Exploratory Data Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "    <a href=\"https://cocl.us/corsera_da0101en_notebook_top\">\n",
    "         <img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/TopAd.png\" width=\"750\" align=\"center\">\n",
    "    </a>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://www.bigdatauniversity.com\"><img src = \"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/CCLog.png\" width = 300, align = \"center\"></a>\n",
    "\n",
    "<h1 align=center><font size = 5>Data Analysis with Python</font></h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exploratory Data Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Welcome!</h3>\n",
    "In this section, we will explore several methods to see if certain characteristics or features can be used to predict car price. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Table of content</h2>\n",
    "\n",
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "<ol>\n",
    "    <li><a href=\"#import_data\">Import Data from Module</a></li>\n",
    "    <li><a href=\"#pattern_visualization\">Analyzing Individual Feature Patterns using Visualization</a></li>\n",
    "    <li><a href=\"#discriptive_statistics\">Descriptive Statistical Analysis</a></li>\n",
    "    <li><a href=\"#basic_grouping\">Basics of Grouping</a></li>\n",
    "    <li><a href=\"#correlation_causation\">Correlation and Causation</a></li>\n",
    "    <li><a href=\"#anova\">ANOVA</a></li>\n",
    "</ol>\n",
    "    \n",
    "Estimated Time Needed: <strong>30 min</strong>\n",
    "</div>\n",
    " \n",
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>What are the main characteristics which have the most impact on the car price?</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"import_data\">1. Import Data from Module 2</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Setup</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import libraries "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " load data and store in dataframe df:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dataset was hosted on IBM Cloud object click <a href=\"https://cocl.us/DA101EN_object_storage\">HERE</a> for free storage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>make</th>\n",
       "      <th>aspiration</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>...</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>horsepower-binned</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>13495.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>94.5</td>\n",
       "      <td>0.822681</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>154.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.8</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>24</td>\n",
       "      <td>30</td>\n",
       "      <td>13950.0</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>4wd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.4</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>8.0</td>\n",
       "      <td>115.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>18</td>\n",
       "      <td>22</td>\n",
       "      <td>17450.0</td>\n",
       "      <td>13.055556</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>196</th>\n",
       "      <td>-1</td>\n",
       "      <td>95</td>\n",
       "      <td>volvo</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>109.1</td>\n",
       "      <td>0.907256</td>\n",
       "      <td>...</td>\n",
       "      <td>9.5</td>\n",
       "      <td>114.0</td>\n",
       "      <td>5400.0</td>\n",
       "      <td>23</td>\n",
       "      <td>28</td>\n",
       "      <td>16845.0</td>\n",
       "      <td>10.217391</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>197</th>\n",
       "      <td>-1</td>\n",
       "      <td>95</td>\n",
       "      <td>volvo</td>\n",
       "      <td>turbo</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>109.1</td>\n",
       "      <td>0.907256</td>\n",
       "      <td>...</td>\n",
       "      <td>8.7</td>\n",
       "      <td>160.0</td>\n",
       "      <td>5300.0</td>\n",
       "      <td>19</td>\n",
       "      <td>25</td>\n",
       "      <td>19045.0</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>High</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>-1</td>\n",
       "      <td>95</td>\n",
       "      <td>volvo</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>109.1</td>\n",
       "      <td>0.907256</td>\n",
       "      <td>...</td>\n",
       "      <td>8.8</td>\n",
       "      <td>134.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>18</td>\n",
       "      <td>23</td>\n",
       "      <td>21485.0</td>\n",
       "      <td>13.055556</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>199</th>\n",
       "      <td>-1</td>\n",
       "      <td>95</td>\n",
       "      <td>volvo</td>\n",
       "      <td>turbo</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>109.1</td>\n",
       "      <td>0.907256</td>\n",
       "      <td>...</td>\n",
       "      <td>23.0</td>\n",
       "      <td>106.0</td>\n",
       "      <td>4800.0</td>\n",
       "      <td>26</td>\n",
       "      <td>27</td>\n",
       "      <td>22470.0</td>\n",
       "      <td>9.038462</td>\n",
       "      <td>Medium</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>200</th>\n",
       "      <td>-1</td>\n",
       "      <td>95</td>\n",
       "      <td>volvo</td>\n",
       "      <td>turbo</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>109.1</td>\n",
       "      <td>0.907256</td>\n",
       "      <td>...</td>\n",
       "      <td>9.5</td>\n",
       "      <td>114.0</td>\n",
       "      <td>5400.0</td>\n",
       "      <td>19</td>\n",
       "      <td>25</td>\n",
       "      <td>22625.0</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>201 rows × 29 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     symboling  normalized-losses         make aspiration num-of-doors  \\\n",
       "0            3                122  alfa-romero        std          two   \n",
       "1            3                122  alfa-romero        std          two   \n",
       "2            1                122  alfa-romero        std          two   \n",
       "3            2                164         audi        std         four   \n",
       "4            2                164         audi        std         four   \n",
       "..         ...                ...          ...        ...          ...   \n",
       "196         -1                 95        volvo        std         four   \n",
       "197         -1                 95        volvo      turbo         four   \n",
       "198         -1                 95        volvo        std         four   \n",
       "199         -1                 95        volvo      turbo         four   \n",
       "200         -1                 95        volvo      turbo         four   \n",
       "\n",
       "      body-style drive-wheels engine-location  wheel-base    length  ...  \\\n",
       "0    convertible          rwd           front        88.6  0.811148  ...   \n",
       "1    convertible          rwd           front        88.6  0.811148  ...   \n",
       "2      hatchback          rwd           front        94.5  0.822681  ...   \n",
       "3          sedan          fwd           front        99.8  0.848630  ...   \n",
       "4          sedan          4wd           front        99.4  0.848630  ...   \n",
       "..           ...          ...             ...         ...       ...  ...   \n",
       "196        sedan          rwd           front       109.1  0.907256  ...   \n",
       "197        sedan          rwd           front       109.1  0.907256  ...   \n",
       "198        sedan          rwd           front       109.1  0.907256  ...   \n",
       "199        sedan          rwd           front       109.1  0.907256  ...   \n",
       "200        sedan          rwd           front       109.1  0.907256  ...   \n",
       "\n",
       "     compression-ratio  horsepower  peak-rpm city-mpg highway-mpg    price  \\\n",
       "0                  9.0       111.0    5000.0       21          27  13495.0   \n",
       "1                  9.0       111.0    5000.0       21          27  16500.0   \n",
       "2                  9.0       154.0    5000.0       19          26  16500.0   \n",
       "3                 10.0       102.0    5500.0       24          30  13950.0   \n",
       "4                  8.0       115.0    5500.0       18          22  17450.0   \n",
       "..                 ...         ...       ...      ...         ...      ...   \n",
       "196                9.5       114.0    5400.0       23          28  16845.0   \n",
       "197                8.7       160.0    5300.0       19          25  19045.0   \n",
       "198                8.8       134.0    5500.0       18          23  21485.0   \n",
       "199               23.0       106.0    4800.0       26          27  22470.0   \n",
       "200                9.5       114.0    5400.0       19          25  22625.0   \n",
       "\n",
       "    city-L/100km  horsepower-binned  diesel  gas  \n",
       "0      11.190476             Medium       0    1  \n",
       "1      11.190476             Medium       0    1  \n",
       "2      12.368421             Medium       0    1  \n",
       "3       9.791667             Medium       0    1  \n",
       "4      13.055556             Medium       0    1  \n",
       "..           ...                ...     ...  ...  \n",
       "196    10.217391             Medium       0    1  \n",
       "197    12.368421               High       0    1  \n",
       "198    13.055556             Medium       0    1  \n",
       "199     9.038462             Medium       1    0  \n",
       "200    12.368421             Medium       0    1  \n",
       "\n",
       "[201 rows x 29 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path='https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/automobileEDA.csv'\n",
    "df = pd.read_csv(path)\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"pattern_visualization\">2. Analyzing Individual Feature Patterns using Visualization</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To install seaborn we use the pip which is the python package manager."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "! pip install seaborn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import visualization packages \"Matplotlib\" and \"Seaborn\", don't forget about \"%matplotlib inline\" to plot in a Jupyter notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>How to choose the right visualization method?</h4>\n",
    "<p>When visualizing individual variables, it is important to first understand what type of variable you are dealing with. This will help us find the right visualization method for that variable.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "symboling              int64\n",
      "normalized-losses      int64\n",
      "make                  object\n",
      "aspiration            object\n",
      "num-of-doors          object\n",
      "body-style            object\n",
      "drive-wheels          object\n",
      "engine-location       object\n",
      "wheel-base           float64\n",
      "length               float64\n",
      "width                float64\n",
      "height               float64\n",
      "curb-weight            int64\n",
      "engine-type           object\n",
      "num-of-cylinders      object\n",
      "engine-size            int64\n",
      "fuel-system           object\n",
      "bore                 float64\n",
      "stroke               float64\n",
      "compression-ratio    float64\n",
      "horsepower           float64\n",
      "peak-rpm             float64\n",
      "city-mpg               int64\n",
      "highway-mpg            int64\n",
      "price                float64\n",
