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
    }
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   "outputs": [
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     "data": {
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       "\n",
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       "</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",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 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",
       "    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",
       "   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",
       "  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",
       "[5 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.head()"
   ]
  },
  {
   "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": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "float64\n",
    "\n",
    "-->"
   ]
  },
  {
   "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": 6,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
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       "  <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": 6,
     "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": 7,
   "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": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test = df[['bore','stroke' ,'compression-ratio','horsepower']]\n",
    "test.corr()\n"
   ]
  },
  {
   "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": 8,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 56221.27157520833)"
      ]
     },
     "execution_count": 8,
     "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": 9,
   "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": 9,
     "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": 10,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2dd0671550>"
      ]
     },
     "execution_count": 10,
     "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": 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>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": 11,
     "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": 12,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2dd05edfd0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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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": 13,
   "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": 13,
     "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": 14,
   "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": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " df[[\"stroke\",\"price\"]].corr()\n"
   ]
  },
  {
   "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": 15,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2dd05dc400>"
      ]
     },
     "execution_count": 15,
     "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=\"stroke\", y=\"price\", data=df)\n"
   ]
  },
  {
   "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": 16,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2dd054ae10>"
      ]
     },
     "execution_count": 16,
     "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": 17,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2dd0511d68>"
      ]
     },
     "execution_count": 17,
