exploratory-data-analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "    <a href=\"https://cocl.us/corsera_da0101en_notebook_top\">\n",
    "         <img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/TopAd.png\" width=\"750\" align=\"center\">\n",
    "    </a>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://www.bigdatauniversity.com\"><img src = \"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/CCLog.png\" width = 300, align = \"center\"></a>\n",
    "\n",
    "<h1 align=center><font size = 5>Data Analysis with Python</font></h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exploratory Data Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Welcome!</h3>\n",
    "In this section, we will explore several methods to see if certain characteristics or features can be used to predict car price. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Table of content</h2>\n",
    "\n",
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "<ol>\n",
    "    <li><a href=\"#import_data\">Import Data from Module</a></li>\n",
    "    <li><a href=\"#pattern_visualization\">Analyzing Individual Feature Patterns using Visualization</a></li>\n",
    "    <li><a href=\"#discriptive_statistics\">Descriptive Statistical Analysis</a></li>\n",
    "    <li><a href=\"#basic_grouping\">Basics of Grouping</a></li>\n",
    "    <li><a href=\"#correlation_causation\">Correlation and Causation</a></li>\n",
    "    <li><a href=\"#anova\">ANOVA</a></li>\n",
    "</ol>\n",
    "    \n",
    "Estimated Time Needed: <strong>30 min</strong>\n",
    "</div>\n",
    " \n",
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>What are the main characteristics which have the most impact on the car price?</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"import_data\">1. Import Data from Module 2</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Setup</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import libraries "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " load data and store in dataframe df:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dataset was hosted on IBM Cloud object click <a href=\"https://cocl.us/DA101EN_object_storage\">HERE</a> for free storage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>make</th>\n",
       "      <th>aspiration</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>...</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>horsepower-binned</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>13495.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>94.5</td>\n",
       "      <td>0.822681</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>154.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.8</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>24</td>\n",
       "      <td>30</td>\n",
       "      <td>13950.0</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>4wd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.4</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>8.0</td>\n",
       "      <td>115.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>18</td>\n",
       "      <td>22</td>\n",
       "      <td>17450.0</td>\n",
       "      <td>13.055556</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 29 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   symboling  normalized-losses         make aspiration num-of-doors  \\\n",
       "0          3                122  alfa-romero        std          two   \n",
       "1          3                122  alfa-romero        std          two   \n",
       "2          1                122  alfa-romero        std          two   \n",
       "3          2                164         audi        std         four   \n",
       "4          2                164         audi        std         four   \n",
       "\n",
       "    body-style drive-wheels engine-location  wheel-base    length  ...  \\\n",
       "0  convertible          rwd           front        88.6  0.811148  ...   \n",
       "1  convertible          rwd           front        88.6  0.811148  ...   \n",
       "2    hatchback          rwd           front        94.5  0.822681  ...   \n",
       "3        sedan          fwd           front        99.8  0.848630  ...   \n",
       "4        sedan          4wd           front        99.4  0.848630  ...   \n",
       "\n",
       "   compression-ratio  horsepower  peak-rpm city-mpg highway-mpg    price  \\\n",
       "0                9.0       111.0    5000.0       21          27  13495.0   \n",
       "1                9.0       111.0    5000.0       21          27  16500.0   \n",
       "2                9.0       154.0    5000.0       19          26  16500.0   \n",
