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": 2,
   "metadata": {
    "collapsed": true
   },
   "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": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "<div>\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": 3,
     "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": 4,
   "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": 5,
   "metadata": {
    "collapsed": 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": 6,
   "metadata": {
    "collapsed": 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": 7,
   "metadata": {
    "collapsed": 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": 7,
     "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": 8,
   "metadata": {
    "collapsed": 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>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       bore    stroke  compression-ratio  horsepower\n",
       "bore               1.000000 -0.055390           0.001263    0.566936\n",
       "stroke            -0.055390  1.000000           0.187923    0.098462\n",
       "compression-ratio  0.001263  0.187923           1.000000   -0.214514\n",
       "horsepower         0.566936  0.098462          -0.214514    1.000000"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df[['bore','stroke' ,'compression-ratio','horsepower']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "df[['bore', 'stroke', 'compression-ratio', 'horsepower']].corr()  \n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Continuous numerical variables:</h2> \n",
    "\n",
    "<p>Continuous numerical variables are variables that may contain any value within some range. Continuous numerical variables can have the type \"int64\" or \"float64\". A great way to visualize these variables is by using scatterplots with fitted lines.</p>\n",
    "\n",
    "<p>In order to start understanding the (linear) relationship between an individual variable and the price. We can do this by using \"regplot\", which plots the scatterplot plus the fitted regression line for the data.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's see several examples of different linear relationships:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Positive linear relationship</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's find the scatterplot of \"engine-size\" and \"price\" "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/lib/python3.6/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0, 56195.63150503675)"
      ]
     },
     "execution_count": 9,
     "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": 10,
   "metadata": {
    "collapsed": 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": 10,
     "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": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2cf8291f60>"
      ]
     },
     "execution_count": 11,
     "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": 12,
   "metadata": {
    "collapsed": 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": 12,
     "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": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2cf8225cf8>"
      ]
     },
     "execution_count": 13,
     "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": 14,
   "metadata": {
    "collapsed": 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": 14,
     "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": 15,
   "metadata": {
    "collapsed": 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": 15,
     "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": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2cf81fbb70>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 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": 17,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2cf81cbda0>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"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": 18,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2cf8099d30>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "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": 19,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2cf81e8630>"
      ]
     },
     "execution_count": 19,
     "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": 20,
   "metadata": {
    "collapsed": 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": 20,
     "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": 21,
   "metadata": {
    "collapsed": 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": 21,
     "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": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fwd    118\n",
       "rwd     75\n",
       "4wd      8\n",
       "Name: drive-wheels, dtype: int64"
      ]
     },
     "execution_count": 22,
     "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": 23,
   "metadata": {
    "collapsed": 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": 23,
     "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": 24,
   "metadata": {
    "collapsed": 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": 24,
     "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": 25,
   "metadata": {
    "collapsed": 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": 25,
     "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": 26,
   "metadata": {
    "collapsed": 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": 26,
     "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": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['rwd', 'fwd', '4wd'], dtype=object)"
      ]
     },
     "execution_count": 27,
     "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": 28,
   "metadata": {
    "collapsed": true
   },
   "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": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "<style scoped>\n",
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       "\n",
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       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>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": 29,
     "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": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>body-style</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4wd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7603.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4wd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>12647.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4wd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>fwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>11595.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>8249.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>8396.387755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9811.800000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>23949.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>24202.714286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>14337.777778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>21711.833333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   drive-wheels   body-style         price\n",
       "0           4wd    hatchback   7603.000000\n",
       "1           4wd        sedan  12647.333333\n",