     "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": 18,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2dd04a7278>"
      ]
     },
     "execution_count": 18,
     "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": 19,
   "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>count</th>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.00000</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>197.000000</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>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.840796</td>\n",
       "      <td>122.00000</td>\n",
       "      <td>98.797015</td>\n",
       "      <td>0.837102</td>\n",
       "      <td>0.915126</td>\n",
       "      <td>53.766667</td>\n",
       "      <td>2555.666667</td>\n",
       "      <td>126.875622</td>\n",
       "      <td>3.330692</td>\n",
       "      <td>3.256904</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>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>6.066366</td>\n",
       "      <td>0.059213</td>\n",
       "      <td>0.029187</td>\n",
       "      <td>2.447822</td>\n",
       "      <td>517.296727</td>\n",
       "      <td>41.546834</td>\n",
       "      <td>0.268072</td>\n",
       "      <td>0.319256</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>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>86.600000</td>\n",
       "      <td>0.678039</td>\n",
       "      <td>0.837500</td>\n",
       "      <td>47.800000</td>\n",
       "      <td>1488.000000</td>\n",
       "      <td>61.000000</td>\n",
       "      <td>2.540000</td>\n",
       "      <td>2.070000</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>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>94.500000</td>\n",
       "      <td>0.801538</td>\n",
       "      <td>0.890278</td>\n",
       "      <td>52.000000</td>\n",
       "      <td>2169.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>3.150000</td>\n",
       "      <td>3.110000</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>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>97.000000</td>\n",
       "      <td>0.832292</td>\n",
       "      <td>0.909722</td>\n",
       "      <td>54.100000</td>\n",
       "      <td>2414.000000</td>\n",
       "      <td>120.000000</td>\n",
       "      <td>3.310000</td>\n",
       "      <td>3.290000</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>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>102.400000</td>\n",
       "      <td>0.881788</td>\n",
       "      <td>0.925000</td>\n",
       "      <td>55.500000</td>\n",
       "      <td>2926.000000</td>\n",
       "      <td>141.000000</td>\n",
       "      <td>3.580000</td>\n",
       "      <td>3.410000</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>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>120.900000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>59.800000</td>\n",
       "      <td>4066.000000</td>\n",
       "      <td>326.000000</td>\n",
       "      <td>3.940000</td>\n",
       "      <td>4.170000</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>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        symboling  normalized-losses  wheel-base      length       width  \\\n",
       "count  201.000000          201.00000  201.000000  201.000000  201.000000   \n",