       "3               10.0       102.0    5500.0       24          30  13950.0   \n",
       "4                8.0       115.0    5500.0       18          22  17450.0   \n",
       "\n",
       "  city-L/100km  horsepower-binned  diesel  gas  \n",
       "0    11.190476             Medium       0    1  \n",
       "1    11.190476             Medium       0    1  \n",
       "2    12.368421             Medium       0    1  \n",
       "3     9.791667             Medium       0    1  \n",
       "4    13.055556             Medium       0    1  \n",
       "\n",
       "[5 rows x 29 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path='https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/automobileEDA.csv'\n",
    "df = pd.read_csv(path)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"pattern_visualization\">2. Analyzing Individual Feature Patterns using Visualization</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To install seaborn we use the pip which is the python package manager."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "! pip install seaborn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import visualization packages \"Matplotlib\" and \"Seaborn\", don't forget about \"%matplotlib inline\" to plot in a Jupyter notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>How to choose the right visualization method?</h4>\n",
    "<p>When visualizing individual variables, it is important to first understand what type of variable you are dealing with. This will help us find the right visualization method for that variable.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "symboling              int64\n",
      "normalized-losses      int64\n",
      "make                  object\n",
      "aspiration            object\n",
      "num-of-doors          object\n",
      "body-style            object\n",
      "drive-wheels          object\n",
      "engine-location       object\n",
      "wheel-base           float64\n",
      "length               float64\n",
      "width                float64\n",
      "height               float64\n",
      "curb-weight            int64\n",
      "engine-type           object\n",
      "num-of-cylinders      object\n",
      "engine-size            int64\n",
      "fuel-system           object\n",
      "bore                 float64\n",
      "stroke               float64\n",
      "compression-ratio    float64\n",
      "horsepower           float64\n",
      "peak-rpm             float64\n",
      "city-mpg               int64\n",
      "highway-mpg            int64\n",
      "price                float64\n",
      "city-L/100km         float64\n",
      "horsepower-binned     object\n",
      "diesel                 int64\n",
      "gas                    int64\n",
      "dtype: object\n"
     ]
    }
   ],
   "source": [
    "# list the data types for each column\n",
    "print(df.dtypes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h3>Question  #1:</h3>\n",
    "\n",
    "<b>What is the data type of the column \"peak-rpm\"? </b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "float64\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "for example, we can calculate the correlation between variables  of type \"int64\" or \"float64\" using the method \"corr\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>symboling</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.466264</td>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.365404</td>\n",
       "      <td>-0.242423</td>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.233118</td>\n",
       "      <td>-0.110581</td>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.008245</td>\n",
       "      <td>-0.182196</td>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.279740</td>\n",
       "      <td>-0.035527</td>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.066171</td>\n",
       "      <td>-0.196735</td>\n",
       "      <td>0.196735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>normalized-losses</th>\n",
       "      <td>0.466264</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.101546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wheel-base</th>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>-0.307237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>length</th>\n",
       "      <td>-0.365404</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>-0.211187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>width</th>\n",
