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": 13,
   "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": 14,
   "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": 14,
     "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": 15,
   "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": 16,
   "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": 17,
   "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": 18,
   "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": 18,
     "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": 19,
   "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>price</th>\n",
       "      <th>horsepower</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.809575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.809575</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               price  horsepower\n",
       "price       1.000000    0.809575\n",
       "horsepower  0.809575    1.000000"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df[['bore','stroke','compression-ratio','horsepower']].corr()\n",
    "df[['price','horsepower']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "df[['bore', 'stroke', 'compression-ratio', 'horsepower']].corr()  \n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Continuous numerical variables:</h2> \n",
    "\n",
    "<p>Continuous numerical variables are variables that may contain any value within some range. Continuous numerical variables can have the type \"int64\" or \"float64\". A great way to visualize these variables is by using scatterplots with fitted lines.</p>\n",
    "\n",
    "<p>In order to start understanding the (linear) relationship between an individual variable and the price. We can do this by using \"regplot\", which plots the scatterplot plus the fitted regression line for the data.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's see several examples of different linear relationships:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Positive linear relationship</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's find the scatterplot of \"engine-size\" and \"price\" "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 56445.72207140238)"
      ]
     },
     "execution_count": 20,
     "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": 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>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": 11,
     "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": 21,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f94fc9a17f0>"
      ]
     },
     "execution_count": 21,
     "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": 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>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": 22,
     "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": 23,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f94fc90e588>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x=\"peak-rpm\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Peak rpm does not seem like a good predictor of the price at all since the regression line is close to horizontal. Also, the data points are very scattered and far from the fitted line, showing lots of variability. Therefore it's it is not a reliable variable.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'peak-rpm' and 'price' and see it's approximately -0.101616 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 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>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": 24,
     "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": 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>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": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute\n",
    "df[['stroke','price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "#The correlation is 0.0823, the non-diagonal elements of the table.\n",
    "#code:\n",
    "df[[\"stroke\",\"price\"]].corr() \n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question  3 b):</h1>\n",
    "\n",
    "<p>Given the correlation results between \"price\" and \"stroke\" do you expect a linear relationship?</p> \n",
    "<p>Verify your results using the function \"regplot()\".</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f94fc874828>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "sns.regplot(x='stroke',y='price',data=df)"
   ]
  },
  {
   "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": 27,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f94fc86e978>"
      ]
     },
     "execution_count": 27,
     "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": 28,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f94fc77f978>"
      ]
     },
     "execution_count": 28,
     "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": 29,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f94fc72bda0>"
      ]
     },
     "execution_count": 29,
     "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": 30,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead 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": 30,
     "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": 31,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead 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": 31,
     "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": 32,
   "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": 32,
     "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": 33,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 33,
     "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": 34,
   "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": 34,
     "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": 35,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 35,