       "mean     0.840796          122.00000   98.797015    0.837102    0.915126   \n",
       "std      1.254802           31.99625    6.066366    0.059213    0.029187   \n",
       "min     -2.000000           65.00000   86.600000    0.678039    0.837500   \n",
       "25%      0.000000          101.00000   94.500000    0.801538    0.890278   \n",
       "50%      1.000000          122.00000   97.000000    0.832292    0.909722   \n",
       "75%      2.000000          137.00000  102.400000    0.881788    0.925000   \n",
       "max      3.000000          256.00000  120.900000    1.000000    1.000000   \n",
       "\n",
       "           height  curb-weight  engine-size        bore      stroke  \\\n",
       "count  201.000000   201.000000   201.000000  201.000000  197.000000   \n",
       "mean    53.766667  2555.666667   126.875622    3.330692    3.256904   \n",
       "std      2.447822   517.296727    41.546834    0.268072    0.319256   \n",
       "min     47.800000  1488.000000    61.000000    2.540000    2.070000   \n",
       "25%     52.000000  2169.000000    98.000000    3.150000    3.110000   \n",
       "50%     54.100000  2414.000000   120.000000    3.310000    3.290000   \n",
       "75%     55.500000  2926.000000   141.000000    3.580000    3.410000   \n",
       "max     59.800000  4066.000000   326.000000    3.940000    4.170000   \n",
       "\n",
       "       compression-ratio  horsepower     peak-rpm    city-mpg  highway-mpg  \\\n",
       "count         201.000000  201.000000   201.000000  201.000000   201.000000   \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      diesel         gas  \n",
       "count    201.000000    201.000000  201.000000  201.000000  \n",
       "mean   13207.129353      9.944145    0.099502    0.900498  \n",
       "std     7947.066342      2.534599    0.300083    0.300083  \n",
       "min     5118.000000      4.795918    0.000000    0.000000  \n",
       "25%     7775.000000      7.833333    0.000000    1.000000  \n",
       "50%    10295.000000      9.791667    0.000000    1.000000  \n",
       "75%    16500.000000     12.368421    0.000000    1.000000  \n",
       "max    45400.000000     18.076923    1.000000    1.000000  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "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": 20,
   "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>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>engine-type</th>\n",
       "      <th>num-of-cylinders</th>\n",
       "      <th>fuel-system</th>\n",
       "      <th>horsepower-binned</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\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</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>unique</th>\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>6</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>top</th>\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>ohc</td>\n",
       "      <td>four</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>Low</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>freq</th>\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>145</td>\n",
       "      <td>157</td>\n",
       "      <td>92</td>\n",
       "      <td>115</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          make aspiration num-of-doors body-style drive-wheels  \\\n",