       "      <td>-0.242423</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>-0.244356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>height</th>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>-0.281578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>curb-weight</th>\n",
       "      <td>-0.233118</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>-0.221046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>-0.110581</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>-0.070779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>-0.054458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.008245</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>-0.241303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>-0.182196</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.985231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>0.169053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>0.279740</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.475812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-mpg</th>\n",
       "      <td>-0.035527</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>-0.265676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>-0.198690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.110326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-L/100km</th>\n",
       "      <td>0.066171</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>0.241282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diesel</th>\n",
       "      <td>-0.196735</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gas</th>\n",
       "      <td>0.196735</td>\n",
       "      <td>0.101546</td>\n",
       "      <td>-0.307237</td>\n",
       "      <td>-0.211187</td>\n",
       "      <td>-0.244356</td>\n",
       "      <td>-0.281578</td>\n",
       "      <td>-0.221046</td>\n",
       "      <td>-0.070779</td>\n",
       "      <td>-0.054458</td>\n",
       "      <td>-0.241303</td>\n",
       "      <td>-0.985231</td>\n",
       "      <td>0.169053</td>\n",
       "      <td>0.475812</td>\n",
       "      <td>-0.265676</td>\n",
       "      <td>-0.198690</td>\n",
       "      <td>-0.110326</td>\n",
       "      <td>0.241282</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   symboling  normalized-losses  wheel-base    length  \\\n",
       "symboling           1.000000           0.466264   -0.535987 -0.365404   \n",
       "normalized-losses   0.466264           1.000000   -0.056661  0.019424   \n",
       "wheel-base         -0.535987          -0.056661    1.000000  0.876024   \n",
       "length             -0.365404           0.019424    0.876024  1.000000   \n",
       "width              -0.242423           0.086802    0.814507  0.857170   \n",
       "height             -0.550160          -0.373737    0.590742  0.492063   \n",
       "curb-weight        -0.233118           0.099404    0.782097  0.880665   \n",
       "engine-size        -0.110581           0.112360    0.572027  0.685025   \n",
       "bore               -0.140019          -0.029862    0.493244  0.608971   \n",
       "stroke             -0.008245           0.055563    0.158502  0.124139   \n",
       "compression-ratio  -0.182196          -0.114713    0.250313  0.159733   \n",
       "horsepower          0.075819           0.217299    0.371147  0.579821   \n",
       "peak-rpm            0.279740           0.239543   -0.360305 -0.285970   \n",
       "city-mpg           -0.035527          -0.225016   -0.470606 -0.665192   \n",
       "highway-mpg         0.036233          -0.181877   -0.543304 -0.698142   \n",
       "price              -0.082391           0.133999    0.584642  0.690628   \n",
       "city-L/100km        0.066171           0.238567    0.476153  0.657373   \n",
       "diesel             -0.196735          -0.101546    0.307237  0.211187   \n",
       "gas                 0.196735           0.101546   -0.307237 -0.211187   \n",
       "\n",
       "                      width    height  curb-weight  engine-size      bore  \\\n",
       "symboling         -0.242423 -0.550160    -0.233118    -0.110581 -0.140019   \n",
       "normalized-losses  0.086802 -0.373737     0.099404     0.112360 -0.029862   \n",
       "wheel-base         0.814507  0.590742     0.782097     0.572027  0.493244   \n",
       "length             0.857170  0.492063     0.880665     0.685025  0.608971   \n",
       "width              1.000000  0.306002     0.866201     0.729436  0.544885   \n",
       "height             0.306002  1.000000     0.307581     0.074694  0.180449   \n",
       "curb-weight        0.866201  0.307581     1.000000     0.849072  0.644060   \n",
       "engine-size        0.729436  0.074694     0.849072     1.000000  0.572609   \n",