      "city-L/100km         float64\n",
      "horsepower-binned     object\n",
      "diesel                 int64\n",
      "gas                    int64\n",
      "dtype: object\n"
     ]
    }
   ],
   "source": [
    "# list the data types for each column\n",
    "print(df.dtypes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h3>Question  #1:</h3>\n",
    "\n",
    "<b>What is the data type of the column \"peak-rpm\"? </b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "for example, we can calculate the correlation between variables  of type \"int64\" or \"float64\" using the method \"corr\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>symboling</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.466264</td>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.365404</td>\n",
       "      <td>-0.242423</td>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.233118</td>\n",
       "      <td>-0.110581</td>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.008245</td>\n",
       "      <td>-0.182196</td>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.279740</td>\n",
       "      <td>-0.035527</td>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.066171</td>\n",
       "      <td>-0.196735</td>\n",
       "      <td>0.196735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>normalized-losses</th>\n",
       "      <td>0.466264</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.101546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wheel-base</th>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>-0.307237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>length</th>\n",
       "      <td>-0.365404</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>-0.211187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>width</th>\n",
       "      <td>-0.242423</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>-0.244356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>height</th>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>-0.281578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>curb-weight</th>\n",
       "      <td>-0.233118</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>-0.221046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>-0.110581</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>-0.070779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>-0.054458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.008245</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>-0.241303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>-0.182196</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.985231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>0.169053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>0.279740</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.475812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-mpg</th>\n",
       "      <td>-0.035527</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>-0.265676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>-0.198690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.110326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-L/100km</th>\n",
       "      <td>0.066171</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>0.241282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diesel</th>\n",
       "      <td>-0.196735</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gas</th>\n",
       "      <td>0.196735</td>\n",
       "      <td>0.101546</td>\n",
       "      <td>-0.307237</td>\n",
       "      <td>-0.211187</td>\n",
       "      <td>-0.244356</td>\n",
       "      <td>-0.281578</td>\n",
       "      <td>-0.221046</td>\n",
       "      <td>-0.070779</td>\n",
       "      <td>-0.054458</td>\n",
       "      <td>-0.241303</td>\n",
       "      <td>-0.985231</td>\n",
       "      <td>0.169053</td>\n",
       "      <td>0.475812</td>\n",
       "      <td>-0.265676</td>\n",
       "      <td>-0.198690</td>\n",
       "      <td>-0.110326</td>\n",
       "      <td>0.241282</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   symboling  normalized-losses  wheel-base    length  \\\n",
       "symboling           1.000000           0.466264   -0.535987 -0.365404   \n",
       "normalized-losses   0.466264           1.000000   -0.056661  0.019424   \n",
       "wheel-base         -0.535987          -0.056661    1.000000  0.876024   \n",
       "length             -0.365404           0.019424    0.876024  1.000000   \n",
       "width              -0.242423           0.086802    0.814507  0.857170   \n",
       "height             -0.550160          -0.373737    0.590742  0.492063   \n",
       "curb-weight        -0.233118           0.099404    0.782097  0.880665   \n",
       "engine-size        -0.110581           0.112360    0.572027  0.685025   \n",
       "bore               -0.140019          -0.029862    0.493244  0.608971   \n",
       "stroke             -0.008245           0.055563    0.158502  0.124139   \n",
       "compression-ratio  -0.182196          -0.114713    0.250313  0.159733   \n",
       "horsepower          0.075819           0.217299    0.371147  0.579821   \n",
       "peak-rpm            0.279740           0.239543   -0.360305 -0.285970   \n",
       "city-mpg           -0.035527          -0.225016   -0.470606 -0.665192   \n",
       "highway-mpg         0.036233          -0.181877   -0.543304 -0.698142   \n",
       "price              -0.082391           0.133999    0.584642  0.690628   \n",
       "city-L/100km        0.066171           0.238567    0.476153  0.657373   \n",
       "diesel             -0.196735          -0.101546    0.307237  0.211187   \n",
       "gas                 0.196735           0.101546   -0.307237 -0.211187   \n",
       "\n",
       "                      width    height  curb-weight  engine-size      bore  \\\n",
       "symboling         -0.242423 -0.550160    -0.233118    -0.110581 -0.140019   \n",
       "normalized-losses  0.086802 -0.373737     0.099404     0.112360 -0.029862   \n",
       "wheel-base         0.814507  0.590742     0.782097     0.572027  0.493244   \n",
       "length             0.857170  0.492063     0.880665     0.685025  0.608971   \n",
       "width              1.000000  0.306002     0.866201     0.729436  0.544885   \n",
       "height             0.306002  1.000000     0.307581     0.074694  0.180449   \n",
       "curb-weight        0.866201  0.307581     1.000000     0.849072  0.644060   \n",
       "engine-size        0.729436  0.074694     0.849072     1.000000  0.572609   \n",
       "bore               0.544885  0.180449     0.644060     0.572609  1.000000   \n",
       "stroke             0.188829 -0.062704     0.167562     0.209523 -0.055390   \n",
       "compression-ratio  0.189867  0.259737     0.156433     0.028889  0.001263   \n",
       "horsepower         0.615077 -0.087027     0.757976     0.822676  0.566936   \n",
       "peak-rpm          -0.245800 -0.309974    -0.279361    -0.256733 -0.267392   \n",
       "city-mpg          -0.633531 -0.049800    -0.749543    -0.650546 -0.582027   \n",
       "highway-mpg       -0.680635 -0.104812    -0.794889    -0.679571 -0.591309   \n",
       "price              0.751265  0.135486     0.834415     0.872335  0.543155   \n",
       "city-L/100km       0.673363  0.003811     0.785353     0.745059  0.554610   \n",
       "diesel             0.244356  0.281578     0.221046     0.070779  0.054458   \n",
       "gas               -0.244356 -0.281578    -0.221046    -0.070779 -0.054458   \n",
       "\n",
       "                     stroke  compression-ratio  horsepower  peak-rpm  \\\n",
       "symboling         -0.008245          -0.182196    0.075819  0.279740   \n",
       "normalized-losses  0.055563          -0.114713    0.217299  0.239543   \n",
       "wheel-base         0.158502           0.250313    0.371147 -0.360305   \n",
       "length             0.124139           0.159733    0.579821 -0.285970   \n",
       "width              0.188829           0.189867    0.615077 -0.245800   \n",
       "height            -0.062704           0.259737   -0.087027 -0.309974   \n",
       "curb-weight        0.167562           0.156433    0.757976 -0.279361   \n",
       "engine-size        0.209523           0.028889    0.822676 -0.256733   \n",
       "bore              -0.055390           0.001263    0.566936 -0.267392   \n",
       "stroke             1.000000           0.187923    0.098462 -0.065713   \n",
       "compression-ratio  0.187923           1.000000   -0.214514 -0.435780   \n",
       "horsepower         0.098462          -0.214514    1.000000  0.107885   \n",
       "peak-rpm          -0.065713          -0.435780    0.107885  1.000000   \n",
       "city-mpg          -0.034696           0.331425   -0.822214 -0.115413   \n",
       "highway-mpg       -0.035201           0.268465   -0.804575 -0.058598   \n",
       "price              0.082310           0.071107    0.809575 -0.101616   \n",
       "city-L/100km       0.037300          -0.299372    0.889488  0.115830   \n",
       "diesel             0.241303           0.985231   -0.169053 -0.475812   \n",
       "gas               -0.241303          -0.985231    0.169053  0.475812   \n",
       "\n",
       "                   city-mpg  highway-mpg     price  city-L/100km    diesel  \\\n",
       "symboling         -0.035527     0.036233 -0.082391      0.066171 -0.196735   \n",
       "normalized-losses -0.225016    -0.181877  0.133999      0.238567 -0.101546   \n",
       "wheel-base        -0.470606    -0.543304  0.584642      0.476153  0.307237   \n",
       "length            -0.665192    -0.698142  0.690628      0.657373  0.211187   \n",
       "width             -0.633531    -0.680635  0.751265      0.673363  0.244356   \n",
       "height            -0.049800    -0.104812  0.135486      0.003811  0.281578   \n",
       "curb-weight       -0.749543    -0.794889  0.834415      0.785353  0.221046   \n",
       "engine-size       -0.650546    -0.679571  0.872335      0.745059  0.070779   \n",
       "bore              -0.582027    -0.591309  0.543155      0.554610  0.054458   \n",
       "stroke            -0.034696    -0.035201  0.082310      0.037300  0.241303   \n",
       "compression-ratio  0.331425     0.268465  0.071107     -0.299372  0.985231   \n",
       "horsepower        -0.822214    -0.804575  0.809575      0.889488 -0.169053   \n",
       "peak-rpm          -0.115413    -0.058598 -0.101616      0.115830 -0.475812   \n",
       "city-mpg           1.000000     0.972044 -0.686571     -0.949713  0.265676   \n",
       "highway-mpg        0.972044     1.000000 -0.704692     -0.930028  0.198690   \n",
       "price             -0.686571    -0.704692  1.000000      0.789898  0.110326   \n",
       "city-L/100km      -0.949713    -0.930028  0.789898      1.000000 -0.241282   \n",
       "diesel             0.265676     0.198690  0.110326     -0.241282  1.000000   \n",
       "gas               -0.265676    -0.198690 -0.110326      0.241282 -1.000000   \n",
       "\n",
       "                        gas  \n",
       "symboling          0.196735  \n",
       "normalized-losses  0.101546  \n",
       "wheel-base        -0.307237  \n",
       "length            -0.211187  \n",
       "width             -0.244356  \n",
       "height            -0.281578  \n",
       "curb-weight       -0.221046  \n",
       "engine-size       -0.070779  \n",
       "bore              -0.054458  \n",
       "stroke            -0.241303  \n",
       "compression-ratio -0.985231  \n",
       "horsepower         0.169053  \n",
       "peak-rpm           0.475812  \n",
       "city-mpg          -0.265676  \n",
       "highway-mpg       -0.198690  \n",
       "price             -0.110326  \n",
       "city-L/100km       0.241282  \n",
       "diesel            -1.000000  \n",