       "count      201        201          201        201          201   \n",
       "unique      22          2            2          5            3   \n",
       "top     toyota        std         four      sedan          fwd   \n",
       "freq        32        165          115         94          118   \n",
       "\n",
       "       engine-location engine-type num-of-cylinders fuel-system  \\\n",
       "count              201         201              201         201   \n",
       "unique               2           6                7           8   \n",
       "top              front         ohc             four        mpfi   \n",
       "freq               198         145              157          92   \n",
       "\n",
       "       horsepower-binned  \n",
       "count                200  \n",
       "unique                 3  \n",
       "top                  Low  \n",
       "freq                 115  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe(include=['object'])"
   ]
  },
  {
   "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": 21,
   "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": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can convert the series to a Dataframe as follows :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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": 22,
     "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": 23,
   "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": 23,
     "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": 24,
   "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": 24,
     "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": 25,
   "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": 25,
     "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.head(10)"
   ]
  },
  {
   "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": 26,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['rwd', 'fwd', '4wd'], dtype=object)"
      ]
     },
     "execution_count": 26,
     "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": 27,
   "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": 28,
   "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",
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       "\n",
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       "<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": 28,
     "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",
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       "\n",
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       "<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",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
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       "\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",
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       "\n",
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       "  <thead>\n",
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       "      <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",
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       "      <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": 32,
   "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",