       "bore               0.544885  0.180449     0.644060     0.572609  1.000000   \n",
       "stroke             0.188829 -0.062704     0.167562     0.209523 -0.055390   \n",
       "compression-ratio  0.189867  0.259737     0.156433     0.028889  0.001263   \n",
       "horsepower         0.615077 -0.087027     0.757976     0.822676  0.566936   \n",
       "peak-rpm          -0.245800 -0.309974    -0.279361    -0.256733 -0.267392   \n",
       "city-mpg          -0.633531 -0.049800    -0.749543    -0.650546 -0.582027   \n",
       "highway-mpg       -0.680635 -0.104812    -0.794889    -0.679571 -0.591309   \n",
       "price              0.751265  0.135486     0.834415     0.872335  0.543155   \n",
       "city-L/100km       0.673363  0.003811     0.785353     0.745059  0.554610   \n",
       "diesel             0.244356  0.281578     0.221046     0.070779  0.054458   \n",
       "gas               -0.244356 -0.281578    -0.221046    -0.070779 -0.054458   \n",
       "\n",
       "                     stroke  compression-ratio  horsepower  peak-rpm  \\\n",
       "symboling         -0.008245          -0.182196    0.075819  0.279740   \n",
       "normalized-losses  0.055563          -0.114713    0.217299  0.239543   \n",
       "wheel-base         0.158502           0.250313    0.371147 -0.360305   \n",
       "length             0.124139           0.159733    0.579821 -0.285970   \n",
       "width              0.188829           0.189867    0.615077 -0.245800   \n",
       "height            -0.062704           0.259737   -0.087027 -0.309974   \n",
       "curb-weight        0.167562           0.156433    0.757976 -0.279361   \n",
       "engine-size        0.209523           0.028889    0.822676 -0.256733   \n",
       "bore              -0.055390           0.001263    0.566936 -0.267392   \n",
       "stroke             1.000000           0.187923    0.098462 -0.065713   \n",
       "compression-ratio  0.187923           1.000000   -0.214514 -0.435780   \n",
       "horsepower         0.098462          -0.214514    1.000000  0.107885   \n",
       "peak-rpm          -0.065713          -0.435780    0.107885  1.000000   \n",
       "city-mpg          -0.034696           0.331425   -0.822214 -0.115413   \n",
       "highway-mpg       -0.035201           0.268465   -0.804575 -0.058598   \n",
       "price              0.082310           0.071107    0.809575 -0.101616   \n",
       "city-L/100km       0.037300          -0.299372    0.889488  0.115830   \n",
       "diesel             0.241303           0.985231   -0.169053 -0.475812   \n",
       "gas               -0.241303          -0.985231    0.169053  0.475812   \n",
       "\n",
       "                   city-mpg  highway-mpg     price  city-L/100km    diesel  \\\n",
       "symboling         -0.035527     0.036233 -0.082391      0.066171 -0.196735   \n",
       "normalized-losses -0.225016    -0.181877  0.133999      0.238567 -0.101546   \n",
       "wheel-base        -0.470606    -0.543304  0.584642      0.476153  0.307237   \n",
       "length            -0.665192    -0.698142  0.690628      0.657373  0.211187   \n",
       "width             -0.633531    -0.680635  0.751265      0.673363  0.244356   \n",
       "height            -0.049800    -0.104812  0.135486      0.003811  0.281578   \n",
       "curb-weight       -0.749543    -0.794889  0.834415      0.785353  0.221046   \n",
       "engine-size       -0.650546    -0.679571  0.872335      0.745059  0.070779   \n",
       "bore              -0.582027    -0.591309  0.543155      0.554610  0.054458   \n",
       "stroke            -0.034696    -0.035201  0.082310      0.037300  0.241303   \n",
       "compression-ratio  0.331425     0.268465  0.071107     -0.299372  0.985231   \n",
       "horsepower        -0.822214    -0.804575  0.809575      0.889488 -0.169053   \n",
       "peak-rpm          -0.115413    -0.058598 -0.101616      0.115830 -0.475812   \n",
       "city-mpg           1.000000     0.972044 -0.686571     -0.949713  0.265676   \n",
       "highway-mpg        0.972044     1.000000 -0.704692     -0.930028  0.198690   \n",
       "price             -0.686571    -0.704692  1.000000      0.789898  0.110326   \n",
       "city-L/100km      -0.949713    -0.930028  0.789898      1.000000 -0.241282   \n",
       "diesel             0.265676     0.198690  0.110326     -0.241282  1.000000   \n",
       "gas               -0.265676    -0.198690 -0.110326      0.241282 -1.000000   \n",
       "\n",
       "                        gas  \n",
       "symboling          0.196735  \n",
       "normalized-losses  0.101546  \n",
       "wheel-base        -0.307237  \n",
       "length            -0.211187  \n",