       "gas                1.000000  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The diagonal elements are always one; we will study correlation more precisely Pearson correlation in-depth at the end of the notebook."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #2: </h1>\n",
    "\n",
    "<p>Find the correlation between the following columns: bore, stroke,compression-ratio , and horsepower.</p>\n",
    "<p>Hint: if you would like to select those columns  use the following syntax: df[['bore','stroke' ,'compression-ratio','horsepower']]</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       bore    stroke  compression-ratio  horsepower\n",
       "bore               1.000000 -0.055390           0.001263    0.566936\n",
       "stroke            -0.055390  1.000000           0.187923    0.098462\n",
       "compression-ratio  0.001263  0.187923           1.000000   -0.214514\n",
       "horsepower         0.566936  0.098462          -0.214514    1.000000"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df[['bore', 'stroke', 'compression-ratio', 'horsepower']].corr()  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "df[['bore', 'stroke', 'compression-ratio', 'horsepower']].corr()  \n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Continuous numerical variables:</h2> \n",
    "\n",
    "<p>Continuous numerical variables are variables that may contain any value within some range. Continuous numerical variables can have the type \"int64\" or \"float64\". A great way to visualize these variables is by using scatterplots with fitted lines.</p>\n",
    "\n",
    "<p>In order to start understanding the (linear) relationship between an individual variable and the price. We can do this by using \"regplot\", which plots the scatterplot plus the fitted regression line for the data.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's see several examples of different linear relationships:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Positive linear relationship</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's find the scatterplot of \"engine-size\" and \"price\" "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 56260.64295129913)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Engine size as potential predictor variable of price\n",
    "sns.regplot(x=\"engine-size\", y=\"price\", data=df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>As the engine-size goes up, the price goes up: this indicates a positive direct correlation between these two variables. Engine size seems like a pretty good predictor of price since the regression line is almost a perfect diagonal line.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can examine the correlation between 'engine-size' and 'price' and see it's approximately  0.87"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>engine-size</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.872335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>0.872335</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             engine-size     price\n",
       "engine-size     1.000000  0.872335\n",
       "price           0.872335  1.000000"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[[\"engine-size\", \"price\"]].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Highway mpg is a potential predictor variable of price "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f29200c17f0>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x=\"highway-mpg\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>As the highway-mpg goes up, the price goes down: this indicates an inverse/negative relationship between these two variables. Highway mpg could potentially be a predictor of price.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'highway-mpg' and 'price' and see it's approximately  -0.704"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             highway-mpg     price\n",
       "highway-mpg     1.000000 -0.704692\n",
       "price          -0.704692  1.000000"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['highway-mpg', 'price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Weak Linear Relationship</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see if \"Peak-rpm\" as a predictor variable of \"price\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2920026668>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x=\"peak-rpm\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Peak rpm does not seem like a good predictor of the price at all since the regression line is close to horizontal. Also, the data points are very scattered and far from the fitted line, showing lots of variability. Therefore it's it is not a reliable variable.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'peak-rpm' and 'price' and see it's approximately -0.101616 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.101616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.101616</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          peak-rpm     price\n",
       "peak-rpm  1.000000 -0.101616\n",
       "price    -0.101616  1.000000"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['peak-rpm','price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " <div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  3 a): </h1>\n",
    "\n",
    "<p>Find the correlation  between x=\"stroke\", y=\"price\".</p>\n",
    "<p>Hint: if you would like to select those columns  use the following syntax: df[[\"stroke\",\"price\"]]  </p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>stroke</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>1.00000</td>\n",
       "      <td>0.08231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>0.08231</td>\n",
       "      <td>1.00000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         stroke    price\n",
       "stroke  1.00000  0.08231\n",
       "price   0.08231  1.00000"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute\n",
    "df[[\"stroke\",\"price\"]].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "#The correlation is 0.0823, the non-diagonal elements of the table.\n",
    "#code:\n",
    "df[[\"stroke\",\"price\"]].corr() \n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question  3 b):</h1>\n",
    "\n",
    "<p>Given the correlation results between \"price\" and \"stroke\" do you expect a linear relationship?</p> \n",
    "<p>Verify your results using the function \"regplot()\".</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'stroking price')"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "sns.regplot(x=\"stroke\", y=\"price\", data=df)\n",
    "plt.title(\"stroking price\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "#There is a weak correlation between the variable 'stroke' and 'price.' as such regression will not work well.  We #can see this use \"regplot\" to demonstrate this.\n",
    "\n",
    "#Code: \n",
    "sns.regplot(x=\"stroke\", y=\"price\", data=df)\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Categorical variables</h3>\n",
    "\n",
    "<p>These are variables that describe a 'characteristic' of a data unit, and are selected from a small group of categories. The categorical variables can have the type \"object\" or \"int64\". A good way to visualize categorical variables is by using boxplots.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the relationship between \"body-style\" and \"price\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2908ecf828>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"body-style\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We see that the distributions of price between the different body-style categories have a significant overlap, and so body-style would not be a good predictor of price. Let's examine engine \"engine-location\" and \"price\":</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2908e19748>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"engine-location\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Here we see that the distribution of price between these two engine-location categories, front and rear, are distinct enough to take engine-location as a potential good predictor of price.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's examine \"drive-wheels\" and \"price\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2908d93a20>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# drive-wheels\n",
    "sns.boxplot(x=\"drive-wheels\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Here we see that the distribution of price between the different drive-wheels categories differs; as such drive-wheels could potentially be a predictor of price.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"discriptive_statistics\">3. Descriptive Statistical Analysis</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Let's first take a look at the variables by utilizing a description method.</p>\n",
    "\n",
    "<p>The <b>describe</b> function automatically computes basic statistics for all continuous variables. Any NaN values are automatically skipped in these statistics.</p>\n",
    "\n",
    "This will show:\n",
    "<ul>\n",
    "    <li>the count of that variable</li>\n",
    "    <li>the mean</li>\n",
    "    <li>the standard deviation (std)</li> \n",
    "    <li>the minimum value</li>\n",
    "    <li>the IQR (Interquartile Range: 25%, 50% and 75%)</li>\n",
    "    <li>the maximum value</li>\n",
    "<ul>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can apply the method \"describe\" as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fwd    118\n",
       "rwd     75\n",
       "4wd      8\n",
       "Name: drive-wheels, dtype: int64"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"drive-wheels\"].value_counts()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The default setting of \"describe\" skips variables of type object. We can apply the method \"describe\" on the variables of type 'object' as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>make</th>\n",
       "      <th>aspiration</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>...</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>horsepower-binned</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.00000</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>200</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>unique</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>22</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>top</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>toyota</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Low</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>freq</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>32</td>\n",
       "      <td>165</td>\n",
       "      <td>115</td>\n",
       "      <td>94</td>\n",
       "      <td>118</td>\n",
       "      <td>198</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>115</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.840796</td>\n",
       "      <td>122.00000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>98.797015</td>\n",
       "      <td>0.837102</td>\n",
       "      <td>...</td>\n",
       "      <td>10.164279</td>\n",
       "      <td>103.405534</td>\n",
       "      <td>5117.665368</td>\n",
       "      <td>25.179104</td>\n",
       "      <td>30.686567</td>\n",
       "      <td>13207.129353</td>\n",
       "      <td>9.944145</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.099502</td>\n",
       "      <td>0.900498</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.254802</td>\n",
       "      <td>31.99625</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.066366</td>\n",
       "      <td>0.059213</td>\n",
       "      <td>...</td>\n",
       "      <td>4.004965</td>\n",
       "      <td>37.365700</td>\n",
       "      <td>478.113805</td>\n",
       "      <td>6.423220</td>\n",
       "      <td>6.815150</td>\n",
       "      <td>7947.066342</td>\n",