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       "        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": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\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"
   ]
  },
  {
   "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": 33,
   "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": 34,
   "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": [
    "#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": 35,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAEmCAYAAABoGYshAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAeYklEQVR4nO3deZRlVX328e9T3UwKjUwidoMQ7GgAB2QQBXw1aGyNEWPQtEsFI4oaVDSJcYhDhhejWXHOC4pxAByAkERxQCQYBIQAjRIQEGlBoQVFBrEdGLrref84u+R2U911q+6tOnX3eT5rnVX37lvn3N/t4Ve7fnufvWWbiIioz1jbAURExOxIgo+IqFQSfEREpZLgIyIqlQQfEVGphW0H0EsLN7c226rtMIar0llKv7d057ZDGLqVN/+i7RBmxY7bPajtEGbFTdd+9zbbOwxyjbFFS8yau/v6Xv/m9rNsLxvk/eba/Erwm23Fpnv8SdthDNX4mnvbDmFWnPbVD7YdwtA99+/ObjuEWfH6l+7ddgiz4g0H7f6jgS+y5m4WPuq5fX3rfZd/avuB32+OzasEHxExpyQ0tqDtKGZNEnxEdJgYW7hp20HMmiT4iOiu9OAjIuokQAuS4CMi6iMxlh58RESdUqKJiKhRavAREXUSYmzhJm2HMWuS4COiu9KDj4ioVxJ8RESNpEyTjIiokUgPPiKiThpjQZYqiIiokNKDj4ioksgsmoiIaiXBR0TUKPPgIyJqlQQfEVElSYxtklk0ERH1SYkmIqJeSfAREZUaG1PbIcyaJPiI6CxJKAk+IqJOCxaMtR3CrEmCj4juEunBR0TUqFlNMgk+IqJCYkxJ8BER9UmJJiKiXknwEREVkmDBwiT4iIgqqeIa/JxMAJX0VElfnov3iojolyTGxvo7RtGMevBqfuTJ9viQ44mImFM11+D77sFL2lXSNZKOA64HPlHaj5F0fXm8u6QLyuNlkr5Xnj9/FmKPiBiYxtTXsdFrSDtL+u+SI6+SdExp31bS2ZKuK1+36TnnrZJWSrpW0jN72veRdGV57cOlQ42kzSSdWtovlrTrVJ9tuiWaRwEnAU8C9iptBwO3S1oMHAScL2lz4OPAH5XXHzbN94mImH2CMamvYwprgL+0/XvAAcDRkvYA3gKcY3spcE55TnltObAnsAw4TtLEspbHA0cBS8uxrLQfCdxp+5HAB4D3ThXUdBP8j2z/j+2fAFtK2grYGfgc8BSaZH4+8GjgBtvX2TbwmQ1dUNJRklZIWuE1d08znIiImRNibOFYX8fG2L7F9rfL49XANcBi4FDgxPJtJwLPK48PBU6xfY/tG4CVwP6SdgIW2b6o5M6T1jtn4lqnA4dM9O43ZLoJ/lc9jy8C/gy4liapH0zTs//WxGfu54K2T7C9r+19tXDzaYYTETEAMZ1B1u0nOqPlOGrSSzalk72Bi4Edbd8CzQ8B4KHl2xYDN/Wctqq0LS6P129f5xzba4C7gO029vEGmSZ5HvD35fgO8DTgN7bvkvQ9YDdJu9v+AfCiAd4nImLWTGOa5G22953iWlsC/w68wfYvNnLtyV7wRto3ds4GDTJN8nya8sx5ttfS/GS5AMD23TQ1pK+UQdYfDfA+ERGzollsrL9jymtJm9Ak98/a/o/S/NNSdqF8vbW0r6LJnxOWADeX9iWTtK9zjqSFwNbAHRuLqe8evO0fcv/AKqVnrp7nf7De93+NphYfETE/aTg7OpVa+CeAa2y/v+elM4AjgPeUr1/saf+cpPcDD6cZTL3E9lpJqyUdQFPiORz4yHrXugg4DPhGqdNvUO5kjYgOE2PD2fDjQOClwJWSLi9tb6NJ7KdJOhK4EXgBgO2rJJ0GXE0zA+foUgkBeA3waWAL4MxyQPMD5GRJK2l67sunCioJPiI6S0Pqwdu+gMlr5ACHbOCcY4FjJ2lfQU+1pKf9bsoPiH4lwUdEp9V8J2sSfER0lgQLkuAjIuqUBB8RUSGhJPiIiBpJsOkUyxCMsiT4iOgsCRamBx8RUR+RGnxERJ2UGnxERJWaHnxq8BERVUoPPiKiQmNSZtFERNRqQf/rwY+cJPiI6KwsVRARUbEk+IiICuVGp4iISokMskZEVCk1+IiISmWpgoiIWqUHHxFRp6wHHxFRsST4iIgKjWXDj4iISqUGHxFRJ6GsRRMRUauxJPiIiPoIWFBvfk+Cj4gOE4ylBh8RUR8Bm2TLvoiI+qREM4f2/t3FXHjOu9sOY7gu+WLbEcyOa77QdgRDd92bHt12CLPCYz9vO4RZ8YZhXERKiSYiokYis2giIqqVEk1ERIUk2GRBBlkjIqqTEk1ERMVSoomIqJBQ1T34eotPERFTKatJ9nNMeSnpk5JulfTdnra/lfRjSZeX49k9r71V0kpJ10p6Zk/7PpKuLK99WGp+AknaTNKppf1iSbtOFVMSfER0VlOD7+/ow6eBZZO0f8D248vxVQBJewDLgT3LOcdJWlC+/3jgKGBpOSaueSRwp+1HAh8A3jtVQEnwEdFZE0sV9HNMxfZ5wB19vvWhwCm277F9A7AS2F/STsAi2xfZNnAS8Lyec04sj08HDpno3W9IEnxEdJdgwVh/B7C9pBU9x1F9vstrJV1RSjjblLbFwE0937OqtC0uj9dvX+cc22uAu4DtNvbGGWSNiM6a5jTJ22zvO823OB74B8Dl6/uAl5e3Xp830s4Ur00qCT4iOmx2d3Sy/dPfvpP0ceDL5ekqYOeeb10C3Fzal0zS3nvOKkkLga2ZoiSUEk1EdNZED76fY0bXb2rqE/4YmJhhcwawvMyM2Y1mMPUS27cAqyUdUOrrhwNf7DnniPL4MOAbpU6/QenBR0RnNUsVDKcHL+nzwFNpavWrgHcBT5X0eJpSyg+BVwHYvkrSacDVwBrgaNtry6VeQzMjZwvgzHIAfAI4WdJKmp778qliSoKPiE4bVoXG9osmaf7ERr7/WODYSdpXAHtN0n438ILpxJQEHxGdNjbp2GUdkuAjorPE8Hrw81ESfER0WsUbOiXBR0SHKT34iIgqaZbnwbctCT4iOi0lmoiISlWc35PgI6K7smVfRETFKs7vSfAR0W01L8iVBB8RnaWyZV+tkuAjotNSoomIqJBIiSYiolpTbGs60pLgI6K7lBudIiKqJGBI+33MS0nwEdFpNZdopjW+IOn1kq6R9NlpnneupOnuRh4RMauaO1n7O0bRdHvwfw48y/YNsxFMRMRcG9Hc3Ze+e/CSPgr8DnCGpNWSHqLG7ZIOL99zsqSnS9pC0imSrpB0Ks3msRER84wYU3/HKOo7wdt+NXAz8DTgs8CBwJ7A9cDB5dsOAP6HZlfwX9t+LM2msvts6LqSjpK0QtKKn91++4w+RETEjJQNP/o5RtFM5/ifDzylHMcDj5G0GLjD9i9L+2cAbF8BXLGhC9k+wfa+tvfdYbvtZhhORMT0yUbja/s6RtFME/x5NL32g4FzgZ8Bh9Ek/gkeKLKIiDkgj/d1jKIZJXjbNwHbA0ttXw9cAPwV9yf484AXA0jaC3js4KFGRAybweP9HSNokGUYLga+Xx6fDyymSfTQlG22lHQF8NfAJQO8T0TE7LH7O0bQtKZJ2t615/FLex5fSM8PC9u/AZYPIb6IiNljj2zvvB+5kzUiOm1U6+v9SIKPiA4zjK9pO4hZkwQfEd1lUqKJiKiTYTwJPiKiSqnBR0TUKgk+IqJCNozoMgT9SIKPiE5LiSYiokq50Skiol4VJ/hB1qKJiBhtHt5iY5I+KelWSd/tadtW0tmSritft+l57a2SVkq6VtIze9r3kXRlee3DKpvGStpM0qml/WJJu04VUxJ8RHSWGOpywZ8Glq3X9hbgHNtLgXPKcyTtQbNe157lnOMkLSjnHA8cBSwtx8Q1jwTutP1I4APAe6cKKAk+IjrMsHZtf8dUV7LPA+5Yr/lQ4MTy+ETgeT3tp9i+p+xxvRLYX9JOwCLbF9k2cNJ650xc63TgkIne/YakBh8R3TW9pQq2l7Si5/kJtk+Y4pwdbd8CYPsWSQ8t7YtptjedsKq03Vcer98+cc5N5VprJN0FbAfctqE3T4KPiE6bxjTJ22zvO6y3naTNG2nf2DkblBJNRHTYrO/o9NNSdqF8vbW0rwJ27vm+JcDNpX3JJO3rnCNpIbA1DywJrSMJPiK6bXYT/BnAEeXxEcAXe9qXl5kxu9EMpl5SyjmrJR1Q6uuHr3fOxLUOA75R6vQblBJNRHTXEJcqkPR54Kk0tfpVwLuA9wCnSToSuBF4QfO2vkrSacDVwBrgaNsTgbyGZkbOFsCZ5QD4BHCypJU0Pfcpd81Lgo+IDjNec99wrmS/aAMvHbKB7z8WOHaS9hXAXpO03035AdGvJPiI6C6TxcYiImpkjPuY4z6qkuAjortMdnSKiKhT1oOPiKiThzfIOh8lwUdEhxmnBx8RUaHMoomIqJUzyBoRUSWTaZIREXXKLJqIiDplFk1ERK3Sg58zN15+Dcds/YS2w4g+vP/017YdwtD9Zv/D2g5hVmx53XlthzB/ZRZNRESdjHFm0UREVCg9+IiIStn4vnvbjmLWJMFHRIflRqeIiHqlRBMRUSFnsbGIiGplFk1ERI1svDYJPiKiOrYZv29N22HMmiT4iOgukx58REStkuAjIipkm/GsBx8RUafMoomIqFFm0URE1CmzaCIiKjaeHnxERIUyTTIiolKpwUdE1MlkFk1ERJ1sxu/NIGtERH0M4+nBR0TUx6QGHxFRJ4MrXqpgrO0AIiLaYzw+3tcxFUk/lHSlpMslrSht20o6W9J15es2Pd//VkkrJV0r6Zk97fuU66yU9GFJmumnS4KPiO4q8+D7Ofr0NNuPt71vef4W4BzbS4FzynMk7QEsB/YElgHHSVpQzjkeOApYWo5lM/14SfAR0Vm2WXvvmr6OGToUOLE8PhF4Xk/7KbbvsX0DsBLYX9JOwCLbF9k2cFLPOdOWBB8RHTatEs32klb0HEc94GLwdUmX9by2o+1bAMrXh5b2xcBNPeeuKm2Ly+P122ckg6wR0V3TW6rgtp7Sy2QOtH2zpIcCZ0v63ka+d7K6ujfSPiNJ8BHRXQavnXH+XPdS9s3l662S/hPYH/ippJ1s31LKL7eWb18F7Nxz+hLg5tK+ZJL2GUmJJiI6y5jxteN9HRsj6cGStpp4DPwB8F3gDOCI8m1HAF8sj88AlkvaTNJuNIOpl5QyzmpJB5TZM4f3nDNt6cFHRHcZPD6UHvyOwH+WGY0Lgc/Z/pqkS4HTJB0J3Ai8AMD2VZJOA64G1gBH256YkP8a4NPAFsCZ5ZiRvhN8mcKzAvix7edM940k/dL2ltM9LyJittiw9t7Bb3SyfT3wuEnabwcO2cA5xwLHTtK+Athr4KCYXg/+GOAaYNEw3jgionX20Grw81FfNXhJS4A/BP61PH+opMvK48dJsqRdyvMfSHqQpN0kXSTpUkn/MFsfICJiEONr3dcxivodZP0g8NfAODSjxMDmkhYBB9OUbg6W9AjgVtu/Bj4EHG97P+AnQ488ImJQw7+TdV6ZMsFLeg5N0r5svZcuBA4EngK8u3w9GDi/vH4g8Pny+OSNXP+oiRsH7qbeRX8iYv4xMD7uvo5R1E8N/kDguZKeDWwOLJL0GeDrNAn9ETTTeN5M8+f15Z5zp/xTsX0CcALADtpsNP8UI2I02UMZZJ2vpuzB236r7SW2d6VZHOcbtl8CnAe8BLjO9jhwB/Bs4Fvl1G+V7wd48bADj4gYlMuNTv0co2jGNzrZ/mF5eF75egHwc9t3lufHAEeXeaBbzzjCiIjZUnmCn9aNTrbPBc7teb5Lz+N309TiJ57fADyp5/T3zDTIiIjZ4SnvUh1luZM1IrpreHeyzktJ8BHRWYaRnePejyT4iOgum/GKZ9EkwUdEZ9npwUdEVKufDbVHVRJ8RHSXR3edmX4kwUdEdw1xR6f5KAk+IjrLTGtP1pGTBB8R3WWz9t4k+IiI6tgw7pRoIiKqtDYJPiKiPgYqHmNNgo+IbksPPiKiQuOGe7PYWEREnVKiiYiokHFKNBERNcoga0RExZLgIyIqZGcWTURElUxm0UREVCk1+IiIiqVEExFRoaYG33YUsycJPiI6LT34iIgKGah3Nfgk+IjoMOPMoomIqFEziyYJPiKiPpUPso61HUBERFsmevD9HFORtEzStZJWSnrL7Ec/tfTgI6LThtGDl7QA+H/AM4BVwKWSzrB99eBXn7kk+IjorHGGtlTB/sBK29cDSDoFOBRoNcHL82iAQdLPgB/N0dttD9w2R+81V2r8TJDPNUrm8jM9wvYOg1xA0tdoYu7H