       "width             -0.244356  \n",
       "height            -0.281578  \n",
       "curb-weight       -0.221046  \n",
       "engine-size       -0.070779  \n",
       "bore              -0.054458  \n",
       "stroke            -0.241303  \n",
       "compression-ratio -0.985231  \n",
       "horsepower         0.169053  \n",
       "peak-rpm           0.475812  \n",
       "city-mpg          -0.265676  \n",
       "highway-mpg       -0.198690  \n",
       "price             -0.110326  \n",
       "city-L/100km       0.241282  \n",
       "diesel            -1.000000  \n",
       "gas                1.000000  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The diagonal elements are always one; we will study correlation more precisely Pearson correlation in-depth at the end of the notebook."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #2: </h1>\n",
    "\n",
    "<p>Find the correlation between the following columns: bore, stroke,compression-ratio , and horsepower.</p>\n",
    "<p>Hint: if you would like to select those columns  use the following syntax: df[['bore','stroke' ,'compression-ratio','horsepower']]</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       bore    stroke  compression-ratio  horsepower\n",
       "bore               1.000000 -0.055390           0.001263    0.566936\n",
       "stroke            -0.055390  1.000000           0.187923    0.098462\n",
       "compression-ratio  0.001263  0.187923           1.000000   -0.214514\n",
       "horsepower         0.566936  0.098462          -0.214514    1.000000"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df1=df[['bore','stroke','compression-ratio','horsepower']]\n",
    "df1.corr()"
   ]
  },
  {
   "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": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "df[['bore', 'stroke', 'compression-ratio', 'horsepower']].corr()  \n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Continuous numerical variables:</h2> \n",
    "\n",
    "<p>Continuous numerical variables are variables that may contain any value within some range. Continuous numerical variables can have the type \"int64\" or \"float64\". A great way to visualize these variables is by using scatterplots with fitted lines.</p>\n",
    "\n",
    "<p>In order to start understanding the (linear) relationship between an individual variable and the price. We can do this by using \"regplot\", which plots the scatterplot plus the fitted regression line for the data.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's see several examples of different linear relationships:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Positive linear relationship</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's find the scatterplot of \"engine-size\" and \"price\" "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 56028.49315064714)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Engine size as potential predictor variable of price\n",
    "sns.regplot(x=\"engine-size\", y=\"price\", data=df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>As the engine-size goes up, the price goes up: this indicates a positive direct correlation between these two variables. Engine size seems like a pretty good predictor of price since the regression line is almost a perfect diagonal line.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can examine the correlation between 'engine-size' and 'price' and see it's approximately  0.87"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>engine-size</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.872335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>0.872335</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             engine-size     price\n",
       "engine-size     1.000000  0.872335\n",
       "price           0.872335  1.000000"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[[\"engine-size\", \"price\"]].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Highway mpg is a potential predictor variable of price "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f40945bc208>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x=\"highway-mpg\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>As the highway-mpg goes up, the price goes down: this indicates an inverse/negative relationship between these two variables. Highway mpg could potentially be a predictor of price.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'highway-mpg' and 'price' and see it's approximately  -0.704"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             highway-mpg     price\n",
       "highway-mpg     1.000000 -0.704692\n",