       "      <td>2.534599</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.300083</td>\n",
       "      <td>0.300083</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-2.000000</td>\n",
       "      <td>65.00000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>86.600000</td>\n",
       "      <td>0.678039</td>\n",
       "      <td>...</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>48.000000</td>\n",
       "      <td>4150.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>5118.000000</td>\n",
       "      <td>4.795918</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>101.00000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>94.500000</td>\n",
       "      <td>0.801538</td>\n",
       "      <td>...</td>\n",
       "      <td>8.600000</td>\n",
       "      <td>70.000000</td>\n",
       "      <td>4800.000000</td>\n",
       "      <td>19.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>7775.000000</td>\n",
       "      <td>7.833333</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>122.00000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>97.000000</td>\n",
       "      <td>0.832292</td>\n",
       "      <td>...</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>95.000000</td>\n",
       "      <td>5125.369458</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>10295.000000</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2.000000</td>\n",
       "      <td>137.00000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>102.400000</td>\n",
       "      <td>0.881788</td>\n",
       "      <td>...</td>\n",
       "      <td>9.400000</td>\n",
       "      <td>116.000000</td>\n",
       "      <td>5500.000000</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>34.000000</td>\n",
       "      <td>16500.000000</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>256.00000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>120.900000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>23.000000</td>\n",
       "      <td>262.000000</td>\n",
       "      <td>6600.000000</td>\n",
       "      <td>49.000000</td>\n",
       "      <td>54.000000</td>\n",
       "      <td>45400.000000</td>\n",
       "      <td>18.076923</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>11 rows × 29 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         symboling  normalized-losses    make aspiration num-of-doors  \\\n",
       "count   201.000000          201.00000     201        201          201   \n",
       "unique         NaN                NaN      22          2            2   \n",
       "top            NaN                NaN  toyota        std         four   \n",
       "freq           NaN                NaN      32        165          115   \n",
       "mean      0.840796          122.00000     NaN        NaN          NaN   \n",
       "std       1.254802           31.99625     NaN        NaN          NaN   \n",
       "min      -2.000000           65.00000     NaN        NaN          NaN   \n",
       "25%       0.000000          101.00000     NaN        NaN          NaN   \n",
       "50%       1.000000          122.00000     NaN        NaN          NaN   \n",
       "75%       2.000000          137.00000     NaN        NaN          NaN   \n",
       "max       3.000000          256.00000     NaN        NaN          NaN   \n",
       "\n",
       "       body-style drive-wheels engine-location  wheel-base      length  ...  \\\n",
       "count         201          201             201  201.000000  201.000000  ...   \n",
       "unique          5            3               2         NaN         NaN  ...   \n",
       "top         sedan          fwd           front         NaN         NaN  ...   \n",
       "freq           94          118             198         NaN         NaN  ...   \n",
       "mean          NaN          NaN             NaN   98.797015    0.837102  ...   \n",
       "std           NaN          NaN             NaN    6.066366    0.059213  ...   \n",
       "min           NaN          NaN             NaN   86.600000    0.678039  ...   \n",
       "25%           NaN          NaN             NaN   94.500000    0.801538  ...   \n",
       "50%           NaN          NaN             NaN   97.000000    0.832292  ...   \n",
       "75%           NaN          NaN             NaN  102.400000    0.881788  ...   \n",
       "max           NaN          NaN             NaN  120.900000    1.000000  ...   \n",
       "\n",
       "        compression-ratio  horsepower     peak-rpm    city-mpg highway-mpg  \\\n",
       "count          201.000000  201.000000   201.000000  201.000000  201.000000   \n",
       "unique                NaN         NaN          NaN         NaN         NaN   \n",
       "top                   NaN         NaN          NaN         NaN         NaN   \n",
       "freq                  NaN         NaN          NaN         NaN         NaN   \n",
       "mean            10.164279  103.405534  5117.665368   25.179104   30.686567   \n",
       "std              4.004965   37.365700   478.113805    6.423220    6.815150   \n",
       "min              7.000000   48.000000  4150.000000   13.000000   16.000000   \n",
       "25%              8.600000   70.000000  4800.000000   19.000000   25.000000   \n",
       "50%              9.000000   95.000000  5125.369458   24.000000   30.000000   \n",
       "75%              9.400000  116.000000  5500.000000   30.000000   34.000000   \n",
       "max             23.000000  262.000000  6600.000000   49.000000   54.000000   \n",
       "\n",
       "               price city-L/100km  horsepower-binned      diesel         gas  \n",
       "count     201.000000   201.000000                200  201.000000  201.000000  \n",
       "unique           NaN          NaN                  3         NaN         NaN  \n",
       "top              NaN          NaN                Low         NaN         NaN  \n",
       "freq             NaN          NaN                115         NaN         NaN  \n",
       "mean    13207.129353     9.944145                NaN    0.099502    0.900498  \n",
       "std      7947.066342     2.534599                NaN    0.300083    0.300083  \n",
       "min      5118.000000     4.795918                NaN    0.000000    0.000000  \n",
       "25%      7775.000000     7.833333                NaN    0.000000    1.000000  \n",
       "50%     10295.000000     9.791667                NaN    0.000000    1.000000  \n",
       "75%     16500.000000    12.368421                NaN    0.000000    1.000000  \n",
       "max     45400.000000    18.076923                NaN    1.000000    1.000000  \n",
       "\n",
       "[11 rows x 29 columns]"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe(include=\"all\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Value Counts</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Value-counts is a good way of understanding how many units of each characteristic/variable we have. We can apply the \"value_counts\" method on the column 'drive-wheels'. Don’t forget the method \"value_counts\" only works on Pandas series, not Pandas Dataframes. As a result, we only include one bracket \"df['drive-wheels']\" not two brackets \"df[['drive-wheels']]\".</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      rwd\n",
       "1      rwd\n",
       "2      rwd\n",
       "3      fwd\n",
       "4      4wd\n",
       "      ... \n",
       "196    rwd\n",
       "197    rwd\n",
       "198    rwd\n",
       "199    rwd\n",
       "200    rwd\n",
       "Name: drive-wheels, Length: 201, dtype: object"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can convert the series to a Dataframe as follows :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     drive-wheels\n",
       "fwd           118\n",
       "rwd            75\n",
       "4wd             8"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].value_counts().to_frame()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's repeat the above steps but save the results to the dataframe \"drive_wheels_counts\" and rename the column  'drive-wheels' to 'value_counts'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value_counts</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     value_counts\n",
       "fwd           118\n",
       "rwd            75\n",
       "4wd             8"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "drive_wheels_counts = df['drive-wheels'].value_counts().to_frame()\n",
    "drive_wheels_counts.rename(columns={'drive-wheels': 'value_counts'}, inplace=True)\n",
    "drive_wheels_counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Now let's rename the index to 'drive-wheels':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value_counts</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              value_counts\n",
       "drive-wheels              \n",
       "fwd                    118\n",
       "rwd                     75\n",
       "4wd                      8"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "drive_wheels_counts.index.name = 'drive-wheels'\n",
    "drive_wheels_counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can repeat the above process for the variable 'engine-location'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value_counts</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-location</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>front</th>\n",
       "      <td>198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rear</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 value_counts\n",
       "engine-location              \n",
       "front                     198\n",
       "rear                        3"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# engine-location as variable\n",
    "engine_loc_counts = df['engine-location'].value_counts().to_frame()\n",
    "engine_loc_counts.rename(columns={'engine-location': 'value_counts'}, inplace=True)\n",
    "engine_loc_counts.index.name = 'engine-location'\n",
    "engine_loc_counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Examining the value counts of the engine location would not be a good predictor variable for the price. This is because we only have three cars with a rear engine and 198 with an engine in the front, this result is skewed. Thus, we are not able to draw any conclusions about the engine location.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"basic_grouping\">4. Basics of Grouping</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The \"groupby\" method groups data by different categories. The data is grouped based on one or several variables and analysis is performed on the individual groups.</p>\n",
    "\n",
    "<p>For example, let's group by the variable \"drive-wheels\". We see that there are 3 different categories of drive wheels.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['rwd', 'fwd', '4wd'], dtype=object)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>If we want to know, on average, which type of drive wheel is most valuable, we can group \"drive-wheels\" and then average them.</p>\n",
    "\n",
    "<p>We can select the columns 'drive-wheels', 'body-style' and 'price', then assign it to the variable \"df_group_one\".</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_group_one = df[['drive-wheels','body-style','price']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then calculate the average price for each of the different categories of data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4wd</td>\n",
       "      <td>10241.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>fwd</td>\n",
       "      <td>9244.779661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>rwd</td>\n",
       "      <td>19757.613333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  drive-wheels         price\n",
       "0          4wd  10241.000000\n",
       "1          fwd   9244.779661\n",