5sDdPc9PsH1Cuc5hwDLbryjPXwo80fZrB4lvUPOqBz/oX9Z0SFphe9+5er+5UONngnyuUTJqn8n2siFdSpNdfkjXnrEMskZEDG4VsHPP8yXAzS3F8ltJ8BERg7sUWCppN0mbAsuBM1qOaX6VaObYCW0HMAtq/EyQzzVKavxMU7K9RtJrgbOABcAnbV/Vcljza5A1IiKGJyWaiIhKJcFHRFQqCT4iolJJ8BERlerULBpJBwFLbX9K0g7AlrZvaDuuQUl6PnAQzY0VF9j+z5ZDGpikZ9k+c722V9v+aFsxDYOkJwO70vN/z/ZJrQU0JGUtlh1Z93Pd2F5EAR2aRSPpXcC+wKNs/66khwP/ZvvAlkMbiKTjgEcCny9Nfwr8wPbR7UU1OEkXAm+3/Y3y/M3AU20/q93IZk7SycDuwOXA2tJs269vL6rBSXod8C7gp9y/QZJtP7a9qAK6leAvB/YGvm1779J2xaj/I5R0FbCXy1+kpDHgStt7thvZYCRtD3wZeBOwDHg0sNz2fa0GNgBJ1wB7uLL/dJJW0qy7cnvbscS6ulSDv7f8x5pIhA9uOZ5huRbYpef5zsAVLcUyNLZvA55LswTrw4HDRjm5F98FHtZ2ELPgJuCutoOIB+pSDf40SR8DHiLplcDLgY+3HNMwbAdcI+mS8nw/4CJJZwDYfm5rkc2ApNU0P4RVvm4K/A5wmCTbXtRmfAPaHri6/F3dM9E4an9Hk7geOFfSV1j3c72/vZACOpTgbf+zpGcAvwAeBbzT9tkthzUM72w7gGGyvVXbMcyiv207gFlyYzk2LUfME52pwddM0o40PXeAS2zf2mY8wyDpj4Fv2L6rPH8IzSDrF9qNLDZE0lY0g6u/bDuWaFRfg5e0WtIvJjlWS/pF2/ENStILgUuAFwAvBC4umw+MundNJHcA2z+nmakxsiQdIOlSSb+UdK+ktZX8G9xL0ndoxhiuknSZpJEe5K9F9SWayn/lB/gbYL+JXnuZ3/9fwOmtRjW4yTofo/7v9V9olpH9N5opu4cDS1uNaDhOAP7C9n8DSHoqzfjWk9sMKkb/P8y0SHoC694Q9J2WQxqGsfVKMrdTx29mKyS9n2YWjYHXAZe1G9LgbK+UtMD2WuBTZb7/qHvwRHIHsH1uRbPURloNiaAvkt4JnEgz62R74NOS3t5uVEPxNUlnSXqZpJcBXwHOnOKcUfA64F7gVJoe793ASN+8Bfy6bAZxuaR/kvRGoIZEeL2kd0jatRxvB0b+DvEadGaQtdxksrftu8vzLWhuevq9diMbXM9SBQLOq2GpghpJegRwK7AJ8EZga+A42ytbDWxAkrYB/o6ef4PA39q+s9XAolMJ/kzgRWWwbmJWxmdsP6fdyAYj6b223zxV26gpYwl/DexJs5s9ALZ/v7WgIkZM9TV4SR+hqeHeQzPCf3Z5/gzggjZjG5JnAOsn82dN0jZqPktTnnkO8GrgCOBnrUY0Q5KupNxBPZkKlsv4Eg/8fHcBK4CPTfzWHHOv+h68pCM29rrtE+cqlmGS9Brgz2nu8vxBz0tbAd+y/ZJWAhsSSZfZ3qd3vSBJ37T9f9qObbpKaQbuH0M4uXx9MfBr238/91ENj6QPATuw7oJ3PwG2ABbZfmlbsXVd9Qm+VpK2BrYB/hF4S89Lq23f0U5UwyPpf2wfIOks4MPAzcDptndvObQZk/St9Vcvnaxt1Eg6z/ZTJmuTdNWoL3w3yrpQojnN9gs39GvyCP96vIBm2YUHzCyRtG0FSf7/lh9ifwl8BFhEMzA5yh4s6SDbF8Bv14avYRbNDpJ2mVj/XdIuNDPVoJkJFS2pvgcvaSfbt/T8mrwO2z+a65iGQdIN3L8o1y7AneXxQ4Abbe/WYngxCUn7AJ+kmT1jmjr1y21/u9XABiTp2cBHaUqFAnajKR+eC7zS9gfbi67bqk/wEyqebfJR4AzbXy3PnwU83fZfthvZYCT9DvAh4Ek0m0hcBLzR9vWtBjYEkhbR/N+rZoldSZvRrNkv4HsZWJ0fOnOjE81sk/WN7O5APfabSO4AZZu7kRuInMTngNNo1k9/OM3NTp/f6BnznKQdJX0CONX2XZL2kHRk23ENyVKaVVofC7xQ0uEtxxN0IMFLek2pvz9a0hU9xw1UsDEGcJukt5c7CB8h6W9olisYdbJ9su015fgMG5lqOCI+DZxF8wML4PvAG1qLZkjUbIf5kXI8Dfgnms1aomXVl2g6MNtkW5pVFp9CkwDPA/5+VD9b+TzQ3OT0c+AUms/1p8Bmtv+hrdgGJelS2/tJ+k7PtpGX235827ENonSgHgd8x/bjyvLV/2r7j1oOrfOqn0VTfhVeDTxmVAdUN0TNTvZvtX1M27EM0WXcP3gM8Kqe1wyMbIIHfiVpO+7fNvIA6tjq7m7b45LWlPGFW2nuz4iWVZ/gAco/vv/tncpVA9try8yMalQ+++cvgDOA3SV9i+bmoBrW7r+0LP3xcZof0L+k2aMgWtaJBF/sRLNUwSXAryYaK9gP8ztq9l/9N9b9XP/RXkjDUeaJ70rPv1PbJ7UW0OB2pxnY3xn4E+CJ1PF/cCuaDWfOBb5Gc/dqDeNbI6/6GvwESZPOLLH9zbmOZZgkfWqSZtt++ZwHM0SSTqZJiJcDa0uzbb++vagGM7HsgqSDgHcD7wPeZvuJLYc2EEm/T7OS5ME0pZnLaVY1/VCrgUV3Ejz8dk2Qpbb/S9KDgAW2V7cdVzxQWd55D1f0D3RicFXSPwJX2v5c74DrKCvjQfvRzKJ5NfAb249uN6qo4dfDvkh6JXAUsC1Nz3Axzd13h7QZ16AkbQ4cyQOX1R3pHjzN/p4PA25pO5Ah+rGkjwFPB95bbg4a+anKks6hWXLhIuB8eraQjHaN/D+uaTgaOJBm/RZsXwc8tNWIhuNkmkT4TOCbwBJgZH8rkfSlMqawPXB12a3qjImj7fgG9EKaefDLyr4E2wJvajekobiCZs2ZvWhudNqrbKgTLetMiUbSxbaf2PNr8kKaHZ1GdbExYJ1f+yfqu5sAZ43qxhgbGiuZMOpjJjWTtCXwZ8BfAQ+zvVnLIXVeZ0o0wDclvQ3YQtIzaBZD+lLLMQ3DfeXrzyXtRbMO967thTOYiQQuaTfglvW2WNyxzdhicpJeSzPAug/wI5oF1c5vNagAutWDH6OpVf8BzU00Z9HcbTfSfwCSXgH8O/AYmlvhtwTeYftjbcY1KEkrgCfbvrc835RmI5P92o0s1ifpTTR3UF9me03b8cT9upTg/xj4qu172o5lmMpA3Z/Q9No3Kc2uYJegB9zCL+l/bT+urZgiRk2XBlmfC3xf0smS/rDU4GvwReBQYA3NHYS/pOeGpxH