       "2           4wd        wagon   9095.750000\n",
       "3           fwd  convertible  11595.000000\n",
       "4           fwd      hardtop   8249.000000\n",
       "5           fwd    hatchback   8396.387755\n",
       "6           fwd        sedan   9811.800000\n",
       "7           fwd        wagon   9997.333333\n",
       "8           rwd  convertible  23949.600000\n",
       "9           rwd      hardtop  24202.714286\n",
       "10          rwd    hatchback  14337.777778\n",
       "11          rwd        sedan  21711.833333\n",
       "12          rwd        wagon  16994.222222"
      ]
     },
     "execution_count": 30,
     "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": 31,
   "metadata": {
    "collapsed": 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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       "</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": 31,
     "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": 32,
   "metadata": {
    "collapsed": 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",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>body-style</th>\n",
       "      <th>convertible</th>\n",
       "      <th>hardtop</th>\n",
       "      <th>hatchback</th>\n",
       "      <th>sedan</th>\n",
       "      <th>wagon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7603.000000</td>\n",
       "      <td>12647.333333</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>11595.0</td>\n",
       "      <td>8249.000000</td>\n",
       "      <td>8396.387755</td>\n",
       "      <td>9811.800000</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>23949.6</td>\n",
       "      <td>24202.714286</td>\n",
       "      <td>14337.777778</td>\n",
       "      <td>21711.833333</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   price                                            \\\n",
       "body-style   convertible       hardtop     hatchback         sedan   \n",
       "drive-wheels                                                         \n",
       "4wd                  0.0      0.000000   7603.000000  12647.333333   \n",
       "fwd              11595.0   8249.000000   8396.387755   9811.800000   \n",
       "rwd              23949.6  24202.714286  14337.777778  21711.833333   \n",
       "\n",
       "                            \n",
       "body-style           wagon  \n",
       "drive-wheels                \n",
       "4wd            9095.750000  \n",
       "fwd            9997.333333  \n",
       "rwd           16994.222222  "
      ]
     },
     "execution_count": 32,
     "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": 33,
   "metadata": {
    "collapsed": 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": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "grouped_price = df[['price','body-style']].groupby(['body-style'],as_index=False).mean()\n",
    "grouped_price"
   ]
  },
  {
   "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": 34,
   "metadata": {
    "collapsed": true
   },
   "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": 35,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#use the grouped results\n",
    "plt.pcolor(grouped_pivot, cmap='RdBu')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The heatmap plots the target variable (price) proportional to colour with respect to the variables 'drive-wheel' and 'body-style' in the vertical and horizontal axis respectively. This allows us to visualize how the price is related to 'drive-wheel' and 'body-style'.</p>\n",
    "\n",
    "<p>The default labels convey no useful information to us. Let's change that:</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": 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": 37,
   "metadata": {
    "collapsed": 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": 37,
     "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": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Wheel-base vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the  Pearson Correlation Coefficient and P-value of 'wheel-base' and 'price'. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": 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": 40,
   "metadata": {
    "collapsed": 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": 41,
   "metadata": {
    "collapsed": 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": 42,
   "metadata": {
    "collapsed": 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": 43,
   "metadata": {
    "collapsed": 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": 44,
   "metadata": {
    "collapsed": 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": 45,
   "metadata": {
    "collapsed": 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": 46,
   "metadata": {
    "collapsed": 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": 47,
   "metadata": {
    "collapsed": 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": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
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      ],
      "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": 48,
     "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": 49,
   "metadata": {},
   "outputs": [
    {
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       "      <th>7</th>\n",
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       "      <td>wagon</td>\n",
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       "      <th>8</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>23875.0</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>16430.0</td>\n",
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       "      <th>10</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>16925.0</td>\n",
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       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
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       "      <th>12</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
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       "      <th>13</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>24565.0</td>\n",
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       "      <th>14</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>30760.0</td>\n",
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       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>41315.0</td>\n",
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       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>36880.0</td>\n",
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       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>5151.0</td>\n",
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       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6295.0</td>\n",
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       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>6575.0</td>\n",
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       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
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       "      <th>21</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6377.0</td>\n",
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       "      <th>22</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7957.0</td>\n",