       "2          rwd  19757.613333"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# grouping results\n",
    "df_group_one = df_group_one.groupby(['drive-wheels'],as_index=False).mean()\n",
    "df_group_one"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>From our data, it seems rear-wheel drive vehicles are, on average, the most expensive, while 4-wheel and front-wheel are approximately the same in price.</p>\n",
    "\n",
    "<p>You can also group with multiple variables. For example, let's group by both 'drive-wheels' and 'body-style'. This groups the dataframe by the unique combinations 'drive-wheels' and 'body-style'. We can store the results in the variable 'grouped_test1'.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>body-style</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4wd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7603.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4wd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>12647.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4wd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>fwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>11595.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>8249.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>8396.387755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9811.800000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>23949.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>24202.714286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>14337.777778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>21711.833333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   drive-wheels   body-style         price\n",
       "0           4wd    hatchback   7603.000000\n",
       "1           4wd        sedan  12647.333333\n",
       "2           4wd        wagon   9095.750000\n",
       "3           fwd  convertible  11595.000000\n",
       "4           fwd      hardtop   8249.000000\n",
       "5           fwd    hatchback   8396.387755\n",
       "6           fwd        sedan   9811.800000\n",
       "7           fwd        wagon   9997.333333\n",
       "8           rwd  convertible  23949.600000\n",
       "9           rwd      hardtop  24202.714286\n",
       "10          rwd    hatchback  14337.777778\n",
       "11          rwd        sedan  21711.833333\n",
       "12          rwd        wagon  16994.222222"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# grouping results\n",
    "df_gptest = df[['drive-wheels','body-style','price']]\n",
    "grouped_test1 = df_gptest.groupby(['drive-wheels','body-style'],as_index=False).mean()\n",
    "grouped_test1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>This grouped data is much easier to visualize when it is made into a pivot table. A pivot table is like an Excel spreadsheet, with one variable along the column and another along the row. We can convert the dataframe to a pivot table using the method \"pivot \" to create a pivot table from the groups.</p>\n",
    "\n",
    "<p>In this case, we will leave the drive-wheel variable as the rows of the table, and pivot body-style to become the columns of the table:</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>body-style</th>\n",
       "      <th>convertible</th>\n",
       "      <th>hardtop</th>\n",
       "      <th>hatchback</th>\n",
       "      <th>sedan</th>\n",
       "      <th>wagon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7603.000000</td>\n",
       "      <td>12647.333333</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>11595.0</td>\n",
       "      <td>8249.000000</td>\n",
       "      <td>8396.387755</td>\n",
       "      <td>9811.800000</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>23949.6</td>\n",
       "      <td>24202.714286</td>\n",
       "      <td>14337.777778</td>\n",
       "      <td>21711.833333</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   price                                            \\\n",
       "body-style   convertible       hardtop     hatchback         sedan   \n",
       "drive-wheels                                                         \n",
       "4wd                  NaN           NaN   7603.000000  12647.333333   \n",
       "fwd              11595.0   8249.000000   8396.387755   9811.800000   \n",
       "rwd              23949.6  24202.714286  14337.777778  21711.833333   \n",
       "\n",
       "                            \n",
       "body-style           wagon  \n",
       "drive-wheels                \n",
       "4wd            9095.750000  \n",
       "fwd            9997.333333  \n",
       "rwd           16994.222222  "
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_pivot = grouped_test1.pivot(index='drive-wheels',columns='body-style')\n",
    "grouped_pivot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Often, we won't have data for some of the pivot cells. We can fill these missing cells with the value 0, but any other value could potentially be used as well. It should be mentioned that missing data is quite a complex subject and is an entire course on its own.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>body-style</th>\n",
       "      <th>convertible</th>\n",
       "      <th>hardtop</th>\n",
       "      <th>hatchback</th>\n",
       "      <th>sedan</th>\n",
       "      <th>wagon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7603.000000</td>\n",
       "      <td>12647.333333</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>11595.0</td>\n",
       "      <td>8249.000000</td>\n",
       "      <td>8396.387755</td>\n",
       "      <td>9811.800000</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>23949.6</td>\n",
       "      <td>24202.714286</td>\n",
       "      <td>14337.777778</td>\n",
       "      <td>21711.833333</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   price                                            \\\n",
       "body-style   convertible       hardtop     hatchback         sedan   \n",
       "drive-wheels                                                         \n",
       "4wd                  0.0      0.000000   7603.000000  12647.333333   \n",
       "fwd              11595.0   8249.000000   8396.387755   9811.800000   \n",
       "rwd              23949.6  24202.714286  14337.777778  21711.833333   \n",
       "\n",
       "                            \n",
       "body-style           wagon  \n",
       "drive-wheels                \n",
       "4wd            9095.750000  \n",
       "fwd            9997.333333  \n",
       "rwd           16994.222222  "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_pivot = grouped_pivot.fillna(0) #fill missing values with 0\n",
    "grouped_pivot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question 4:</h1>\n",
    "\n",
    "<p>Use the \"groupby\" function to find the average \"price\" of each car based on \"body-style\" ? </p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>body-style</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>convertible</td>\n",
       "      <td>21890.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>hardtop</td>\n",
       "      <td>22208.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>hatchback</td>\n",
       "      <td>9957.441176</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>sedan</td>\n",
       "      <td>14459.755319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>wagon</td>\n",
       "      <td>12371.960000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    body-style         price\n",
       "0  convertible  21890.500000\n",
       "1      hardtop  22208.500000\n",
       "2    hatchback   9957.441176\n",
       "3        sedan  14459.755319\n",
       "4        wagon  12371.960000"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df_gptest2 = df[['body-style','price']]\n",
    "grouped_test_bodystyle = df_gptest2.groupby(['body-style'],as_index= 0).mean()\n",
    "grouped_test_bodystyle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "# grouping results\n",
    "df_gptest2 = df[['body-style','price']]\n",
    "grouped_test_bodystyle = df_gptest2.groupby(['body-style'],as_index= False).mean()\n",
    "grouped_test_bodystyle\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you did not import \"pyplot\" let's do it again. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Variables: Drive Wheels and Body Style vs Price</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use a heat map to visualize the relationship between Body Style vs Price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXMAAAD8CAYAAACFK0QrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAXRElEQVR4nO3dbYxc1Z3n8e+v2+ZhIYQEE+K1PQFNrMwA0vBgOUSsVuwwMzEMihkNkRxpA8ogeYOIFrSjrMK8mNnsiFXyYsksSwLxDiw4mwmx8oSVNZNBJCOCxJNhzaPD0hqS4LWFF5IAVgDT3b99UaezRVHddbu72tX33t9HOupbp8699S8Q/zqce865sk1ERNTb2KgDiIiIxUsyj4hogCTziIgGSDKPiGiAJPOIiAZIMo+IaICByVzSMZIelvS4pKclfb5PG0m6UdKEpCcknbM04UZERD8rKrR5E/h924ckrQTul3S37Qe72lwErC/lw8DN5W9ERBwBA3vm7jhUXq4spXel0WZge2n7IHCipNXDDTUiImZTpWeOpHHgUeCDwJdtP9TTZA3wQtfrfaXuQM91tgJbARhbca6OOXFhUS9XDV1N+7vr1406hKGb2P/qqENYEqec9M9GHcKSeOHZp16yffJirjF2wloz+Ualtn795R/Y3rSYzzvSKiVz21PAWZJOBL4r6UzbT3U1Ub/T+lxnG7ANYOy4k33U6X+6gJCXr+nJw6MOYUns2PU3ow5h6D72+XtGHcKS+LefPHvUISyJa//Fb/9s0ReZfIMVH/pYpaZv7fnvqxb9eUdYpWQ+w/avJP0jsAnoTub7gO7u21pg/6Kji4gYFgmNjY86iiVTZTbLyaVHjqRjgT8AftLTbCdweZnVch7wiu0DREQsG2JsxVGVSh1V6ZmvBu4o4+ZjwA7b35f0aQDbtwC7gIuBCeDXwKeWKN6IiIVpeM98YDK3/QTwjoG4ksRnjg1cPdzQIiKGR4DGW5zMIyIaQWKszT3ziIimaPUwS0REI7R9zDwiogmEGFuxctRhLJkk84hoh/TMIyKaIck8IqLupExNjIioO5GeeURE/WmM8Zou1a8iyTwi2kHpmUdE1J7IbJaIiEZIMo+IqLvMM4+IaIIk84iI2pPE2MrMZomIqLcMs0RENEOSeUREA4yNadQhLJkk84hoBUkoyTwiov7Gx8dGHcKSSTKPiHYQ6ZlHRNRdZ9fEJPOIiJoTY0oyj4iotwyzREQ0Q5J5RETNSTC+Isk8IqL21OAx84GTLiWtk/QjSXslPS3pmj5tLpD0iqQ9pfzl0oQbEbEwkhgbq1bqqErPfBL4c9uPSXoX8Kike2w/09Pux7YvGX6IERHD0eQx84E9c9sHbD9Wjl8D9gJrljqwiIhh05gqlTmvMctohaT3SrpH0nPl73u6zrlO0oSkZyV9tKv+XElPlvduVBkHknS0pG+W+ocknTrou81rbWu54NnAQ33e/oikxyXdLemM+Vw3ImLJCcakSmWAmdGK3wXOA66WdDrwOeBe2+uBe8tryntbgDOATcBXJM1s33gzsBVYX8qmUn8l8EvbHwS+BHxxUFCVk7mk44FvA9fafrXn7ceAD9j+PeC/At+b5RpbJe2WtNuTb1T96IiIRRNibMVYpTKXOUYrNgN3lGZ3AJeW483AnbbftP08MAFslLQaOMH2A7YNbO85Z+Za3wIunOm1z6ZSMpe0kk4i/7rt7/T5cq/aPlSOdwErJa3q026b7Q22N2jFMVU+OiJiOMR8boCumul4lrK17yXfPlpxiu0D0En4wPtKszXAC12n7St1a8pxb/3bzrE9CbwCnDTX1xt4A7T8GtwK7LV9wyxt3g+8aNuSNtL5kXh50LUjIo6keUxNfMn2hgHXettoxRzX7veG56if65xZVZnNcj7wSeBJSXtK3V8AvwVg+xbgMuAqSZPA68CW8r8NERHLQmejrSFdq/9oxYuSVts+UIZQDpb6fcC6rtPXAvtL/do+9d3n7JO0Ang38Iu5YhqYzG3fT/9fie42NwE3DbpWRMTIaDhPGppjtGIncAXwhfL3rq76v5N0A/DP6dzofNj2lKTXJJ1HZ5jmcjr3HLuv9QCdzvIPB3WQswI0IlpCjA3n4RSzjVZ8Adgh6Urg58DHAWw/LWkH8AydmTBX254q510F3A4cC9xdCnR+LL4maYJOj3zLoKCSzCOiFTSknvmA0YoLZznneuD6PvW7gTP71L9B+TGoKsk8IlqjyStAk8wjohUkGE8yj4iovyTziIiaE0oyj4ioOwmOGrBUv86SzCOiFSRYkZ55RES9iYyZR0TUnzJmHhFRe52eecbMIyJqLz3ziIiaG5MymyUiognGq+9nXjtJ5hHRClnOHxHREEnmERE1l0VDERENIHIDNCKi9jJmHhHRAFnOHxHRBOmZR0TUX/Yzj4hoiCTziIiaG8vDKSIiGiBj5hER9SeUvVkiIppgLMk8IqLeBIw3N5cz8G6ApHWSfiRpr6SnJV3Tp40k3ShpQtITks5ZmnAjIhZIMDamSqWOqvTMJ4E/t/2YpHcBj0q6x/YzXW0uAtaX8mHg5vI3ImJZELCywY+NG/jNbB+w/Vg5fg3YC6zpabYZ2O6OB4ETJa0eerQREQs0M8xSpdTRvMbMJZ0KnA081PPWGuCFrtf7St2BnvO3AlsB1q1by3P3/qf5RbvcPXzXqCNYGnu/N+oIhu65z/7OqENYEh771ahDWBLXDuMiqu8QShWV/59D0vHAt4Frbb/a+3afU/yOCnub7Q22N5x80knzizQiYhFEZzZLlVJHlXrmklbSSeRft/2dPk32Aeu6Xq8F9i8+vIiI4anrEEoVVWazCLgV2Gv7hlma7QQuL7NazgNesX1glrYREUecBCvHxyqVOqrSMz8f+CTwpKQ9pe4vgN8CsH0LsAu4GJgAfg18avihRkQs3MwwS1MNTOa276f/mHh3GwNXDyuoiIil0ORhlqwAjYhWEPW9uVlFPQeHIiLmq+yaWKUMvJR0m6SDkp7qqvsPkv6PpD2lXNz13nVlhfyzkj7aVX+upCfLezeWe5RIOlrSN0v9Q2Va+JySzCOiFTpj5tVKBbcDm/rUf8n2WaXsApB0OrAFOKOc8xVJ46X9zXTW3sysoJ+55pXAL21/EPgS8MVBASWZR0QrzCznr1IGsX0f8IuKH70ZuNP2m7afpzNRZGNZJX+C7QfKfcftwKVd59xRjr8FXDjTa59NknlEtINgfKxaAVZJ2t1Vtlb8lM+UzQZvk/SeUjfbCvk15bi3/m3n2J4EXgHmXGmZG6AR0QrznJr4ku0N8/yIm4G/prP6/a+B/wz8GbOvkJ9r5XylVfXdkswjoiWW9klDtl/8zSdJ/w34fnk52wr5feW4t777nH2SVgDvZsCwToZZIqIVlnpvlp6dYv8EmJnpshPYUmaonEbnRufDZZX8a5LOK+PhlwN3dZ1zRTm+DPhhGVefVXrmEdEKneX8w+mZS/oGcAGdsfV9wF8BF0g6i85wyE+BfwNg+2lJO4Bn6Dwf4mrbU+VSV9GZGXMscHcp0NlC5WuSJuj0yLcMiinJPCJaY1ijLLY/0af61jnaXw9c36d+N3Bmn/o3gI/PJ6Yk84hojbG5dyaptSTziGgFMbye+XKUZB4RrdHgBw0lmUdESyg984iI2tMSzzMftSTziGiNDLNERDRAg3N5knlEtEPrHxsXEdEUDc7lSeYR0R5N3owqyTwiWkHlsXFNlWQeEa2RYZaIiJoTGWaJiGiEAY/RrLUk84hoB2XRUERE7QkY0rMplqUk84hojSYPswy8HyDpNkkHJT01y/sXSHpF0p5S/nL4YUZELE5nBWi1UkdVeua3AzcB2+do82PblwwlooiIJVLTPF3JwGRu+z5Jpy59KBERS0mN3ptlWNMuPyLpcUl3SzpjtkaStkraLWn3/3355SF9dEREBeXhFFVKHQ3jBuhjwAdsH5J0MfA9YH2/hra3AdsAzj37LA/hsyMiKpGNpqdGHcaSWXTP3Partg+V413ASkmrFh1ZRMSQydOVSh0tumcu6f3Ai7YtaSOdH4iMoUTEMmOoaaKuYmAyl/QN4AJglaR9wF8BKwFs3wJcBlwlaRJ4HdhiO0MoEbH8NDg1VZnN8okB799EZ+piRMTy5Zb3zCMimqKu4+FVJJlHREsYpidHHcSSSTKPiHYwGWaJiKg/w3SSeURE7WXMPCKiCZLMIyJqzoYGL+dPMo+I1sgwS0RE7WXRUEREMzQ4mQ9rP/OIiOVtZjl/lTJAv8dpSnqvpHskPVf+vqfrveskTUh6VtJHu+rPlfRkee9GlYeUSjpa0jdL/UNVHhCUZB4RrSCGugXu7cCmnrrPAffaXg/cW14j6XRgC3BGOecrksbLOTcDW+k8A2J91zWvBH5p+4PAl4AvDgooyTwiWsIwNVWtDLqSfR/wi57qzcAd5fgO4NKu+jttv2n7eWAC2ChpNXCC7QfKTrPbe86Zuda3gAtneu2zyZh5RLTD/Jbzr5K0u+v1tvKktLmcYvsAgO0Dkt5X6tcAD3a121fq3irHvfUz57xQrjUp6RXgJOCl2T48yTwiWmMeUxNfsr1hWB/bp85z1M91zqwyzBIRLTG8G6CzeLEMnVD+Hiz1+4B1Xe3WAvtL/do+9W87R9IK4N28c1jnbZLMI6I9ljaZ7wSuKMdXAHd11W8pM1ROo3Oj8+EyJPOapPPKePjlPefMXOsy4IeDnuCWYZaIaIchLuef5XGaXwB2SLoS+Dnw8c7H+mlJO4BngEngatszgVxFZ2bMscDdpQDcCnxN0gSdHvmWQTElmUdESxhPvjWcK83+OM0LZ2l/PXB9n/rdwJl96t+g/BhUlWQeEe1gstFWRETdGeMKc8jrKsk8ItrB5ElDERH1l/3MIyLqz8O7AbocJZlHREsYp2ceEVFzmc0SEdEEbvQN0IHL+fttwt7zvsqm6hOSnpB0zvDDjIhYJIOnpiqVOqqyN8vtvHMT9m4X8f83Vt9KZ7P1iIhlpsxmqVJqaOAwi+37BjyyaDOwvWwC86CkEyWtntnXNyJiWchsloF+s4l6MbPB+juSuaStdHrvrFu3tvftiIgllHnmg1TeRL08qWMbwMk62te8O8PrdXDDtz4z6hCG7vWNl406hCVx/HP3jTqE5SuzWQaabeP1iIhlwxi3eTZLBTuBy8uslvOAVzJeHhHLzkzPvK03QGfZhH0lgO1bgF3AxXSeOP1r4FNLFWxExILZ+K3Do45iyVSZzTLbJuwz7xu4emgRRUQsiWYvGsoK0Ihoj5oOoVSRZB4R7eBstBUR0QhNns2SZB4R7WDjqSTziIhas830W5OjDmPJJJlHRDuY9MwjIpogyTwiouZsM13TvcqrSDKPiNbIbJaIiLrLbJaIiPrLbJaIiIaYTs88IqLmMjUxIqIBMmYeEVF/JrNZIiLqz2b6cG6ARkTUm2E6PfOIiHozGTOPiKg/gxu8nH9s1AFERBwZxtPTlcogkn4q6UlJeyTtLnXvlXSPpOfK3/d0tb9O0oSkZyV9tKv+3HKdCUk3StJCv12SeUS0Q5lnXqVU9K9sn2V7Q3n9OeBe2+uBe8trJJ0ObAHOADYBX5E0Xs65GdgKrC9l00K/XpJ5RLSCbaYOT1YqC7QZuKMc3wFc2lV/p+03bT8PTAAbJa0GTrD9gG0D27vOmbck84hoiXkNs6yStLurbH3HxeAfJD3a9d4ptg8AlL/vK/VrgBe6zt1X6taU4976BckN0Ihoh/kt53+pa/ikn/Nt75f0PuAeST+Zo22/cXDPUb8gSeYR0Q4GTy04V779Uvb+8vegpO8CG4EXJa22faAMoRwszfcB67pOXwvsL/Vr+9QvSIZZIqIVjJmemq5U5iLpOEnvmjkG/gh4CtgJXFGaXQHcVY53AlskHS3pNDo3Oh8uQzGvSTqvzGK5vOuceUvPPCLaweDpofTMTwG+W2YRrgD+zvbfS3oE2CHpSuDnwMcBbD8taQfwDDAJXG17ZsL7VcDtwLHA3aUsSKVkLmkT8F+AceBvbX+h5/0L6PyiPF+qvmP7Py40qIiIYbNh6vDiFw3Z/ifg9/rUvwxcOMs51wPX96nfDZy56KCokMzLfMgvA39IZ4znEUk7bT/T0/THti8ZRlAREUNnD23MfDmq0jPfCEyUXyMk3Uln3mRvMo+IWNamG5zMq9wAnW2OZK+PSHpc0t2SzhhKdBERwzL8FaDLSpWeeZW5kI8BH7B9SNLFwPfo3LF9+4U6k+u3AhzPeO/bERFLxsD0cG6ALktVeuazzZH8Dduv2j5UjncBKyWt6r2Q7W22N9jecEySeUQcSTZTh6cqlTqqkswfAdZLOk3SUXQ2jNnZ3UDS+2d2+5K0sVz35WEHGxGxUC6LhqqUOho4zGJ7UtJngB/QmZp4W5k3+eny/i3AZcBVkiaB14EtZeOYiIjlYYgrQJejSvPMy9DJrp66W7qObwJuGm5oERHD5IGrO+ssK0Ajoh2GtwJ0WUoyj4hWMM2eZ55kHhHtYDNd05kqVSSZR0Qr2OmZR0Q0QpWHNddVknlEtIOdnnlERO1lnnlERP2ZeT0DtHaSzCOiHWymDieZR0TUmg3TDd5lJMk8IlpjKsk8IqLeDDT4/meSeUS0R3rmERE1N204nI22IiLqL8MsERE1Z5xhloiIussN0IiIhkgyj4ioOTuzWSIias9kNktERO1lzDwioiEyzBIRUXOdMfNRR7F0kswjojXSM4+IqDkDzd3NPMk8IlrCOLNZIiLqrjObJck8IqLeGn4DdKxKI0mbJD0raULS5/q8L0k3lvefkHTO8EONiFi4mZ55lTLIoJw4CgOTuaRx4MvARcDpwCcknd7T7CJgfSlbgZuHHGdExKJNuVqZS8WceMRV6ZlvBCZs/5Ptw8CdwOaeNpuB7e54EDhR0uohxxoRsWDTdJbzVykDVMmJR1yVMfM1wAtdr/cBH67QZg1woLuRpK10eu4Ab36Vnz01r2jrYRXw0qiDGKavXvbZxn0n+Cw08N8VzfxOAB9a7AVe4vAPvsrPVlVsfoyk3V2vt9neVo6r5MQjrkoyV5+63p+uKm0o/zC2AUjabXtDhc+vlSZ+ryZ+J2jm92rid4LO91rsNWxvGkYsVMx3R1qVYZZ9wLqu12uB/QtoExHRBMsy31VJ5o8A6yWdJukoYAuws6fNTuDyMqvlPOAV2wd6LxQR0QBVcuIRN3CYxfakpM8APwDGgdtsPy3p0+X9W4BdwMXABPBr4FMVPnvb4Ca11MTv1cTvBM38Xk38TrCMvtdsOXHEYSE3eEVURERbVFo0FBERy1uSeUREA4wkmS/HpbCLJek2SQclNWbuvKR1kn4kaa+kpyVdM+qYFkvSMZIelvR4+U6fH3VMwyRpXNL/kvT9UccyLJJ+KulJSXuGMUWxqY74mHlZCvu/gT+kM8XnEeATtp85ooEMmaR/CRyisxL2zFHHMwxlFe9q249JehfwKHBpnf9dSRJwnO1DklYC9wPXlJXLtSfp3wEbgBNsXzLqeIZB0k+BDbabuBhqaEbRM1+WS2EXy/Z9wC9GHccw2T5g+7Fy/Bqwl87qt9oqW04cKi9XltKIWQCS1gJ/DPztqGOJI28UyXy2pf+xjEk6FTgbeGi0kSxeGYrYAxwE7rFd++9U/A3w72neA3UM/IOkR8uWINHHKJL5slwKG7OTdDzwbeBa26+OOp7Fsj1l+yw6K/c2Sqr9sJikS4CDth8ddSxL4Hzb59DZpfDqMqQZPUaRzJflUtjor4wrfxv4uu3vjDqeYbL9K+AfgWHt2TFK5wMfK+PLdwK/L+l/jDak4bC9v/w9CHyXzlBt9BhFMl+WS2HjncrNwluBvbZvGHU8wyDpZEknluNjgT8AfjLaqBbP9nW219o+lc5/Uz+0/a9HHNaiSTqu3HxH0nHAHwGNmTE2TEc8mdueBGaWwu4FdiyHpbCLJekbwAPAhyTtk3TlqGMagvOBT9Lp5e0p5eJRB7VIq4EfSXqCTsfiHtuNmcbXQKcA90t6HHgY+J+2/37EMS1LWc4fEdEAWQEaEdEASeYREQ2QZB4R0QBJ5hERDZBkHhHRAEnmERENkGQeEdEA/w9sx4rJMwWCTgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#use the grouped results\n",
    "plt.pcolor(grouped_pivot, cmap='RdBu')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The heatmap plots the target variable (price) proportional to colour with respect to the variables 'drive-wheel' and 'body-style' in the vertical and horizontal axis respectively. This allows us to visualize how the price is related to 'drive-wheel' and 'body-style'.</p>\n",
    "\n",
    "<p>The default labels convey no useful information to us. Let's change that:</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "im = ax.pcolor(grouped_pivot, cmap='RdBu')\n",
    "\n",
    "#label names\n",
    "row_labels = grouped_pivot.columns.levels[1]\n",
    "col_labels = grouped_pivot.index\n",
    "\n",
    "#move ticks and labels to the center\n",
    "ax.set_xticks(np.arange(grouped_pivot.shape[1]) + 0.5, minor=False)\n",
    "ax.set_yticks(np.arange(grouped_pivot.shape[0]) + 0.5, minor=False)\n",
    "\n",
    "#insert labels\n",
    "ax.set_xticklabels(row_labels, minor=0)\n",
    "ax.set_yticklabels(col_labels, minor=0)\n",
    "\n",
    "#rotate label if too long\n",
    "plt.xticks(rotation=55)\n",
    "\n",
    "fig.colorbar(im)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Visualization is very important in data science, and Python visualization packages provide great freedom. We will go more in-depth in a separate Python Visualizations course.</p>\n",
    "\n",
    "<p>The main question we want to answer in this module, is \"What are the main characteristics which have the most impact on the car price?\".</p>\n",
    "\n",
    "<p>To get a better measure of the important characteristics, we look at the correlation of these variables with the car price, in other words: how is the car price dependent on this variable?</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"correlation_causation\">5. Correlation and Causation</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p><b>Correlation</b>: a measure of the extent of interdependence between variables.</p>\n",
    "\n",
    "<p><b>Causation</b>: the relationship between cause and effect between two variables.</p>\n",
    "\n",
    "<p>It is important to know the difference between these two and that correlation does not imply causation. Determining correlation is much simpler  the determining causation as causation may require independent experimentation.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p3>Pearson Correlation</p>\n",
    "<p>The Pearson Correlation measures the linear dependence between two variables X and Y.</p>\n",
    "<p>The resulting coefficient is a value between -1 and 1 inclusive, where:</p>\n",
    "<ul>\n",
    "    <li><b>1</b>: Total positive linear correlation.</li>\n",
    "    <li><b>0</b>: No linear correlation, the two variables most likely do not affect each other.</li>\n",
    "    <li><b>-1</b>: Total negative linear correlation.</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Pearson Correlation is the default method of the function \"corr\".  Like before we can calculate the Pearson Correlation of the of the 'int64' or 'float64'  variables.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>symboling</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.466264</td>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.365404</td>\n",
       "      <td>-0.242423</td>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.233118</td>\n",
       "      <td>-0.110581</td>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.008245</td>\n",
       "      <td>-0.182196</td>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.279740</td>\n",
       "      <td>-0.035527</td>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.066171</td>\n",
       "      <td>-0.196735</td>\n",
       "      <td>0.196735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>normalized-losses</th>\n",
       "      <td>0.466264</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.101546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wheel-base</th>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>-0.307237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>length</th>\n",
       "      <td>-0.365404</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>-0.211187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>width</th>\n",
       "      <td>-0.242423</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>-0.244356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>height</th>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>-0.281578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>curb-weight</th>\n",
       "      <td>-0.233118</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>-0.221046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>-0.110581</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>-0.070779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>-0.054458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.008245</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>-0.241303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>-0.182196</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.985231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>0.169053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>0.279740</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.475812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-mpg</th>\n",
       "      <td>-0.035527</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>-0.265676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>-0.198690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.110326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-L/100km</th>\n",
       "      <td>0.066171</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>0.241282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diesel</th>\n",
       "      <td>-0.196735</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gas</th>\n",
       "      <td>0.196735</td>\n",
       "      <td>0.101546</td>\n",
       "      <td>-0.307237</td>\n",
       "      <td>-0.211187</td>\n",
       "      <td>-0.244356</td>\n",
       "      <td>-0.281578</td>\n",
       "      <td>-0.221046</td>\n",
       "      <td>-0.070779</td>\n",
       "      <td>-0.054458</td>\n",
       "      <td>-0.241303</td>\n",
       "      <td>-0.985231</td>\n",
       "      <td>0.169053</td>\n",
       "      <td>0.475812</td>\n",
       "      <td>-0.265676</td>\n",
       "      <td>-0.198690</td>\n",
       "      <td>-0.110326</td>\n",
       "      <td>0.241282</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   symboling  normalized-losses  wheel-base    length  \\\n",
       "symboling           1.000000           0.466264   -0.535987 -0.365404   \n",
       "normalized-losses   0.466264           1.000000   -0.056661  0.019424   \n",
       "wheel-base         -0.535987          -0.056661    1.000000  0.876024   \n",
       "length             -0.365404           0.019424    0.876024  1.000000   \n",
       "width              -0.242423           0.086802    0.814507  0.857170   \n",
       "height             -0.550160          -0.373737    0.590742  0.492063   \n",
