn_hourly column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import scipy.stats\n",
    "\n",
    "with_rain_mean = data[data['rain'] == 1.0]['ENTRIESn_hourly'].mean()\n",
    "without_rain_mean = data[data['rain'] == 0.0]['ENTRIESn_hourly'].mean()\n",
    "\n",
    "# Mann-Whitney U-Test\n",
    "U, p = scipy.stats.mannwhitneyu(data[data['rain'] == 1.0]['ENTRIESn_hourly'], data[data['rain'] == 0.0]['ENTRIESn_hourly'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1105.4463767458733\n",
      "1090.278780151855\n",
      "U =  1924409167.0\n",
      "p =  0.0249403922945\n"
     ]
    }
   ],
   "source": [
    "print (with_rain_mean)\n",
    "print (without_rain_mean)\n",
    "print (\"U = \", U)\n",
    "print (\"p = \", p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "My null hypothesis is that the distributions of both groups (rainy and notrainy days) are identical, so that there is a 50% probability that an observation from a value randomly selected from one population exceeds an observation randomly selected from the other population."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "P values less than 0.05 are often reported as “statistically significant”, and interpreted as being small enough to justify rejection of the null hypothesis. Thus, I can make a conclusion that we have different distributions for rainy and not rainy days."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Implementation of Linear Regression in Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def normalize_features(df):\n",
    "    mu = df.mean()\n",
    "    sigma = df.std()\n",
    "    \n",
    "    if (sigma == 0).any():\n",
    "        raise Exception(\"One or more features had the same value for all samples, and thus could \" + \\\n",
    "                         \"not be normalized. Please do not include features with only a single value \" + \\\n",
    "                         \"in your model.\")\n",
    "    df_normalized = (df - df.mean()) / df.std()\n",
    "    return df_normalized, mu, sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def compute_cost(features, values, theta):\n",
    "    m = len(values)\n",
    "    sum_of_square_errors = np.square(np.dot(features, theta) - values).sum()\n",
    "    cost = sum_of_square_errors / (2*m)\n",
    "    return cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def gradient_descent(features, values, theta, alpha, num_iterations):\n",
    "    m = len(values)\n",
    "    cost_history = []\n",
    "\n",
    "    for i in range(num_iterations):\n",
    "        pr_val = np.dot(features, theta)\n",