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       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6229.0</td>\n",
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       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>6692.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7609.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>8558.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>8921.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>12964.0</td>\n",
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       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6479.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
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       "    <tr>\n",
       "      <th>171</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>9988.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>172</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>10898.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>173</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>11248.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>174</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>16558.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>175</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>15998.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>176</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>15690.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>177</th>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>15750.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>178</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7775.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>179</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7975.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>180</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7995.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>181</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>8195.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>182</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>8495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>183</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>184</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9995.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>185</th>\n",
       "      <td>fwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>11595.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>186</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>9980.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>187</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>13295.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>188</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>13845.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>189</th>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>12290.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>190</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>12940.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>191</th>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>13415.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>192</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>15985.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>193</th>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>16515.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>194</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>18420.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>195</th>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>18950.0</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",
       "5            fwd        sedan  15250.0\n",
       "6            fwd        sedan  17710.0\n",
       "7            fwd        wagon  18920.0\n",
       "8            fwd        sedan  23875.0\n",
       "9            rwd        sedan  16430.0\n",
       "10           rwd        sedan  16925.0\n",
       "11           rwd        sedan  20970.0\n",
       "12           rwd        sedan  21105.0\n",
       "13           rwd        sedan  24565.0\n",
       "14           rwd        sedan  30760.0\n",
       "15           rwd        sedan  41315.0\n",
       "16           rwd        sedan  36880.0\n",
       "17           fwd    hatchback   5151.0\n",
       "18           fwd    hatchback   6295.0\n",
       "19           fwd        sedan   6575.0\n",
       "20           fwd    hatchback   5572.0\n",
       "21           fwd    hatchback   6377.0\n",
       "22           fwd    hatchback   7957.0\n",
       "23           fwd    hatchback   6229.0\n",
       "24           fwd        sedan   6692.0\n",
       "25           fwd        sedan   7609.0\n",
       "26           fwd        sedan   8558.0\n",
       "27           fwd        wagon   8921.0\n",
       "28           fwd    hatchback  12964.0\n",
       "29           fwd    hatchback   6479.0\n",
       "..           ...          ...      ...\n",
       "171          fwd    hatchback   9988.0\n",
       "172          fwd        sedan  10898.0\n",
       "173          fwd    hatchback  11248.0\n",
       "174          rwd    hatchback  16558.0\n",
       "175          rwd    hatchback  15998.0\n",
       "176          rwd        sedan  15690.0\n",
       "177          rwd        wagon  15750.0\n",
       "178          fwd        sedan   7775.0\n",
       "179          fwd        sedan   7975.0\n",
       "180          fwd        sedan   7995.0\n",
       "181          fwd        sedan   8195.0\n",
       "182          fwd        sedan   8495.0\n",
       "183          fwd        sedan   9495.0\n",
       "184          fwd        sedan   9995.0\n",
       "185          fwd  convertible  11595.0\n",
       "186          fwd    hatchback   9980.0\n",
       "187          fwd        sedan  13295.0\n",
       "188          fwd        sedan  13845.0\n",
       "189          fwd        wagon  12290.0\n",
       "190          rwd        sedan  12940.0\n",
       "191          rwd        wagon  13415.0\n",
       "192          rwd        sedan  15985.0\n",
       "193          rwd        wagon  16515.0\n",
       "194          rwd        sedan  18420.0\n",
       "195          rwd        wagon  18950.0\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": 49,
     "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": 50,
   "metadata": {
    "collapsed": 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": 50,
     "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": 51,
   "metadata": {
    "collapsed": 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": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 130.5533160959111 , P = 2.2355306355677845e-23\n"
     ]
    }
   ],
   "source": [
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('fwd')['price'], grouped_test2.get_group('rwd')['price'])  \n",
    " \n",
    "print( \"ANOVA results: F=\", f_val, \", P =\", p_val )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's examine the other groups "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4wd and rwd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": 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
   },
   "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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