     "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": 36,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 36,
     "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": 37,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['rwd', 'fwd', '4wd'], dtype=object)"
      ]
     },
     "execution_count": 37,
     "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": 38,
   "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": 39,
   "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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       "\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>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": 39,
     "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": 40,
   "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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       "    }\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>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": 40,
     "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": 41,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
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       "\n",
       "    .dataframe thead tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>body-style</th>\n",
       "      <th>convertible</th>\n",
       "      <th>hardtop</th>\n",
       "      <th>hatchback</th>\n",
       "      <th>sedan</th>\n",
       "      <th>wagon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7603.000000</td>\n",
       "      <td>12647.333333</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>11595.0</td>\n",
       "      <td>8249.000000</td>\n",
       "      <td>8396.387755</td>\n",
       "      <td>9811.800000</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>23949.6</td>\n",
       "      <td>24202.714286</td>\n",
       "      <td>14337.777778</td>\n",
       "      <td>21711.833333</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   price                                            \\\n",
       "body-style   convertible       hardtop     hatchback         sedan   \n",
       "drive-wheels                                                         \n",
       "4wd                  NaN           NaN   7603.000000  12647.333333   \n",
       "fwd              11595.0   8249.000000   8396.387755   9811.800000   \n",
       "rwd              23949.6  24202.714286  14337.777778  21711.833333   \n",
       "\n",
       "                            \n",
       "body-style           wagon  \n",
       "drive-wheels                \n",
       "4wd            9095.750000  \n",
       "fwd            9997.333333  \n",
       "rwd           16994.222222  "
      ]
     },
     "execution_count": 41,
     "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": 42,
   "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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       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
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       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>body-style</th>\n",
       "      <th>convertible</th>\n",
       "      <th>hardtop</th>\n",
       "      <th>hatchback</th>\n",
       "      <th>sedan</th>\n",
       "      <th>wagon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
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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": 42,
     "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": 44,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>body-style</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>convertible</td>\n",
       "      <td>21890.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>hardtop</td>\n",
       "      <td>22208.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>hatchback</td>\n",
       "      <td>9957.441176</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>sedan</td>\n",
       "      <td>14459.755319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>wagon</td>\n",
       "      <td>12371.960000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    body-style         price\n",
       "0  convertible  21890.500000\n",
       "1      hardtop  22208.500000\n",
       "2    hatchback   9957.441176\n",
       "3        sedan  14459.755319\n",
       "4        wagon  12371.960000"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to exe\n",
    "temp_data = df[['body-style','price']]\n",
    "temp_data.groupby(['body-style'],as_index=False).mean()"
   ]
  },
  {
   "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": 45,
   "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": 46,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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npiqVOqqyN8vtvHMT9m4X8f83Vt9KZ7P1iIhlpsxmqVJqaOAwi+37BjyyaDOwvWwC86CkEyWtntnXNyJiWchsloF+s4l6MbPB+juSuaStdHrvrFu3tvftiIgllHnmg1TeRL08qWMbwMk62te8O8PrdXDDtz4z6hCG7vWNl406hCVx/HP3jTqE5SuzWQaabeP1iIhlwxi3eTZLBTuBy8uslvOAVzJeHhHLzkzPvK03QGfZhH0lgO1bgF3AxXSeOP1r4FNLFWxExILZ+K3Do45iyVSZzTLbJuwz7xu4emgRRUQsiWYvGsoK0Ihoj5oOoVSRZB4R7eBstBUR0QhNns2SZB4R7WDjqSTziIhas830W5OjDmPJJJlHRDuY9MwjIpogyTwiouZsM13TvcqrSDKPiNbIbJaIiLrLbJaIiPrLbJaIiIaYTs88IqLmMjUxIqIBMmYeEVF/JrNZIiLqz2b6cG6ARkTUm2E6PfOIiHozGTOPiKg/gxu8nH9s1AFERBwZxtPTlcogkn4q6UlJeyTtLnXvlXSPpOfK3/d0tb9O0oSkZyV9tKv+3HKdCUk3StJCv12SeUS0Q5lnXqVU9K9sn2V7Q3n9OeBe2+uBe8trJJ0ObAHOADYBX5E0Xs65GdgKrC9l00K/XpJ5RLSCbaYOT1YqC7QZuKMc3wFc2lV/p+03bT8PTAAbJa0GTrD9gG0D27vOmbck84hoiXkNs6yStLurbH3HxeAfJD3a9d4ptg8AlL/vK/VrgBe6zt1X6taU4976BckN0Ihoh/kt53+pa/ikn/Nt75f0PuAeST+Zo22/cXDPUb8gSeYR0Q4GTy04V779Uvb+8vegpO8CG4EXJa22faAMoRwszfcB67pOXwvsL/Vr+9QvSIZZIqIVjJmemq5U5iLpOEnvmjkG/gh4CtgJXFGaXQHcVY53AlskHS3pNDo3Oh8uQzGvSTqvzGK5vOuceUvPPCLaweDpofTMTwG+W2YRrgD+zvbfS3oE2CHpSuDnwMcBbD8taQfwDDAJXG17ZsL7VcDtwLHA3aUsSKVkLmkT8F+AceBvbX+h5/0L6PyiPF+qvmP7Py40qIiIYbNh6vDiFw3Z/ifg9/rUvwxcOMs51wPX96nfDZy56KCokMzLfMgvA39IZ4znEUk7bT/T0/THti8ZRlAREUNnD23MfDmq0jPfCEyUXyMk3Uln3mRvMo+IWNamG5zMq9wAnW2OZK+PSHpc0t2SzhhKdBERwzL8FaDLSpWeeZW5kI8BH7B9SNLFwPfo3LF9+4U6k+u3AhzPeO/bERFLxsD0cG6ALktVeuazzZH8Dduv2j5UjncBKyWt6r2Q7W22N9jecEySeUQcSTZTh6cqlTqqkswfAdZLOk3SUXQ2jNnZ3UDS+2d2+5K0sVz35WEHGxGxUC6LhqqUOho4zGJ7UtJngB/QmZp4W5k3+eny/i3AZcBVkiaB14EtZeOYiIjlYYgrQJejSvPMy9DJrp66W7qObwJuGm5oERHD5IGrO+ssK0Ajoh2GtwJ0WUoyj4hWMM2eZ55kHhHtYDNd05kqVSSZR0Qr2OmZR0Q0QpWHNddVknlEtIOdnnlERO1lnnlERP2ZeT0DtHaSzCOiHWymDieZR0TUmg3TDd5lJMk8IlpjKsk8IqLeDDT4/meSeUS0R3rmERE1N204nI22IiLqL8MsERE1Z5xhloiIussN0IiIhkgyj4ioOTuzWSIias9kNktERO1lzDwioiEyzBIRUXOdMfNRR7F0kswjojXSM4+IqDkDzd3NPMk8IlrCOLNZIiLqrjObJck8IqLeGn4DdKxKI0mbJD0raULS5/q8L0k3lvefkHTO8EONiFi4mZ55lTLIoJw4CgOTuaRx4MvARcDpwCcknd7T7CJgfSlbgZuHHGdExKJNuVqZS8WceMRV6ZlvBCZs/5Ptw8CdwOaeNpuB7e54EDhR0uohxxoRsWDTdJbzVykDVMmJR1yVMfM1wAtdr/cBH67QZg1woLuRpK10eu4Ab36Vnz01r2jrYRXw0qiDGKavXvbZxn0n+Cw08N8VzfxOAB9a7AVe4vAPvsrPVlVsfoyk3V2vt9neVo6r5MQjrkoyV5+63p+uKm0o/zC2AUjabXtDhc+vlSZ+ryZ+J2jm92rid4LO91rsNWxvGkYsVMx3R1qVYZZ9wLqu12uB/QtoExHRBMsy31VJ5o8A6yWdJukoYAuws6fNTuDyMqvlPOAV2wd6LxQR0QBVcuIRN3CYxfakpM8APwDGgdtsPy3p0+X9W4BdwMXABPBr4FMVPnvb4Ca11MTv1cTvBM38Xk38TrCMvtdsOXHEYSE3eEVURERbVFo0FBERy1uSeUREA4wkmS/HpbCLJek2SQclNWbuvKR1kn4kaa+kpyVdM+qYFkvSMZIelvR4+U6fH3VMwyRpXNL/kvT9UccyLJJ+KulJSXuGMUWxqY74mHlZCvu/gT+kM8XnEeATtp85ooEMmaR/CRyisxL2zFHHMwxlFe9q249JehfwKHBpnf9dSRJwnO1DklYC9wPXlJXLtSfp3wEbgBNsXzLqeIZB0k+BDbabuBhqaEbRM1+WS2EXy/Z9wC9GHccw2T5g+7Fy/Bqwl87qt9oqW04cKi9XltKIWQCS1gJ/DPztqGOJI28UyXy2pf+xjEk6FTgbeGi0kSxeGYrYAxwE7rFd++9U/A3w72neA3UM/IOkR8uWINHHKJL5slwKG7OTdDzwbeBa26+OOp7Fsj1l+yw6K/c2Sqr9sJikS4CDth8ddSxL4Hzb59DZpfDqMqQZPUaRzJflUtjor4wrfxv4uu3vjDqeYbL9K+AfgWHt2TFK5wMfK+PLdwK/L+l/jDak4bC9v/w9CHyXzlBt9BhFMl+WS2HjncrNwluBvbZvGHU8wyDpZEknluNjgT8AfjLaqBbP9nW219o+lc5/Uz+0/a9HHNaiSTqu3HxH0nHAHwGNmTE2TEc8mdueBGaWwu4FdiyHpbCLJekbwAPAhyTtk3TlqGMagvOBT9Lp5e0p5eJRB7VIq4EfSXqCTsfiHtuNmcbXQKcA90t6HHgY+J+2/37EMS1LWc4fEdEAWQEaEdEASeYREQ2QZB4R0QBJ5hERDZBkHhHRAEnmERENkGQeEdEA/w9sx4rJMwWCTgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#use the grouped results\n",
    "plt.pcolor(grouped_pivot, cmap='RdBu')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The heatmap plots the target variable (price) proportional to colour with respect to the variables 'drive-wheel' and 'body-style' in the vertical and horizontal axis respectively. This allows us to visualize how the price is related to 'drive-wheel' and 'body-style'.</p>\n",
    "\n",
    "<p>The default labels convey no useful information to us. Let's change that:</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "im = ax.pcolor(grouped_pivot, cmap='RdBu')\n",
    "\n",
    "#label names\n",
    "row_labels = grouped_pivot.columns.levels[1]\n",
    "col_labels = grouped_pivot.index\n",
    "\n",
    "#move ticks and labels to the center\n",
    "ax.set_xticks(np.arange(grouped_pivot.shape[1]) + 0.5, minor=False)\n",
    "ax.set_yticks(np.arange(grouped_pivot.shape[0]) + 0.5, minor=False)\n",
    "\n",
    "#insert labels\n",
    "ax.set_xticklabels(row_labels, minor=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": 48,
   "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": 48,
     "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": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n"
   ]
  },
  {
   "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": 54,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.5846418222655081  with a P-value of P = 8.076488270732955e-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": 55,
   "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 =  6.36905742825998e-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": 56,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.690628380448364  with a P-value of P =  8.016477466159053e-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": 57,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.7512653440522674  with a P-value of P = 9.200335510481426e-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": 58,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8344145257702846  with a P-value of P =  2.1895772388936997e-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": 59,
   "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 = 9.265491622197996e-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": 60,
   "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 =   8.049189483935364e-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": 61,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.6865710067844677  with a P-value of P =  2.3211320655676368e-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": 62,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.7046922650589529  with a P-value of P =  1.7495471144476807e-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": 63,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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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>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": 63,
     "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": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\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": 64,
     "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": 65,
   "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": 65,
     "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": 66,
   "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": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "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": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [],
   "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": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "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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