    "        theta = theta - alpha/m * np.dot((pr_val - values), features)\n",
    "        cost = compute_cost(features, values, theta)\n",
    "        cost_history.append(cost)\n",
    "    return theta, pandas.Series(cost_history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Select Features \n",
    "features = data[['rain', 'precipi', 'Hour', 'meantempi', 'fog']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Add UNIT to features using dummy variables\n",
    "dummy_units = pandas.get_dummies(data['UNIT'], prefix='unit')\n",
    "features = features.join(dummy_units)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Values\n",
    "values = data['ENTRIESn_hourly']\n",
    "m = len(values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "features, mu, sigma = normalize_features(features)\n",
    "features['ones'] = np.ones(m) # Add a column of 1s (y intercept)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Convert features and values to numpy arrays\n",
    "features_array = np.array(features)\n",
    "values_array = np.array(values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "471"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(features_array[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Set values for alpha, number of iterations.\n",
    "alpha = 0.01 \n",
    "num_iterations = 75"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Initialize theta, perform gradient descent\n",
    "theta_gradient_descent = np.zeros(len(features.columns))\n",
    "theta_gradient_descent, cost_history = gradient_descent(features_array, \n",
    "                                                            values_array, \n",
    "                                                            theta_gradient_descent, \n",
    "                                                            alpha, \n",
    "                                                            num_iterations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10d39a908>"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TQ4YM4YwzzuDMM89kyZIlPPTQQzRv3pxevXrtdB41a9bkjDPOYNKkSey9997bLDkuFttb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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d39dd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cost_df = pandas.DataFrame({\n",
    "      'Cost_History': cost_history,\n",
    "      'Iteration': range(len(cost_history))\n",
    "   })\n",
    "cost_df.plot(x='Iteration', y='Cost_History')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "predictions = np.dot(features_array, theta_gradient_descent)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#coefficient of determination\n",
    "def compute_r_squared(data, predictions):\n",
    "    r_squared = 1 - np.sum((data - predictions)**2) / np.sum((data - np.mean(data))**2)\n",
    "    return r_squared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.30638411548946054"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compute_r_squared(values_array, predictions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Plotting Residuals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's  make a histogram of the residuals (the difference between the original hourly entry data and the predicted values)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11cfedcc0>"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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77wCuA5ab2THNxSBZajQaeXehgpR5aBrn4Snzcpvo4ZATAQeeT00/Pz4E1GdmN5vZWxPz\n5hLt9XhgcIK77wb6gfnxpHnAvrh4GXR/vK5zE22ecPfkCN0BnAC8c2KbJZNp2bJleXehgpR5aBrn\n4Snzcht3gWJmRnSoptvdn0zM+hZwJfDbRA8E+QCwPW4P0SGfV939pdQi98bzBts8m5zp7geJCqFk\nm70jLINEGymAzs7OvLtQQZ15d6ByNM7DU+blNpE9KDcDvwVcnpzo7ne6+73u/gN33wZcApwDnD+B\ndU2qRYsWUavVhrzmz5/P1q1bh7TbuXMntVpt2PuXL19OV1fXkGm9vb3UarVhuxzXrFkz7Fr9/v5+\narXasCdxbtiwgVWrVg2ZNjAwQK1Wo7u7e8j0er1Oe3v7sL4tXry4cNvR1tZWiu2AfD6Pjo6OYW1h\nDcPvddIP1IieZNyW3BJgVartQNy2OzW9TnTEddiWAFtT03bGy0hbDnQNm9rR0VGKz2O0cfWd73yn\nFNsxlT4PoBTbUcTPo16vv/G7saWlhVqtNsp3UXbM3Zt/k9lG4MPAee7efwTtnwX+h7vfamYXEB2u\nOSm5F8XMfgJ8yd3/t5m1A3/i7r+WmH80sB/4XXe/x8zWAh9297ZEm7cDPwbOcvfvj9CPNqCnp6eH\ntra29GyRQurt7WXu3LlAD0MLj8lyO7A0w+X3AnPRvzuRqe3N7yLmuntv1utreg9KXJxcClxwhMXJ\n24BfA34eT+oBXie6OmewzRyik20fiSc9ApxoZmclFnUhYMCjiTbvNrOZiTYLgReB5CEnERERmWKa\nvQ/KzcDHgSuAV8xsVvw6Lp5/fHwvknPN7DfM7EKi/cI/JDqBlXivSRdwo5mdb2ZzgT8DHnL3x+I2\nfXH7W83svWb2PqL91HV33xN3ZydRIXKbmZ1pZhcBNwAb3f21CWQik2yk3bKSNWUemsZ5eMq83Jrd\ng/IZYAbwN8AzidfH4vkHgTOBe4DdwK3A3wELUkVDB3AvcFdiWZel1nUF0cH0++O23wWuGpzp7oeI\nzm85CDwMfB34GtHBeSmQ3t7M9wTKMMo8NI3z8JR5uTV1vxB3P2xB4+77gYuPYDkHiO5rsvIwbV4g\nOjB+uOU8TVSkSIFt2rQp7y5UkDIPTeM8PGVebrotvIiIiBSOChQREREpHBUoIiIiUjgqUCRzI92s\nSLKmzEPTOA9PmZebChTJ3IoVK/LuQgUp89A0zsNT5uWmAkUyt3Dhwry7UEHKPDSN8/CUebmpQBER\nEZHCUYEiIiIihaMCRTKXfsqnhKDMQ9M4D0+Zl5sKFMlcvV7PuwsVpMxD0zgPT5mXmwoUydwdd9yR\ndxcqSJmHpnEenjIvNxUoIiIiUjgqUERERKRwVKCIiIhI4ahAkcy1t7fn3YUKUuahaZyHp8zLTQWK\nZE53e8yDMg9N4zw8ZV5uKlAkc0uWLMm7CxWkzEPTOA9PmZebChQREREpHBUoIiIiUjgqUCRz3d3d\neXehgpR5aBrn4SnzclOBIplbv3593l2oIGUemsZ5eMq83FSgSOa2bNmSdxcqSJmHpnEenjIvNxUo\nkrnp06fn3YUKUuahaZyHp8zLTQWKiIiIFI4KFBERESkcFSiSuVWrVuXdhQpS5qFpnIenzMtNBYpk\nbvbs2Xl3oYKUeWga5+Ep83JTgSKZW7lyZd5dqCBlHprGeXjKvNxUoIiIiEjhqEARERGRwjkm7w5I\n+fX19XHGGWfk3Y1M9ff302g0Mln2rl27xvGuPqDcmRdNFcZ50SjzclOBIplbvXo127Zty7sbmenv\n72fOnFb27x/IuysJq4HyZl5EZR/nRaTMy00FimRu48aNeXchU41GIy5ONgOtGaxhO3Bdk+8pd+ZF\nVPZxXkTKvNyaKlDM7PeBjxLtO/4l8DBwrbv/MNXueuD3gBOBh4DPuvuPEvOnATcCi4FpwA7gc+7+\nbKLNSUTfspcAh4C7gavd/ZVEm9OA/wOcD7wMfB34b+5+qJntkmxV51LAVqAtg+WO5xBPVTIvjuqM\n8+JQ5uXW7Emy5wEbgHOB3wF+BdhpZm8ZbGBm1wIrgE8D5wCvADvM7NjEcm4CPgRcBiwATiUqQJK+\nQfSNf2HcdgFwS2I9RxH9aXkMMA/4BPBJ4Pomt0lEREQKpqk9KO6+KPmzmX0SeBaYC3THk68GbnD3\ne+M2VwJ7gY8Ad5rZDGAZcLm7Pxi3aQd2mdk57v6YmbUCFwFz3f3xuM1K4D4zu8bd98TzzwAucPcG\n8ISZXQd8wcw63f31ZsMQERGRYpjoZcYnAg48D2Bm7wBagAcGG7j7S8CjwPx40tlEhVGyzW6gP9Fm\nHrBvsDiJ3R+v69xEmyfi4mTQDuAE4J0T3C6ZROvWrcu7CxWkzEPTOA9PmZfbuAsUMzOiQzXd7v5k\nPLmFqIjYm2q+N54HMAt4NS5cRmvTQrRn5g3ufpCoEEq2GWk9JNpIAQwMFOnqlqpQ5qFpnIenzMtt\nIntQbgZ+C7h8kvoSzKJFi6jVakNe8+fPZ+vWrUPa7dy5k1qtNuz9y5cvp6ura8i03t5earXasHth\nrFmzZliV39/fT61Wo6+vb8j0DRs2DHv41cDAALVaje7u7iHT6/U67e3tw/q2ePHiwm3H2rVrS7Ed\nMPrnEekcYdpiYGtq2k5g+HbAcqArNa0X+OIIbdcwfC9Jf7zcPmBtYvoGhj88cCBum96OOjD885j4\ndkBHR0ep/31Mnz69FNsxlT6PSy+9tBTbUcTPo16vv/G7saWlhVqtRkdHx7D3ZMrdm34RXV3zz8Ds\n1PR3EF1xc2Zq+t8AX4r//wLgIDAj1eYnRFfpQPQN+Vxq/tHAa8Cl8c9rgd5Um7fH63/PKP1uA7yn\np8dFJktPT48DDj0OnsFr8xRffpSP/t2JTG1vftfR5uOoHZp9Nb0Hxcw2ApcSnZzanyp2ngL2EF15\nM9h+BtF5Iw/Hk3qA11Nt5hBdF/lIPOkR4EQzOyux+AsBIzqfZbDNu81sZqLNQuBF4ElERERkymqq\nQDGzm4GPA1cAr5jZrPh1XKLZTcDnzezDZvZuonuT/BS4B944abYLuNHMzjezucCfAQ+5+2Nxmz6i\nE15vNbP3mtn7iPZT1z26ggei/ctPAreZ2ZlmdhFwA7DR3V8bRxaSkaxuAS+Ho8xD0zgPT5mXW7N7\nUD4DzCA6ZPNM4vWxwQbuvp6omLiFaG/HW4APuvurieV0APcCdyWWdVlqXVcQHUy/P277XeCqxHoO\nEd3E7SDR3pmvA18jOjgvBbJs2bK8u1BByjw0jfPwlHm5NXsflCMqaNy9k5HPGBycfwBYGb9Ga/MC\nsHSM9TxNVKRIgXV2dubdhQrqzLsDlaNxHp4yL7eJ3gdFZExtbVnc/l0OT5mHpnEenjIvNxUoIiIi\nUjgqUERERKRwVKBI5tI3JZIQlHloGufhKfNyU4Eimevt7c27CxWkzEPTOA9PmZebChTJ3KZNm/Lu\nQgUp89A0zsNT5uWmAkVEREQKRwWKiIiIFI4KFBERESkcFSiSuZEeOS5ZU+ahaZyHp8zLTQWKZG7F\nihV5d6GClHloGufhKfNyU4EimVu4cGHeXaggZR6axnl4yrzcVKCIiIhI4ahAERERkcJRgSKZ27p1\na95dqCBlHprGeXjKvNxUoEjm6vV63l2oIGUemsZ5eMq83FSgSObuuOOOvLtQQco8NI3z8JR5ualA\nERERkcJRgSIiIiKFowJFRERECkcFimSuvb097y5UkDIPTeM8PGVebipQJHO622MelHloGufhKfNy\nU4EimVuyZEneXaggZR6axnl4yrzcVKCIiIhI4ahAERERkcJRgSKZ6+7uzrsLFaTMQ9M4D0+Zl5sK\nFMnc+vXr8+5CBSnz0DTOw1Pm5aYCRTK3ZcuWvLtQQco8NI3z8JR5ualAkcxNnz497y5UkDIPTeM8\nPGVebipQREREpHBUoIiIiEjhqECRzK1atSrvLlSQMg9N4zw8ZV5uKlAkc7Nnz867CxWkzEPTOA9P\nmZdb0wWKmZ1nZtvM7GdmdsjMaqn5X42nJ1/bU22mmdkmM2uY2ctmdpeZnZxqc5KZ3W5mL5rZPjP7\nipkdn2pzmpndZ2avmNkeM1tvZiq6CmblypV5d6GClHloGufhKfNyG88v8+OBvwc+B/gobb4FzAJa\n4lf6gQk3AR8CLgMWAKcCd6fafANoBS6M2y4AbhmcGRci24FjgHnAJ4BPAtePY5tERESkQI5p9g3u\n/m3g2wBmZqM0O+DuvxhphpnNAJYBl7v7g/G0dmCXmZ3j7o+ZWStwETDX3R+P26wE7jOza9x9Tzz/\nDOACd28AT5jZdcAXzKzT3V9vdttERESkGLI6HHK+me01sz4zu9nM3pqYN5eoMHpgcIK77wb6gfnx\npHnAvsHiJHY/0R6bcxNtnoiLk0E7gBOAd07q1siE9PX15d2FClLmoWmch6fMyy2LAuVbwJXAbwOr\ngQ8A2xN7W1qAV939pdT79sbzBts8m5zp7geB51Nt9o6wDBJtpABWr16ddxcqSJmHpnEenjIvt6YP\n8YzF3e9M/PgDM3sC+CfgfOCvJ3t9UnwbN27MuwsVpMxD0zgPT5mXW+ZXvLj7U0ADOD2etAc4Nj4X\nJWlWPG+wTfqqnqOBt6bazBphGSTajGjRokXUarUhr/nz57N169Yh7Xbu3EmtVhv2/uXLl9PV1TVk\nWm9vL7VajUajMWT6mjVrWLdu3ZBp/f391Gq1YbsnN2zYMOy6/oGBAWq12rCndtbrddrb24f1bfHi\nxYXbjtmzZ5diO2D0zyPSOcK0xcDW1LSdwPDtgOVAV2paL/DFEdquAdalpvXHy+1j6GXGGxh+X5SB\nuG16O+rA8M9j4tsBHR0dpf73Ua/XS7EdU+nzaDQapdiOIn4e9Xr9jd+NLS0t1Go1Ojo6hr0nU+4+\n7hdwCKiN0eZtwEHgkvjnGcAB4KOJNnPiZZ0T/3xG/J6zEm0WAq8DLfHPFwOvATMTbT4N7AN+ZZS+\ntAHe09PjIpOlp6fHAYceB8/gtXmKLz/KR//uRKa2N7/raPMJ1A5H+mr6EE98L5LTgcFzSv6Nmb2H\n6PyQ54n+tLubaC/G6UR/5v2Q6ARW3P0lM+sCbjSzfcDLwJeBh9z9sbhNn5ntAG41s88CxxL9GVj3\n6AoeiP58exK4zcyuBU4BbgA2uvtrzW6XiIiIFMd4DvGcDTwO9BBVUl8k2g+9lmivx5nAPcBu4Fbg\n74AFqaKhA7gXuAv4G+AZonuiJF1BtK/6/rjtd4GrBme6+yHgknidDwNfB75GVCBJgaR3UUoIyjw0\njfPwlHm5jec+KA9y+MLm4iNYxgGiW12OehtAd38BWDrGcp4mKlKkwAYGBvLuQgUp89A0zsNT5uWm\n28JL5tauXZt3FypImYemcR6eMi83FSgiIiJSOCpQREREpHBUoEjm0tf2SwjKPDSN8/CUebmpQJHM\nLVu2LO8uVJAyD03jPDxlXm4qUCRznZ2deXehgjrz7kDlaJyHp8zLTQWKZK6trS3vLlSQMg9N4zw8\nZV5uKlBERESkcFSgiIiISOGoQJHMpZ/cKSEo89A0zsNT5uWmAkUy19vbm3cXKkiZh6ZxHp4yLzcV\nKJK5TZs25d2FClLmoWmch6fMy00FioiIiBSOChQREREpHBUoIiIiUjgqUCRztVot7y5UkDIPTeM8\nPGVebipQJHMrVqzIuwsVpMxD0zgPT5mXmwoUydzChQvz7kIFKfPQNM7DU+blpgJFRERECkcFioiI\niBSOChTJ3NatW/PuQgUp89A0zsNT5uWmAkUyV6/X8+5CBSnz0DTOw1Pm5aYCRTJ3xx135N2FClLm\noWmch6fMy00FioiIiBSOChQREREpHBUoIiIiUjgqUCRz7e3teXehgpR5aBrn4SnzclOBIpnT3R7z\noMxD0zgPT5mXmwoUydySJUvy7kIFKfPQNM7DU+blpgJFRERECkcFioiIiBSOChTJXHd3d95dqCBl\nHprGeXjKvNxUoEjm1q9fn3cXKkiZh6ZxHp4yL7emCxQzO8/MtpnZz8zskJnVRmhzvZk9Y2YDZvYd\nMzs9NX+amW0ys4aZvWxmd5nZyak2J5nZ7Wb2opntM7OvmNnxqTanmdl9ZvaKme0xs/VmpqKrYLZs\n2ZJ3Fyq4tmynAAAVd0lEQVRImYemcR6eMi+38fwyPx74e+BzgKdnmtm1wArg08A5wCvADjM7NtHs\nJuBDwGXAAuBU4O7Uor4BtAIXxm0XALck1nMUsB04BpgHfAL4JHD9OLZJMjR9+vS8u1BByjw0jfPw\nlHm5HdPsG9z928C3AczMRmhyNXCDu98bt7kS2At8BLjTzGYAy4DL3f3BuE07sMvMznH3x8ysFbgI\nmOvuj8dtVgL3mdk17r4nnn8GcIG7N4AnzOw64Atm1unurze7bSIiIlIMk3o4xMzeAbQADwxOc/eX\ngEeB+fGks4kKo2Sb3UB/os08YN9gcRK7n2iPzbmJNk/ExcmgHcAJwDsnaZNEREQkB5N9vkYLURGx\nNzV9bzwPYBbwaly4jNamBXg2OdPdDwLPp9qMtB4SbaQAVq1alXcXKkiZh6ZxHp4yLzedUCqZmz17\ndt5dqCBlHprGeXjKvNwmu0DZAxjRXpKkWfG8wTbHxueiHK5N+qqeo4G3ptqMtB4SbUa0aNEiarXa\nkNf8+fPZunXrkHY7d+6kVht2kRLLly+nq6tryLTe3l5qtRqNRmPI9DVr1rBu3boh0/r7+6nVavT1\n9Q2ZvmHDhmF/EQwMDFCr1YZd71+v10d8UNbixYsLtx0rV64sxXbA6J9HpHOEaYuBralpO4Hh2wHL\nga7UtF7giyO0