       "curb-weight        -0.233118           0.099404    0.782097  0.880665   \n",
       "engine-size        -0.110581           0.112360    0.572027  0.685025   \n",
       "bore               -0.140019          -0.029862    0.493244  0.608971   \n",
       "stroke             -0.008245           0.055563    0.158502  0.124139   \n",
       "compression-ratio  -0.182196          -0.114713    0.250313  0.159733   \n",
       "horsepower          0.075819           0.217299    0.371147  0.579821   \n",
       "peak-rpm            0.279740           0.239543   -0.360305 -0.285970   \n",
       "city-mpg           -0.035527          -0.225016   -0.470606 -0.665192   \n",
       "highway-mpg         0.036233          -0.181877   -0.543304 -0.698142   \n",
       "price              -0.082391           0.133999    0.584642  0.690628   \n",
       "city-L/100km        0.066171           0.238567    0.476153  0.657373   \n",
       "diesel             -0.196735          -0.101546    0.307237  0.211187   \n",
       "gas                 0.196735           0.101546   -0.307237 -0.211187   \n",
       "\n",
       "                      width    height  curb-weight  engine-size      bore  \\\n",
       "symboling         -0.242423 -0.550160    -0.233118    -0.110581 -0.140019   \n",
       "normalized-losses  0.086802 -0.373737     0.099404     0.112360 -0.029862   \n",
       "wheel-base         0.814507  0.590742     0.782097     0.572027  0.493244   \n",
       "length             0.857170  0.492063     0.880665     0.685025  0.608971   \n",
       "width              1.000000  0.306002     0.866201     0.729436  0.544885   \n",
       "height             0.306002  1.000000     0.307581     0.074694  0.180449   \n",
       "curb-weight        0.866201  0.307581     1.000000     0.849072  0.644060   \n",
       "engine-size        0.729436  0.074694     0.849072     1.000000  0.572609   \n",
       "bore               0.544885  0.180449     0.644060     0.572609  1.000000   \n",
       "stroke             0.188829 -0.062704     0.167562     0.209523 -0.055390   \n",
       "compression-ratio  0.189867  0.259737     0.156433     0.028889  0.001263   \n",
       "horsepower         0.615077 -0.087027     0.757976     0.822676  0.566936   \n",
       "peak-rpm          -0.245800 -0.309974    -0.279361    -0.256733 -0.267392   \n",
       "city-mpg          -0.633531 -0.049800    -0.749543    -0.650546 -0.582027   \n",
       "highway-mpg       -0.680635 -0.104812    -0.794889    -0.679571 -0.591309   \n",
       "price              0.751265  0.135486     0.834415     0.872335  0.543155   \n",
       "city-L/100km       0.673363  0.003811     0.785353     0.745059  0.554610   \n",
       "diesel             0.244356  0.281578     0.221046     0.070779  0.054458   \n",
       "gas               -0.244356 -0.281578    -0.221046    -0.070779 -0.054458   \n",
       "\n",
       "                     stroke  compression-ratio  horsepower  peak-rpm  \\\n",
       "symboling         -0.008245          -0.182196    0.075819  0.279740   \n",
       "normalized-losses  0.055563          -0.114713    0.217299  0.239543   \n",
       "wheel-base         0.158502           0.250313    0.371147 -0.360305   \n",
       "length             0.124139           0.159733    0.579821 -0.285970   \n",
       "width              0.188829           0.189867    0.615077 -0.245800   \n",
       "height            -0.062704           0.259737   -0.087027 -0.309974   \n",
       "curb-weight        0.167562           0.156433    0.757976 -0.279361   \n",
       "engine-size        0.209523           0.028889    0.822676 -0.256733   \n",
       "bore              -0.055390           0.001263    0.566936 -0.267392   \n",
       "stroke             1.000000           0.187923    0.098462 -0.065713   \n",
       "compression-ratio  0.187923           1.000000   -0.214514 -0.435780   \n",
       "horsepower         0.098462          -0.214514    1.000000  0.107885   \n",
       "peak-rpm          -0.065713          -0.435780    0.107885  1.000000   \n",
       "city-mpg          -0.034696           0.331425   -0.822214 -0.115413   \n",
       "highway-mpg       -0.035201           0.268465   -0.804575 -0.058598   \n",
       "price              0.082310           0.071107    0.809575 -0.101616   \n",
       "city-L/100km       0.037300          -0.299372    0.889488  0.115830   \n",
       "diesel             0.241303           0.985231   -0.169053 -0.475812   \n",
       "gas               -0.241303          -0.985231    0.169053  0.475812   \n",
       "\n",
       "                   city-mpg  highway-mpg     price  city-L/100km    diesel  \\\n",
       "symboling         -0.035527     0.036233 -0.082391      0.066171 -0.196735   \n",
       "normalized-losses -0.225016    -0.181877  0.133999      0.238567 -0.101546   \n",
       "wheel-base        -0.470606    -0.543304  0.584642      0.476153  0.307237   \n",
       "length            -0.665192    -0.698142  0.690628      0.657373  0.211187   \n",
       "width             -0.633531    -0.680635  0.751265      0.673363  0.244356   \n",
       "height            -0.049800    -0.104812  0.135486      0.003811  0.281578   \n",
       "curb-weight       -0.749543    -0.794889  0.834415      0.785353  0.221046   \n",
       "engine-size       -0.650546    -0.679571  0.872335      0.745059  0.070779   \n",
       "bore              -0.582027    -0.591309  0.543155      0.554610  0.054458   \n",
       "stroke            -0.034696    -0.035201  0.082310      0.037300  0.241303   \n",
       "compression-ratio  0.331425     0.268465  0.071107     -0.299372  0.985231   \n",
       "horsepower        -0.822214    -0.804575  0.809575      0.889488 -0.169053   \n",
       "peak-rpm          -0.115413    -0.058598 -0.101616      0.115830 -0.475812   \n",
       "city-mpg           1.000000     0.972044 -0.686571     -0.949713  0.265676   \n",
       "highway-mpg        0.972044     1.000000 -0.704692     -0.930028  0.198690   \n",
       "price             -0.686571    -0.704692  1.000000      0.789898  0.110326   \n",
       "city-L/100km      -0.949713    -0.930028  0.789898      1.000000 -0.241282   \n",
       "diesel             0.265676     0.198690  0.110326     -0.241282  1.000000   \n",
       "gas               -0.265676    -0.198690 -0.110326      0.241282 -1.000000   \n",
       "\n",
       "                        gas  \n",
       "symboling          0.196735  \n",
       "normalized-losses  0.101546  \n",
       "wheel-base        -0.307237  \n",
       "length            -0.211187  \n",
       "width             -0.244356  \n",
       "height            -0.281578  \n",
       "curb-weight       -0.221046  \n",
       "engine-size       -0.070779  \n",
       "bore              -0.054458  \n",
       "stroke            -0.241303  \n",
       "compression-ratio -0.985231  \n",
       "horsepower         0.169053  \n",
       "peak-rpm           0.475812  \n",
       "city-mpg          -0.265676  \n",
       "highway-mpg       -0.198690  \n",
       "price             -0.110326  \n",
       "city-L/100km       0.241282  \n",
       "diesel            -1.000000  \n",
       "gas                1.000000  "
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " sometimes we would like to know the significant of the correlation estimate. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>P-value</b>: \n",
    "<p>What is this P-value? The P-value is the probability value that the correlation between these two variables is statistically significant. Normally, we choose a significance level of 0.05, which means that we are 95% confident that the correlation between the variables is significant.</p>\n",
    "\n",
    "By convention, when the\n",
    "<ul>\n",
    "    <li>p-value is $<$ 0.001: we say there is strong evidence that the correlation is significant.</li>\n",
    "    <li>the p-value is $<$ 0.05: there is moderate evidence that the correlation is significant.</li>\n",
    "    <li>the p-value is $<$ 0.1: there is weak evidence that the correlation is significant.</li>\n",
    "    <li>the p-value is $>$ 0.1: there is no evidence that the correlation is significant.</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can obtain this information using  \"stats\" module in the \"scipy\"  library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Wheel-base vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the  Pearson Correlation Coefficient and P-value of 'wheel-base' and 'price'. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.584641822265508  with a P-value of P = 8.076488270733218e-20\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['wheel-base'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between wheel-base and price is statistically significant, although the linear relationship isn't extremely strong (~0.585)</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Horsepower vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the  Pearson Correlation Coefficient and P-value of 'horsepower' and 'price'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8095745670036559  with a P-value of P =  6.369057428260101e-48\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['horsepower'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between horsepower and price is statistically significant, and the linear relationship is quite strong (~0.809, close to 1)</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Length vs Price</h3>\n",
    "\n",
    "Let's calculate the  Pearson Correlation Coefficient and P-value of 'length' and 'price'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.6906283804483638  with a P-value of P =  8.016477466159556e-30\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['length'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between length and price is statistically significant, and the linear relationship is moderately strong (~0.691).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Width vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the Pearson Correlation Coefficient and P-value of 'width' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.7512653440522673  with a P-value of P = 9.200335510481646e-38\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['width'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Conclusion:\n",
    "\n",
    "Since the p-value is < 0.001, the correlation between width and price is statistically significant, and the linear relationship is quite strong (~0.751)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Curb-weight vs Price"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the Pearson Correlation Coefficient and P-value of 'curb-weight' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8344145257702843  with a P-value of P =  2.189577238894065e-53\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['curb-weight'], df['price'])\n",
    "print( \"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between curb-weight and price is statistically significant, and the linear relationship is quite strong (~0.834).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Engine-size vs Price</h3>\n",
    "\n",