2M0m/vQlN0qHAbS3GEzFyOtODBygDkM+iWbjqIOBs269oN6rBSPqu7b3ajmPYJO1Os/H2xMqLq4CX2v7Bhs+KiF619GL7Yvs+SWfSLPa0BU3Pd6QTPHChpMfYvrLtQIZsvOzJuiVNR2R1GXiNiD51pgcvaRmwnOZOu3OBU4Gvj+qgUM8eswtpNlu4HriHZgDZFUz//LbtJ6zXdpntqhZXi5hNXerBv4xmbfFXVTLQ+py2A5gNkh5Nc1fu1pKe3/PSInru1I2IqXUmwdte3nYMw1Tb2vY9HkXzw+shQO+GEauBV7YSUcSI6lKJ5vnAe2mWJxD3lzIWtRpYTErSk2xf1HYcEaOsSwl+JfBHtq9pO5aYWsWLqEXMmS7Ng/9pkvtIqWoRtYg2dKkH/yGahPEFmtkmQB07H9WotkXUItrQmUFWmlkYv6ZZi2aCgST4+amqRdQi2tCZBG/7z9qOIablBEnbAG+n2ah6S+Ad7YYUMVq6VKJZAnyEZtMPAxcAx9he1WpgMalaF1GLmEtdGmT9FE1P8OE02/V9qbTF/FTrImoRc6ZLPfjJlp99QFvMD7UuohYxl7rUg79N0kskLSjHS4Db2w4qNuhCSY9pO4iIUdalHvwuwL8AT6KpwV8IvN72ja0GFuuofRG1iLnUpQR/IvAG23eW59sC/5w7I+cXSY/Y2OsVr8ETMXSdmSYJPHYiuQPYvkPS3m0GFA+UBB4xPF2qwY+VedXAb3vwXfoBFxEd06UE9z6agbvTaWq8LwSObTekiIjZ05kaPICkPYDfpxmwO8f21S2HFBExazqV4CMiuqRLNfiIiE5Jgo+IqFQSfEREpZLgIyIq9f8BIWcfq+n+b1cAAAAASUVORK5CYII=\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=False)\n",
    "ax.set_yticklabels(col_labels, minor=False)\n",
    "\n",
    "#rotate label if too long\n",
    "plt.xticks(rotation=90)\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": 36,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
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       "<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": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "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": 37,
   "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": 38,
   "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": 39,
   "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": 40,
   "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": 41,
   "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": 42,
   "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": 43,
   "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": 44,
   "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": 45,
   "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": 46,
   "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": 47,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "    }\n",
       "\n",
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       "        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>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>136</th>\n",
       "      <td>4wd</td>\n",
       "      <td>7603.0</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",
       "3            fwd  13950.0\n",
       "4            4wd  17450.0\n",
       "5            fwd  15250.0\n",
       "136          4wd   7603.0"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_test2=df_gptest[['drive-wheels', 'price']].groupby(['drive-wheels'])\n",
    "grouped_test2.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\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": 48,
     "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": 49,
   "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": 49,
     "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": 50,
   "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": 51,
   "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": 52,
   "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": 53,
   "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>"
   ]
  }
 ],
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