XQOsS03rj5fbB6xMTN/A8D0qA3Hb9HbUGflBgxPdDujo6Cj1v4+BgYFSbMdU+jze\n9773lWI7ivh51Ov1N343trS0UKvV6OjoGPaeLJn7sAtxjvzNZoeAj7j7tsS0Z4A/dvcvxT/PIDr0\ncqW7/0X88y+ITpL9ZtxmDrALmBefJHsG8APg7MRJsguJrtp5m7vvMbOLgb8EThk8D8XMPk30rX2y\nu782Qn/bgJ6enh7a2trGvd0iSb29vcydOxfoAbIYV7cDS6fw8nuBuWzevJnW1tYMlg8zZ87UX9Mi\nGXvzu4657t6b9fqavoonvhfJ6UR7SgD+jZm9B3je3Z8muoT482b2I+AnwA3AT4F7IDpp1sy6gBvN\nbB/wMvBl4CF3fyxu02dmO4BbzeyzwLFEfwbW4yt4IPrz7UngtvjS5lPidW0cqTgRkbz8HDiKpUuX\nZraG446bzu7du1SkiJRI0wUK0VU4f010Mqzz5v7nPweWuft6M5tOdM+SE4HvAR9091cTy+gADgJ3\nAdOILltenlrPFcBGoqt3DsVtrx6c6e6HzOwS4E+Bh4nut/I1on3fUiB9fX2cccYZeXejYvqIrsIv\ngheI/glvJrq10WTbxf79S2k0GrkWKBrn4SnzchvPfVAeZIxzV9y9k5EPyA/OP0B0kHzlYdq8QLTf\n+XDreRq45HBtJH+rV69m27ZtYzeUSbQaKFrmrWRzCKkYNM7DU+blpqt4JHMbN27MuwsVpMxD0zgP\nT5mXmwoUyZzOC8iDMg9N4zw8ZV5uKlBERESkcFSgiIiISOGoQJHMpW80JCEo89A0zsNT5uWmAkUy\nl77DpoSgzEPTOA9PmZebChTJ3Nq1a/PuQgUp89A0zsNT5uWmAkVEREQKRwWKiIiIFI4KFMlc+gmd\nEoIyD03jPDxlXm4qUCRzy5Yty7sLFaTMQ9M4D0+Zl5sKFMlcZ2dn3l2ooM68O1A5GufhKfNyU4Ei\nmWtrK+8D4opLmYemcR6eMi83FSgiIiJSOCpQREREpHBUoEjmurq68u5CBSnz0DTOw1Pm5aYCRTLX\n29ubdxcqSJmHpnEenjIvNxUokrlNmzbl3YUKUuahaZyHp8zLTQWKiIiIFI4KFBERESkcFSgiIiJS\nOCpQJHO1Wi3vLlSQMg9N4zw8ZV5uKlAkcytWrMi7CxWkzEPTOA9PmZebChTJ3MKFC/PuQgUp89A0\nzsNT5uWmAkVEREQKRwWKiIiIFI4KFMnc1q1b8+5CBSnz0DTOw1Pm5aYCRTJXr9fz7kIFKfPQNM7D\nU+bldkzeHZDyu+OOO/LuAv39/TQajUyWvWvXrkyWOzH5Z141RRjnVaPMy00FipRef38/c+a0sn//\nQN5dERGRI6QCRUqv0WjExclmoDWDNWwHrstguSIi1aUCRSqkFWjLYLlFPMQjIjK16SRZyVx7e3ve\nXaggZR6axnl4yrzcVKBI5nS3xzwo89A0zsNT5uU26QWKma0xs0Op15OpNteb2TNmNmBm3zGz01Pz\np5nZJjNrmNnLZnaXmZ2canOSmd1uZi+a2T4z+4qZHT/Z2yMTt2TJkry7UEHKPDSN8/CUeblltQfl\n/wGzgJb49f7BGWZ2LdGTzD4NnAO8Auwws2MT778J+BBwGbAAOBW4O7WObxCdVHBh3HYBcEsG2yIi\nIiKBZXWS7Ovu/otR5l0N3ODu9wKY2ZXAXuAjwJ1mNgNYBlzu7g/GbdqBXWZ2jrs/ZmatwEXAXHd/\nPG6zErjPzK5x9z0ZbZeIiIgEkFWB8u/M7GfAfuAR4Pfd/WkzewfRHpUHBhu6+0tm9igwH7gTODvu\nV7LNbjPrj9s8BswD9g0WJ7H7AQfOBe7JaLtkHLq7u3n/+98/dkOZRN0kdlxWQpY3zJs5cyazZ88+\nbBuN8/CUebllUaD8LfBJYDdwCtAJfNfM3kVUnDjRHpOkvfE8iA4NveruLx2mTQvwbHKmux80s+cT\nbaQg1q9fry+R4NZTnQLl58BRLF26NLM1HHfcdHbv3nXYIkXjPDxlXm6Tfg6Ku+9w97vd/f+5+3eA\nRcBJwMcme13jtWjRImq12pDX/Pnzhz14aufOndRqtWHvX758OV1dXUOm9fb2UqvVht1Ofc2aNaxb\nt27ItP7+fmq1Gn19fUOmb9iwgVWrVg2ZNjAwQK1Wo7u7e8j0er0+4iV2ixcvLtx2bNmypTDbAWuA\ndalp/UAN6EtN3wCsSk0biNt2M1znCNMWM/zBfTvjZaQtB7pS03qBL47Qdqzt2JKY3sx21Bn5EuWJ\nbgdAB5DF53EdcIjoRnw98et/AR9O/Dz4+g/An6SmbSQ6hS3d9j/Fy97M/v0DNBqNw/77eO973zt0\nKyr27zyP7bj22mtLsR1F/Dzq9fobvxtbWlqo1Wp0dHQMe0+m3D3zF9Fhmf8FvIPom+TM1Py/Ab4U\n//8FwEFgRqrNT4Cr4/9vB55LzT8aeA249DD9aAO8p6fHpTp6enoccOhx8Axem7X8Ui8/Gj/63pCq\ne/O7lDb37GuHzO+DYmb/CjgdeMbdnwL2EF15Mzh/BtF5Iw/Hk3qA11