    "Let's calculate the Pearson Correlation Coefficient and P-value of 'engine-size' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8723351674455185  with a P-value of P = 9.265491622198389e-64\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['engine-size'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between engine-size and price is statistically significant, and the linear relationship is very strong (~0.872).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Bore vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the  Pearson Correlation Coefficient and P-value of 'bore' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.5431553832626602  with a P-value of P =   8.049189483935489e-17\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['bore'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =  \", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between bore and price is statistically significant, but the linear relationship is only moderate (~0.521).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can relate the process for each 'City-mpg'  and 'Highway-mpg':"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>City-mpg vs Price</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.6865710067844678  with a P-value of P =  2.321132065567641e-29\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['city-mpg'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between city-mpg and price is statistically significant, and the coefficient of ~ -0.687 shows that the relationship is negative and moderately strong.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Highway-mpg vs Price</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.704692265058953  with a P-value of P =  1.7495471144476358e-31\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['highway-mpg'], df['price'])\n",
    "print( \"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Conclusion:\n",
    "Since the p-value is < 0.001, the correlation between highway-mpg and price is statistically significant, and the coefficient of ~ -0.705 shows that the relationship is negative and moderately strong."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"anova\">6. ANOVA</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>ANOVA: Analysis of Variance</h3>\n",
    "<p>The Analysis of Variance  (ANOVA) is a statistical method used to test whether there are significant differences between the means of two or more groups. ANOVA returns two parameters:</p>\n",
    "\n",
    "<p><b>F-test score</b>: ANOVA assumes the means of all groups are the same, calculates how much the actual means deviate from the assumption, and reports it as the F-test score. A larger score means there is a larger difference between the means.</p>\n",
    "\n",
    "<p><b>P-value</b>:  P-value tells how statistically significant is our calculated score value.</p>\n",
    "\n",
    "<p>If our price variable is strongly correlated with the variable we are analyzing, expect ANOVA to return a sizeable F-test score and a small p-value.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Drive Wheels</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Since ANOVA analyzes the difference between different groups of the same variable, the groupby function will come in handy. Because the ANOVA algorithm averages the data automatically, we do not need to take the average before hand.</p>\n",
    "\n",
    "<p>Let's see if different types 'drive-wheels' impact  'price', we group the data.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's see if different types 'drive-wheels' impact  'price', we group the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>rwd</td>\n",
       "      <td>13495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>rwd</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>rwd</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>fwd</td>\n",
       "      <td>13950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4wd</td>\n",
       "      <td>17450.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>fwd</td>\n",
       "      <td>15250.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>fwd</td>\n",
       "      <td>17710.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>fwd</td>\n",
       "      <td>18920.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>fwd</td>\n",
       "      <td>23875.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>rwd</td>\n",
       "      <td>16430.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>rwd</td>\n",
       "      <td>16925.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>136</th>\n",
       "      <td>4wd</td>\n",
       "      <td>7603.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>140</th>\n",
       "      <td>4wd</td>\n",
       "      <td>9233.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>141</th>\n",
       "      <td>4wd</td>\n",
       "      <td>11259.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>144</th>\n",
       "      <td>4wd</td>\n",
       "      <td>8013.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    drive-wheels    price\n",
       "0            rwd  13495.0\n",
       "1            rwd  16500.0\n",
       "2            rwd  16500.0\n",
       "3            fwd  13950.0\n",
       "4            4wd  17450.0\n",
       "5            fwd  15250.0\n",
       "6            fwd  17710.0\n",
       "7            fwd  18920.0\n",
       "8            fwd  23875.0\n",
       "9            rwd  16430.0\n",
       "10           rwd  16925.0\n",
       "136          4wd   7603.0\n",
       "140          4wd   9233.0\n",
       "141          4wd  11259.0\n",
       "144          4wd   8013.0"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_test2=df_gptest[['drive-wheels', 'price']].groupby(['drive-wheels'])\n",
    "grouped_test2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>body-style</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>13495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>13950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4wd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>17450.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>196</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>16845.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>197</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>19045.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>21485.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>199</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>22470.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>200</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>22625.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>201 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    drive-wheels   body-style    price\n",
       "0            rwd  convertible  13495.0\n",
       "1            rwd  convertible  16500.0\n",
       "2            rwd    hatchback  16500.0\n",
       "3            fwd        sedan  13950.0\n",
       "4            4wd        sedan  17450.0\n",
       "..           ...          ...      ...\n",
       "196          rwd        sedan  16845.0\n",
       "197          rwd        sedan  19045.0\n",
       "198          rwd        sedan  21485.0\n",
       "199          rwd        sedan  22470.0\n",
       "200          rwd        sedan  22625.0\n",
       "\n",
       "[201 rows x 3 columns]"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_gptest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can obtain the values of the method group using the method \"get_group\".  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4      17450.0\n",
       "136     7603.0\n",
       "140     9233.0\n",
       "141    11259.0\n",
       "144     8013.0\n",
       "145    11694.0\n",
       "150     7898.0\n",
       "151     8778.0\n",
       "Name: price, dtype: float64"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_test2.get_group('4wd')['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can use the function 'f_oneway' in the module 'stats'  to obtain the <b>F-test score</b> and <b>P-value</b>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 67.95406500780399 , P = 3.3945443577151245e-23\n"
     ]
    }
   ],
   "source": [
    "# ANOVA\n",
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('fwd')['price'], grouped_test2.get_group('rwd')['price'], grouped_test2.get_group('4wd')['price'])  \n",
    " \n",
    "print( \"ANOVA results: F=\", f_val, \", P =\", p_val)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a great result, with a large F test score showing a strong correlation and a P value of almost 0 implying almost certain statistical significance. But does this mean all three tested groups are all this highly correlated? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Separately: fwd and rwd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 130.5533160959111 , P = 2.2355306355677845e-23\n"
     ]
    }
   ],
   "source": [
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('fwd')['price'], grouped_test2.get_group('rwd')['price'])  \n",
    " \n",
    "print( \"ANOVA results: F=\", f_val, \", P =\", p_val )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's examine the other groups "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4wd and rwd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 8.580681368924756 , P = 0.004411492211225333\n"
     ]
    }
   ],
   "source": [
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('4wd')['price'], grouped_test2.get_group('rwd')['price'])  \n",
    "   \n",
    "print( \"ANOVA results: F=\", f_val, \", P =\", p_val)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>4wd and fwd</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 0.665465750252303 , P = 0.41620116697845666\n"
     ]
    }
   ],
   "source": [
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('4wd')['price'], grouped_test2.get_group('fwd')['price'])  \n",
    " \n",
    "print(\"ANOVA results: F=\", f_val, \", P =\", p_val)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Conclusion: Important Variables</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We now have a better idea of what our data looks like and which variables are important to take into account when predicting the car price. We have narrowed it down to the following variables:</p>\n",
    "\n",
    "Continuous numerical variables:\n",
    "<ul>\n",
    "    <li>Length</li>\n",
    "    <li>Width</li>\n",
    "    <li>Curb-weight</li>\n",
    "    <li>Engine-size</li>\n",
    "    <li>Horsepower</li>\n",
    "    <li>City-mpg</li>\n",
    "    <li>Highway-mpg</li>\n",
    "    <li>Wheel-base</li>\n",
    "    <li>Bore</li>\n",
    "</ul>\n",
    "    \n",
    "Categorical variables:\n",
    "<ul>\n",
    "    <li>Drive-wheels</li>\n",
    "</ul>\n",
    "\n",
    "<p>As we now move into building machine learning models to automate our analysis, feeding the model with variables that meaningfully affect our target variable will improve our model's prediction performance.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Thank you for completing this notebook</h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "\n",
    "    <p><a href=\"https://cocl.us/corsera_da0101en_notebook_bottom\"><img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/BottomAd.png\" width=\"750\" align=\"center\"></a></p>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>About the Authors:</h3>\n",
    "\n",
    "This notebook was written by <a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/\" target=\"_blank\">Mahdi Noorian PhD</a>, <a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>, Bahare Talayian, Eric Xiao, Steven Dong, Parizad, Hima Vsudevan and <a href=\"https://www.linkedin.com/in/fiorellawever/\" target=\"_blank\">Fiorella Wenver</a> and <a href=\" https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n",
    "\n",
    "<p><a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a> is a Data Scientist at IBM, and holds a PhD in Electrical Engineering. His research focused on using Machine Learning, Signal Processing, and Computer Vision to determine how videos impact human cognition. Joseph has been working for IBM since he completed his PhD.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "<p>Copyright &copy; 2018 IBM Developer Skills Network. This notebook and its source code are released under the terms of the <a href=\"https://cognitiveclass.ai/mit-license/\">MIT License</a>.</p>"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python",
   "language": "python",
   "name": "conda-env-python-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}