Nt5gCzic5nIf7viWZ2VmJV\nFwIGPJrNloiIiEgok34Oipn9MfCXwD8D/xpYS7RnY3Cf803A583sR0R7RW4Afkp8YqtHJ812ATea\n2T7gZeDLwEPu/ljcps/MdgC3mtlngWOJ9v/WXVfwiIiITHlZ7EF5G9E9SgYPhP8CmOfuzwG4+3qi\nYuIWor0dbwE+6O6vJpbRAdwL3EV0+OcZonuiJF0Rr+P+uO13gasy2B6ZoPRxUQlBmYemcR6eMi+3\nSd+D4u5j3trP3TsZ+YzCwfkHgJXxa7Q2LwDZnbYvk2asyzMlC8o8NI3z8JR5uelZPJK5lStHrTMl\nM8o8NI3z8JR5ualAERERkcJRgSIiIiKFowJFMpe+oZCEoMxD0zgPT5mXmwoUydzq1avz7kIFKfPQ\nNM7DU+blltXDAkXesHHjxry7UEHKfLKN9TDCq666it7e3nEt+0geRijD6bul3FSgSOb0xZsHZT55\nivEwQhlOeZWbChQRkcN6gTcfRtiawfJ3sX//UhqNhn7hiiSoQBEROSKtRM8bFZEQdJKsZC79uHAJ\nQZmHp8xD03dLualAkcwNDAzk3YUKUubhKfPQ9N1SbipQJHNr167NuwsVpMzDU+ah6bul3HQOiohI\nAYx1GfNE6DJmmYpUoIiI5EqXMYuMRAWKZK7RaDBz5sy8u1ExDUCZhzXezHUZ83jpu6XcVKBI5pYt\nW8a2bdvy7kbFLAOUeVgTzVyXMTdL3y3lpgJFMtfZ2Tlmm/7+fhqNRibrz/LYfnF15t2BCurMuwOV\ncyTfLTJ1qUCRzLW1Hf6vwv7+fubMaWX/fl0yOHn0l3h4xc68jCfhjvXdIlObChTJXaPRiIuTrI7B\nbweuy2C5IlOBTsKVqUkFihRIVsfgq3iIR2SQTsKVqUkFimSuq6uLT33qU3l3o2K6AGUeVtEzL99J\nuPpuKTfdSVYy19vbm3cXKkiZh6fMQ9N3S7lpD4pkbtOmTXl3oYKUeXjVzjyrk3APdwKuvlvKTQWK\niIhMQLYn4eoE3OpSgSIiIhOQ5Um4OgG3ylSgyBHRjdRE5PCyOwm3jPdwkbGpQJEx6UZqU1EN3eo+\nNGU++XQPlypTgSJjmviN1B4B5h9mvm6kNvlW5N2BClLmk2+sw0djfbeMJTqE9L3vfY/W1izuEaM9\nNBOhAkWaMN5duGO9R4d4Jt/CvDtQQco8O6N990z0kFL2e2imTTuOu+++i1NOOSWT5Ze5AFKBUhI6\nR0REpFlZ32X3exw48F+55JJLMlh2pMwFkAqUEtA5IiIiE5HlYzamdgGU5zk6KlACyXoPR7EftrcV\n+Mgk9UWOjDIPT5mHN1Uyn6oF0NBzdELvTVeBEkC4PRxFfdjeOqbGl0iZKPPwlHl4yjyS1Xd/9ufo\nHM6UL1DMbDlwDdACfB9Y6e5/l2+vhpr4VTBjKfpVML+edwcqSJmHp8zDU+bZSp+jswsIV6xM6QLF\nzBYDXwQ+DTwGdAA7zOw33X3U4ykj7aY6cOAA06ZNy6Sfb66vqHs4RERERpPPk7CndIFCVJDc4u5f\nBzCzzwAfApYB60d708i7q44GDmbRRxEREWnSlC1QzOxXgLnAHw5Oc3c3s/sZ88496UMtg4dIqnoI\nRkREpFimbIECzCTa7bE3NX0vMGeU9xwX/eep1ORnGHn6ZBlc/nayORzzUMGX/xBwe4bLP5L1V235\nY2U+0eU3oyrLbybz8Sx/vKby8sda9ngzP9LlT1TZlv/G78jjMljZMObuIdYz6czsFOBnwHx3fzQx\nfR2wwN2H7UUxsyuY2GgWERGpuo+7+zeyXslU3oPSIDppZFZq+ixgzyjv2QF8HPgJsD+znomIiJTP\nccDbiX6XZm7K7kEBMLO/BR5196vjnw3oB77s7n+ca+dERERk3KbyHhSAG4GvmVkPb15mPB34Wp6d\nEhERkYmZ0gWKu99pZjOB64kO7fw9cJG7/yLfnomIiMhETOlDPCIiIlJOR+XdAREREZE0FSgiIiJS\nOFO+QDGz3zCzr5jZj81swMz+0cw64zvNJtudZmb3mdkrZrbHzNab2VGpNmea2XfN7Jdm9s9mtmqE\n9Z1vZj1mtt/Mfmhmn8h6G4vIzP67mT0U5/n8KG2UeWBmttzMnorz/Fsze2/efZoqzOw8M9tmZj8z\ns0NmVhuhzfVm9kz8XfMdMzs9NX+amW0ys4aZvWxmd5nZyak2J5nZ7Wb2opnti7+/js96+4rGzH7f\nzB4zs5fMbK+ZfdPMfnOEdsp8kpjZZ8zs+3EOL5rZw2Z2capNcfJ29yn9Ai4CuoALia7PvoToPijr\nE22OAp4gunb73fF7ngX+INHmV4meLf3nRPe7/xjwCvB7iTZvB/6F6Dk/c4DlwGvAf8g7hxxyXwNc\nDfwJ8PwI85V5+M9kMdH9fa4EzgBuAZ4HZubdt6nwAi4mOuH+UqJ7LNVS86+N87wEeBewFfgn4NhE\nmz8lus/SB4CzgIeB76WW8y2gFzgb+P+AHwKb897+HPLeDvzn+N/+u4F74+zeoswzy/xD8Tj/t8Dp\nwB8AB4DWIuade2AZfQjXAD9K/PzB+JfazMS0q4B9wDHxz58luvnbMYk2fwQ8mfh5HfAPqXXVge15\nb3OOWX+CkQsUZR7+s/hb4H8nfjbgp8DqvPs21V5Ez5hPFyjPAB2Jn2cAvwQ+lvj5APDRRJs58bLO\niX9ujX8+K9HmIuB1oCXv7c4585lxNu9X5kFzfw5oL2LeU/4QzyhOJKoCB80DnnD3RmLaDuAE4J2J\nNt9199dTbeaY2QmJNven1rWDMR9OWEnKPCB78+GZDwxO8+ib4QgeniljMbN3AC0Mzfcl4FHezPds\nols3JNvsJrp55GCbecA+d388sfj7AQfOzar/U8SJRDk8D8o8a2Z2lJldTnTvsIeLmHfpCpT4eNkK\n4P8kJrcw8kMFB+dNtM0MM5s23j6XlDIP63APz2wZ3lya1EL0BXu4fGcBr8Zf6qO1aSE61PkGdz9I\n9Eu5sp+TmRlwE9Dt7k/Gk5V5BszsXWb2MtGekJuJ9obspoB5F7ZAMbM/ik9UG+11MH1ClZn9a6Jj\nX3e4+59NVlcmaTmFN57Ms+pKgHWISHHcDPwWcHneHamAPuA9wDlE55N83czOyLdLIyvynWT/BPjq\nGG1+PPg/ZnYq8FdEFfhVqXZ7gPTVDLMS8wb/O9KDB/0I2rzk7gfG6OtU0FTmY1DmYY3n4Zly5PYQ\nFc6zGPoX5izg8USbY81sRuovzORnsAdIX/FwNPBWKvo5mdlGYBFwnrv/PDFLmWcgPqQ++D3+uJmd\nQ3TBw3oKlndh96C4+3Pu/sMxXq/DG3tO/hr4O2DZCIt7BHi3RbfFH7QQeBF4MtFmQRxkss1ud38x\n0ebC1LIXxtOnvGYyPwLKPCB3fw3oIZFVvNv8QqKz7GUC3P0poi/XZL4ziI6pD+bbQ3QiYLLNHGA2\nb47XR4ATzeysxOIvJPrF8GhW/S+quDi5FLjA3fuT85R5MEcB0wqZd95nEE/CGcinAv8I7Iz/f9bg\nK9HmKOD7RId/ziQ6o3gvcEPqbOVniC55/S2iSzb/BfhUos3bgZeJriyZA3wOeBX4nbxzyCH304h2\nE/5PoqLjPfHreGWe22fyMWCAoZcZPwf8et59mwov4Ph4DP97oqsQ/kv882nx/NVxnh8muix2a/zd\nk7wE82bgKeB8opOWH2L4JZjbgf9LtIfxfcBu4La8tz+HvG8muqrvvOT3NnBcoo0yn9zM/zDO+zeI\nLiP+I6KC47eLmHfugU1C4J8g2rWdfB0CDqbanUZ0nf2/EP2iXAcclWrzLuDB+Eu+H7hmhPUtIKoi\nfxl/cP857wxyyv2rI+R+EFigzHP9XD5HdI+CXxL9JXN23n2aKi+i+zocGmFM/1miTSdRUT1AdDXZ\n6allTAM2EB1yexn4C+DkVJsTgc1Ehf0+4FZget7bn0PeI2V9ELgy1U6ZT17mXyE6vPNLor0lO4mL\nkyLmrYcFioiISOEU9hwUERERqS4VKCIiIlI4KlBERESkcFSgiIiISOGoQBEREZHCUYEiIiIihaMC\nRURERApHBYqIiIgUjgoUERERKRwVKCIiIlI4KlBERESkcP5/8Gn8pli7E98AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11cfedf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.xlim(-2000, 3000)\n",
    "(data['ENTRIESn_hourly'] - predictions).hist(bins=200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This graph confirms that our linear regression works well. For the most of our data the difference between predicted and real values is close to zero. Also, we have almost a normal distribution catered around zero, thus, our algorithm has low bias. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ImportError",
     "evalue": "No module named 'ggplot'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mImportError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-127-02aeb6e281ab>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mggplot\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mImportError\u001b[0m: No module named 'ggplot'"
     ]
    }
   ],
   "source": [
    "from ggplot import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}