       "price          -0.704692  1.000000"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['highway-mpg', 'price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Weak Linear Relationship</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see if \"Peak-rpm\" as a predictor variable of \"price\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f40945212e8>"
      ]
     },
     "execution_count": 12,
     "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": 13,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.101616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.101616</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          peak-rpm     price\n",
       "peak-rpm  1.000000 -0.101616\n",
       "price    -0.101616  1.000000"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['peak-rpm','price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " <div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  3 a): </h1>\n",
    "\n",
    "<p>Find the correlation  between x=\"stroke\", y=\"price\".</p>\n",
    "<p>Hint: if you would like to select those columns  use the following syntax: df[[\"stroke\",\"price\"]]  </p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>stroke</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>1.00000</td>\n",
       "      <td>0.08231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>0.08231</td>\n",
       "      <td>1.00000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         stroke    price\n",
       "stroke  1.00000  0.08231\n",
       "price   0.08231  1.00000"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 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": 15,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f40944b7908>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZIAAAEGCAYAAABPdROvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAgAElEQVR4nO29eZhc5Xng+3tr6b1bakndSKiFJRlhscRsMsYDV1Fszw3ewL4j2+K5Ntw7ONJlyIAnmyE3IQ4eP9eKF2LiMUFexkDiYEXJxIoDODayQpwgQGAWC2TAkrBaCLWWlnqv5dR7/zjfqa6qru6u7q616/09T6mqvrP0d04dnfe8u6gqhmEYhjFbQpWegGEYhlHbmCAxDMMw5oQJEsMwDGNOmCAxDMMw5oQJEsMwDGNORCo9gXKzZMkSXblyZaWnYRiGUVM888wzJ1S1K9+yuhMkK1euZO/evZWehmEYRk0hIq9PtsxMW4ZhGMacMEFiGIZhzAkTJIZhGMacMEFiGIZhzAkTJIZhGMacqLuoLcMw8rN7fx/3PX6Aw/0jrOhsYcv61WxY213paRk1gGkkhmGwe38fd+7cR9/gGAubo/QNjnHnzn3s3t9X6akZNUDJBYmIhEXkZyLyA/f9syJyRESec6/3Z6x7h4i8JiK/EJHfzBi/XERedMvuERFx440i8j03/qSIrCz18RjGfOS+xw8QDQstDRFE/PdoWLjv8QOVnppRA5RDI7kNeDln7G5VvcS9HgYQkQuATcCFwDXA10Uk7Na/F9gMrHGva9z4TUC/qp4L3A1sLemRGMY85XD/CM3RcNZYczRMb/9IhWZk1BIlFSQi0gN8APhmAatfBzykqjFVPQi8BlwhIsuADlV9Qv0uXA8AH87Y5n73eQfwnkBbMQyjcFZ0tjCa8LLGRhMePZ0tFZqRUUuUWiP5c+APgFTO+G+LyAsi8m0R6XRjy4HDGev0urHl7nPueNY2qpoEzgCLcychIptFZK+I7D1+/PgcD8kw5h9b1q8m4Skj8SSq/nvCU7asX13pqRk1QMkEiYh8EOhT1WdyFt0LvBW4BDgKfDnYJM9udIrxqbbJHlDdpqrrVHVdV1femmOGUddsWNvNXddeSHd7E2dGE3S3N3HXtRda1JZREKUM/70KuNY505uADhH5K1X9RLCCiHwD+IH72gusyNi+B3jDjffkGc/cpldEIsAC4FQJjsUw5j0b1nab4DBmRck0ElW9Q1V7VHUlvhN9l6p+wvk8Aj4C/Nx93glscpFYq/Cd6k+p6lFgUESudP6PG4DvZ2xzo/u80f2NCRqJYRiGUToqkZD4ZyJyCb4J6hCwBUBV94nIduAlIAncoqqB9+9m4DtAM/CIewF8C3hQRF7D10Q2lekYDMMwDIfU2wP8unXr1PqRGIZhzAwReUZV1+VbZpnthmEYxpwwQWIYhmHMCRMkhmEYxpwwQWIYhmHMCRMkhmEYxpwwQWIYhmHMCRMkhmEYxpwwQWIYhmHMCRMkhmEYxpywnu2GYUyK9XE3CsE0EsMw8mJ93I1CMY3EMAxgovbRPxxL93EHaGmIMBJPct/jB0wrMbIwjcQwjLzax6vHh0h62c1NrY+7kQ8TJIZhcN/jB9Lah4j/Hg2FODYYy1rP+rgb+TBBYhgGh/tHaI6Gs8bO6mi0Pu5GQZggMQyDFZ0tjCa8rLFIOMR53W3Wx92YlpI720UkDOwFjqjqB0VkEfA9YCV+h8SPqWq/W/cO4CbAA25V1R+68csZ75D4MHCbqqqINAIPAJcDJ4GPq+qhUh+TYcw3tqxfzZ079zEST9IcDTOa8Eh4yh9/YK0JDmNayqGR3Aa8nPH9duAxVV0DPOa+IyIX4LfKvRC4Bvi6E0IA9wKb8fu4r3HLwRc6/ap6LnA3sLW0h2IY85MNa7u569oLTfswZkVJNRIR6QE+AHwe+B03fB2wwX2+H9gNfMaNP6SqMeCg68N+hYgcAjpU9Qm3zweAD+P3bb8O+Kzb1w7gayIiWm/9gw2jCGxY222Cw5gVpdZI/hz4AyAzhvAsVT0K4N6DK3c5cDhjvV43ttx9zh3P2kZVk8AZYHHuJERks4jsFZG9x48fn+sxGYZhGBmUTJCIyAeBPlV9ptBN8ozpFONTbZM9oLpNVdep6rqurq4Cp2MYhmEUQilNW1cB14rI+4EmoENE/go4JiLLVPWoiCwDgnoLvcCKjO17gDfceE+e8cxtekUkAiwATpXqgAzDMIyJlEwjUdU7VLVHVVfiO9F3qeongJ3AjW61G4Hvu887gU0i0igiq/Cd6k8589egiFwpIgLckLNNsK+N7m+Yf8QwDKOMVKLW1heA7SJyE/Ar4KMAqrpPRLYDLwFJ4BZVDQLbb2Y8/PcR9wL4FvCgc8yfwhdYhmEYRhmRenuAX7dune7du7fS0zAMw6gpROQZVV2Xb5llthuGYRhzwgSJYRiGMSdMkBiGYRhzwgSJYRiGMSdMkBiGYRhzwlrtGgYT28xuWb/a6k4ZRoGYIDHqnqDNbDQs6Tazd+7cx11Q98LEBKxRCGbaMuqevG1mw8J9jx+o9NQqSr4+7nfu3Mfu/X3Tb2zUFSZIjLonX5vZ5miY3v6RCs2oOjABaxSKCRKj7snXZnY04dHT2VKhGVUHJmCNQjFBYtQcu/f3cf22PVy9dRfXb9szZ1PLlvWrSXjKSDyJqv+e8JQt61cXaca1iQlYo1BMkBg1RSns9tZmNj8mYI1Csagto6bItNsDtDREGIknue/xA3O68Vub2YlsWNvNXfjnvLd/hB6L2jImwQSJUVMc7h9hYXM0a8zs9qXDBGztU44QbjNtGTWF2e0No3DKFcJdyp7tTSLylIg8LyL7RORP3fhnReSIiDznXu/P2OYOEXlNRH4hIr+ZMX65iLzolt3jOiXiuil+z40/KSIrS3U8RnUwn+z2xQ4aMIxcyhXCXUqNJAa8W1UvBi4BrhGRK92yu1X1Evd6GEBELsDvcHghcA3wdREJYg/vBTbjt99d45YD3AT0q+q5wN3A1hIej1EFzBfHuCX7GeWgXCHcJfORuN7pQ+5r1L2masd4HfCQqsaAg6597hUicgjoUNUnAETkAeDD+O12rwM+67bfAXxNRMT6ts9v5oPdvlRBA4aRyYrOFvoGx9LXGZTGFFxSH4mIhEXkOaAP+JGqPukW/baIvCAi3xaRTje2HDicsXmvG1vuPueOZ22jqkngDLA4zzw2i8heEdl7/PjxIh2dYcweS/YzykG5TMElFSSq6qnqJUAPvnZxEb6Z6q345q6jwJfd6pJvF1OMT7VN7jy2qeo6VV3X1dU1w6MwjOKzorOFk8MxDhwfYv+bAxw4PsTJ4ZgFDRhFpVym4LKE/6rqaRHZDVyjql8KxkXkG8AP3NdeYEXGZj3AG268J8945ja9IhIBFgCnSnEMxvym3FVu37V6EU8dOkVIICQQ91L0Dca5/h2LSvY3jfqkHKbgUkZtdYnIQve5GXgvsF9ElmWs9hHg5+7zTmCTi8Rahe9Uf0pVjwKDInKli9a6Afh+xjY3us8bgV3mHzFmSiUc308cOEVXWwMN4RAphYZwiK62Bp44YM9BRu1RSo1kGXC/i7wKAdtV9Qci8qCIXIJvgjoEbAFQ1X0ish14CUgCt6hqkDBwM/AdoBnfyf6IG/8W8KBzzJ/Cj/oyjBlRCcf34f4RlrQ10tXelB5TVfORGDVJKaO2XgAuzTP+ySm2+Tzw+Tzje4GL8oyPAR+d20yNeqcS2fLliqYxjHJgme1G3VOJbPn5lFhpGCZIjLqnEjf1+ZJYaRhgRRsNo2JVbudDYqVhgGkkhpGFhfwZxswxQWLUPVb3yjDmhpm2jLrH6l4Z8xnrR2IYZcDqXhnzlZrvR2IYtYI1yzLmK/OhH4lh1ASW01FbWEOwwimXtm2CxKh7LKejdrDAiJlRLm3bnO2GgeV01AoWGDEztqxfzZ079zEST9IcDTOa8GqvH4lhGEYxscCImTGv+pEYhlGblLtPy3RYscuZU9P9SAzDqG2q0R9hgRHViQkSwzDyUq7Q0ZlggRHViZm2DMPISyX6tBSCBUZUH6VstdskIk+JyPMisk9E/tSNLxKRH4nIq+69M2ObO0TkNRH5hYj8Zsb45SLyolt2j2u5i2vL+z03/qSIrCzV8RhGvWGJmkahlNK0FQPeraoXA5cA14jIlcDtwGOqugZ4zH1HRC7Ab5V7IXAN8HXXphfgXmAzfh/3NW45wE1Av6qeC9wNbC3h8RhGXWH+CKNQSiZI1GfIfY26lwLXAfe78fuBD7vP1wEPqWpMVQ8CrwFXiMgyoENVn1BVBR7I2SbY1w7gPYG2YhjG3DB/hFEoJfWROI3iGeBc4H+o6pMicpaqHgVQ1aMiElyVy4E9GZv3urGE+5w7Hmxz2O0rKSJngMXAiZx5bMbXaDjnnHOKd4CGMc8xf4RRCCWN2lJVT1UvAXrwtYuLplg9nyahU4xPtU3uPLap6jpVXdfV1TXdtA3DMIwZUJbwX1U9DezG920cc+Yq3HsQlN4LrMjYrAd4w4335BnP2kZEIsAC4FRJDsIwDMPISymjtrpEZKH73Ay8F9gP7ARudKvdCHzffd4JbHKRWKvwnepPOTPYoIhc6fwfN+RsE+xrI7DL+VEMwzCMMlFKH8ky4H7nJwkB21X1ByLyBLBdRG4CfgV8FEBV94nIduAlIAncoqpB7OHNwHeAZuAR9wL4FvCgiLyGr4lsKuHxGIZhGHmQenuAX7dune7du7fS0zAMY5ZUW/2vekFEnlHVdfmWWYkUwzBqht37+/i9Hc/zs8P9HBsY42eH+/m9Hc9bP5IKY4LEMIya4QuPvMzpkQSagrAImoLTIwm+8MjLlZ5aXWO1tgzDqBkOnhwhJBAK+ZH/IqAp5eBJ60dSSUwjMQzDMOaECRLDMGqG1UtaSSmkVFGUlCop9ceNymGCxDCMmuEz16ylsyWKAEkvhQCdLVE+c83aSk+trjFBYhhGzbBhbTdf3Hgxl57TybIFzVx6Tidf3Hixhf9WmIKd7SLyFmCNqv7YZapHVHWwdFMzDMOYiBWSrD4K0khE5Lfwy7Tf54Z6gH8o1aQMwzCM2qFQ09YtwFXAAICqvgrYI4FhGIZRsCCJqWo8+OIq7dZXbRXDMAwjL4UKkn8RkT8EmkXkPwJ/C/xj6aZlGIZh1AqFCpLbgePAi8AW4GHgj0o1KcMwDKN2KDRqqxn4tqp+A9ItdJsBq0tgGEZZseq/1UehGslj+IIjoBn4cfGnYxiGMTm79/dx58599A2OsbA5St/gGHfu3GfVfytMoYKkSVWHgi/uc8tUG4jIChH5iYi8LCL7ROQ2N/5ZETkiIs+51/sztrlDRF4TkV+IyG9mjF8uIi+6Zfe4Tom4borfc+NPisjKwg/dMIxa477HDxANCy0NEUT892hYuO/xA5WeWl1TqCAZFpHLgi8icjkwOs02SeB3VfV84ErgFhG5wC27W1Uvca+H3T4vwO9weCF+b/evOxMawL3AZvz2u2vccoCbgH5VPRe4G9ha4PEYhlGDHO4foTkazhprjobp7TcreyUp1EfyaeBvReQN930Z8PGpNnC91o+6z4Mi8jKwfIpNrgMeUtUYcNC1z71CRA4BHar6BICIPAB8GL/d7nXAZ932O4CviYhY33ZjvlLv/oEVnS30DY7R0jB+6xpNePR0TmkgMUpMQRqJqj4NrMXvnf5fgPNV9ZlC/4gzOV0KPOmGfltEXhCRb4tIpxtbDhzO2KzXjS13n3PHs7ZR1SRwBlic5+9vFpG9IrL3+PHjhU7bMKoK8w/AlvWrSXjKSDyJqv+e8JQt61dXemp1zZSCRETe7d7/D+BDwHn4pqUPubFpEZE24O+AT6vqAL6Z6q3AJfgay5eDVfNsrlOMT7VN9oDqNlVdp6rrurq6Cpm2YVQd5h/w62zdde2FdLc3cWY0QXd7E3dde2FdaWXVyHSmrV8HduELkVwU+PupNhaRKL4Q+WtV/XsAVT2WsfwbwA/c115gRcbmPcAbbrwnz3jmNr0u234BcGqaYzKMmuRw/wgLm6NZY/XoH7CijdXHlIJEVf9ERELAI6q6fSY7dpFV3wJeVtWvZIwvc/4TgI8AP3efdwLfFZGvAGfjaz5PqaonIoMiciW+aewG4C8ytrkReALYCOwy/4gxX6mkf6DefTPG1EzrI1HVFPDbs9j3VcAngXfnhPr+mQvlfQH4DeC/ub+zD9gOvAQ8Ctyiqp7b183AN4HXgF/iO9rBF1SLnWP+d/Az8A1jXlIp/4D5ZozpkEIe4EXkj/HDfb8HDAfjqlpzZqR169bp3r17Kz0Nw5gVgWbQ2z9CT5k0g+u37ZmgCY3Ek3S3N/E3m68s6d82qgcReUZV1+VbVmj473/G94n8l5xxC5UwjDJSCf+A+WaM6Sg0IfEC4H8AzwPP4fsoLizVpAzDqB5WdLYwmvCyxix3w8ikUEFyP3A+cA++EDnfjRmGMc+x3A1jOgo1bb1NVS/O+P4TEXm+FBMyDKO6oqQ2rO3mLii7b8aoHQrVSH7mwm8BEJF3Av9WmikZRn1TzVFSFltv5KNQQfJO4N9F5JCrffUE8OsZYbyGYRSJastgr2bBZlQHhZq2rpl+FcMwZko+E1a1RUllCjaAloYII/Ek9z1+wMxbBlCgIFHV10s9EcOoN4In/WhYsp702xsjjCa8qqlwW22Czag+CjVtGYZRZCYzYalqVUVJWfivMR0mSIy6Y/f+Pq7ftoert+7i+m17Kmbrn6xJ03Dcq6oKtxb+a0xHoT4Sw5gXTGZOugvKfqOeqgjjZBnslQgLtvBfYzpMkBh1RTU5jresX82dO/cxEk/SHA0zmvCmfNLfvb+P39/xPINjSZKpFCcGY/z+juf54saLyyJMTHAYk2GmLaOuqKae3zNt0rT10f30jyRQIBIOoUD/SIKtj+4v67wNIxfTSIy6otp6fs/kSf/AiWFCAiHxG4OKgIpy4MTwNFsaRmkxjcSoK8xxbBjFxwSJUVfUcs/vVYtbSCmkUoqqkkopKfXHDaOSlMy0JSIrgAeApUAK2KaqXxWRRfgNslYCh4CPqWq/2+YO4CbAA25V1R+68cuB7wDNwMPAbaqqItLo/sblwEng46p6qFTHZMwPatVxfPv7zuf3djzPUCyJl1LCIWFhY5Tb33d+padm1Dml1EiSwO+q6vnAlcAtInIBfjvcx1R1DfCY+45btgm/z8k1wNdFJPCK3gtsxu/jvobxki03Af2qei5wN7C1hMdjGBVlw9puvrTxYi5d0cnSjiYuXdHJl6aI2KqWfBlj/lMyjURVjwJH3edBEXkZWA5cB2xwq90P7AY+48YfUtUYcND1Yb/CFYnsUNUnAETkAeDD+H3brwM+6/a1A/iaiIgW0j/YMGqQQrWpasqXMeY/ZfGRiMhK4FLgSeAsJ2QCYRNc1cuBwxmb9bqx5e5z7njWNqqaBM4Ai/P8/c0isldE9h4/frw4B2UYVUy1VRA25jclFyQi0gb8HfBpVR2YatU8YzrF+FTbZA+oblPVdaq6rqura7opG0bNU035Msb8p6R5JCISxRcif62qf++Gj4nIMlU9KiLLgMBw2wusyNi8B3jDjffkGc/cpldEIsAC4FRJDsYwysg9P36Fb/70IMNxj9aGMJ+6ehW3vve8grcvdr5MNXVsNMpPwktNubxkGomICPAt4GVV/UrGop3Aje7zjcD3M8Y3iUijiKzCd6o/5cxfgyJypdvnDTnbBPvaCOwy/4hR69zz41f46q7XGE14REK+APjqrte458evFLyPYubLWGOr+iKW9BgcS3BiKMYbp0c5dGKYN8+MTblNKTWSq4BPAi+KyHNu7A+BLwDbReQm4FfARwFUdZ+IbAdewo/4ukVVg9rVNzMe/vuIe4EvqB50jvlT+FFfhlF1zOSJ/ps/PUhIIBLyn/NCAslUim/+9GDBWkkxCy1WU30yo7jEkh7xZIqYe8WTKfI9i4fzehHGKWXU1k/J78MAeM8k23we+Hye8b3ARXnGx3CCyDCqlZlGUA3HPUIoYwkvy+HnpZKz+vtzVdGrrbGVmdlmTiqlxL0UcS9FLOG/TyY0ZoPV2jKMEnPf4wdIeB4nh5LEvRQN4RAdzZFJn+gbIyFG4t6EcVX/Jrphbfe0N9Nihv9WU30yC2uenlRKnYYxrm1M5+OYKyZIDKPEvNo3yJmRBKGQEA4JyZRyYjBOwhvMu/6i5kheQSKQDt+d7mZaTHPUTMvdT0YxNAkzs2WjqmmzVCzpEUuUXmjkwwSJYZSYeDIFOVV7U6L+eD5CE2NgQkA4LPT2jxR0My2mOWrD2m429p6eEEVWaGLkfY8f4NW+QQbHknS2RFnS1jhrTaLazGzlRNU3T8WSvnkq0DiqASvaaBglJhr2BUhmsUWAhnB+F+KKzhaaIiEaIyGao2Gao2Gi4RDhkNDT2VJQjkgx+6zv3t/Hg3teJ55MIfgC8ME9r08btZUZ7TUSS5JS5eRwnMGx5KwTJOulf7yq7yMbcNFTR06PcujkCEf6RzkxGGNwLFE1QgRMkBhGyTnvrA4WtzYQCQueKpGwsLi1gTVndeRdf8v61bQ3RfBSipdK+S9V2hojbFm/uqCbaTHDf2fbUCtTc0q4IpMhhBNDMWB2msR8bAOQSimjcY8zIwn6BsY4fGqEgyeGeeO0LzQGRhPEEl7RHOOlwASJYZSYLetX0xAJs3RBE287q52lC5poiIQnvfltWNvNFzdezJruNkQEEeHcrtZ0gcZCbqYb1naz8bLlHB+M8fKbgxwfjLHxsuWz8iNkNtQShJAIIWHahlqZmlNDOITnIoeG4x4Hjg9xcjg2Y02iltsAwLimkSk0Dp0c5uiZUU4OxxiKJSvi45gr5iMx5g3VGhY625yOhS0NdLUnJxxLIfvbvb+PHc8eoau9kXOcg3zHs0d4e8/Csp2TzGivtsYIxwZj6WXDcY/RhMf17zhnxvutpTYACefTGEt4U+Zp1DomSMpItd7o5gPVHhY6k5vfVMcCZF1Dn7vuorz7LWZ006rFLbx2fBhJqd/eVyGlcO6SqbWJzGiv0yPxrGUigMIjP39zRqVfqpkgVyMQGmMJDy81/4RGPkyQlIlqv9FVmrkK2ZnmalQTucd+eiSe91i2Prqf4bhX0DU0m+imyX6DmTTUyt3HxsuW88SBU/zy+DACREJCJOxb1L1Uqib7zasqCc8XGgmXo1GOXI1qxnwkZcLKek9OMWo5vdo3yInBOEl3owtyNV7ty5+rUS3kO/ZfHBukbyA24Vhe6xsq+BqaaXTTVL9BoQ218u1jx7NH2LJ+NY2RENHwuBCpFZJeKq1R9Q2M0ds/wqGTI/T2j9A3MEb/SLxm/RrFxDSSMlHP8e/TUQwzzIxzNaqEfMcO4Ck05BxLMqUFl4afaRLhfY8fIJ7M1oLam8Y1ukJMc1P9jrM1j5WLQMsItIu4S/CrF9PUXDFBUiaqqcxEtVEMIRsNC6MJ304d3Khg8lyNaiHfsQcEtbYEP0cxLP41U8g1NFMH/yvHBhgYSxJCCIuQ9Pycj6Q3VQuh6Y8l+B0/d91FVdFvPunqTSWSzjTlpUh6SjJV3Q8c1Y4JkjJRrDIT85FiCNnzzurg4IkhBscyn6ijrFrSVoopF418xx4JCXFPfQniJImm4OzO5nTYbyHX0Ewc/P7TuJJb4jHuFf5EPtXvGJjHilGNuFCCmlOB89s0jNJhgqRMzKXMxHynGEI22MfSBZGqFNSTObLzHXtKlbArIx9oV54qrQ1hbn/f+SW5GceTE2t7TTWej+l+x1KF7Xop3yTlv5SkOb/LjgmSMlENcf3VSjF6ZxSz/0axmS5iL3feZ0YTtDaEOTEUT2tXS9saGY57JbsZJya55wbjhUTVlfI3COpMBYIi7kxSCS9lWkYVUDJBIiLfBj4I9KnqRW7ss8BvAcfdan+oqg+7ZXcANwEecKuq/tCNX854U6uHgdtUVUWkEXgAuBw4CXxcVQ+V6niKEZ5qVUsnpxg3yGpNVJvut8+d9/Xb9tA3OMbqrnGz3Eg8SXd7U8nmGCTJSfCP+kYuVZ1R6Ppcf4Ogmm3C9csIHOCmXZSP4DcYHEsyMJZgcCyZtxp1JqXUSL4DfA3/Zp/J3ar6pcwBEbkAv7vhhcDZwI9F5DzXIfFeYDOwB1+QXIPfIfEmoF9VzxWRTcBW4OOlOJBi5IBY1Fb9MtPfvhL+tLbGCMPxJKq+KU3E78zY2hAp2UNQ0mkY8WSKmOelBUc1Z34/deAUDz19mKMDoyzraGbTO1ZwxepFlZ5WXlSV4bjfNndwLMnAqP8+GEsyOJZgYDTpfx9LMODeA+GRmIFvDErbIfFxEVlZ4OrXAQ+pagw46FrnXiEih4AOVX0CQEQeAD6ML0iuAz7rtt8BfE1EpBQ924vxH8mituqXmf72lTDTferqVXx112uEQ74ASbnw3E9dvYrtz/TO+iFI1Q9bTnpKIuVrGcErVcUCIx9PHTjFV3e9SiQkdDRFODkc46u7XuU21pRUmHgpZSiWfaP3BUP22FBs4lixrH5tjVOLikr4SH5bRG4A9gK/q6r9wHJ8jSOg140l3Ofccdz7YQBVTYrIGWAxcCL3D4rIZnythp4VK+gbGEPEbzIUEhBXhM4vRieEQhmfpTjahEVt1S+z+e2LYaabiTk2KFOSGwxy63vP44kDp6YVhIF2kUgF2d7zzyT10NOHSSQ9Tsc9El6KaDhEa0OYh54+XJAgSXiptAaQJRCCsdHxsczlQ7HZtVjOJSTQ3hSlvSlCe1OEDve5I3OseXysrTHixqM0RcOcc9fk+y63ILkX+By++fVzwJeB/0z+3u46xTjTLMseVN0GbAN4+yWX6Ux/mCVtjZwajtEczfyPlKSrvZGjZ0YRBJFx+7JfJXVcQAnCZSs7ueN9a/mf/3aII6dH6FnYwk1Xr+Jd5y5OJ825/LP09qFQdedAGIVRCQ1jNubYW997Xt66V1vWr+aPv/9zUpqgKTIuCD92eQ+HT42QTFW3OapYHDrph5f7/7chkUxxKpliNDHAP71wNMNENG4uGsoQCLmVBmZLNCzjAqFx/OY/LhSidOQIhlWDyAUAACAASURBVPbGKC2N4XTCbrEpqyBR1WPBZxH5BvAD97UXWJGxag/whhvvyTOeuU2viESABcCpUsx707oVfHXXq6gmaYqGGEukSKaUj12+gtFpnFCZvG1pO1/4T7+WNXakf3TKbTK1pHDITxYLBe8iSMglrGVkQQdIhqzNvX4yhVawT6N0lDsQYCbm2CCr20v5iXn+u6YT9VYuaeWWDefy0NOHeXNglKXON3DxOQtrVuPI9R8EN/8zoxM1hkAonBlNjj+pZsjN4XiKL//olRnPoSkSyhICvgAINAL/e3vzuLAIljVGQkiJBMJsKasgEZFlqnrUff0I8HP3eSfwXRH5Cr6zfQ3wlKp6IjIoIlcCTwI3AH+Rsc2NwBPARmBXKfwjAFesXsRtrJnwH6kcTraUqm9LLsP/V9/U5wuVdP+JHA0reBoTJK0TyvjHtOALtss0HVbbxT+fOdw/woKmCKrq3/PU7wny+slh+gbHXNOs8dd0/OLNAV7tG2Q04TE4luQXbw7M+PovhaO6UP9BtlPZ/1ws/4EASxc05WgI+U1IbU0RFjT7ZqOGSG3VHZuKUob//g2wAVgiIr3AnwAbROQSfHl+CNgCoKr7RGQ78BKQBG5xEVsANzMe/vuIewF8C3jQOeZP4Ud9lYwrVi+q2uiMYuGlFA/1A7BLRKYwAtJmQdxY5vJMAZb2Z+FrYWnznxNaaeFGxr5y/l6tCTJVdTWpFE+VVMpPTFRVUsqE90yNYklbIyeHYlm1uUYTHt3tTQyNzcy0++C/H+L+Pa8TEgiHIJb0uH/P6wB88j+sLGgf0zmqA//BQIavYChWXv9BW/rJP5IhCMY1hJ3PHeX0aIyYs0hEw0JbY5iezja+8vGLizKPWkXqwbaZydsvuUz/4UePV3oaRg6VCqvM1bLyyZrgv4hm2DMm+28zwYRIHpOjjO9D1d/v+N/wefKXJ+d0Pp46cIrP/WAfI4lU2tnYEg3xxx+8cMbn9UN/8VNiSY9waPwJ2kulaIyE+cf/enV6LF/+QSAYvvvUrxgaSxISXxh6KdL1rSKhUFH9B8GTf7ZAGPcfBIJh3KwUpaVhev9BpjDMNHHf9u7SRm1VA9FwiHMWtz6jquvyLbfMdqPiVCqsEsgy/UwSqzHDHU47MC3FOB+/eHMgLUSCWYwkUgWZpPz2vV5aEIzEPQSyChsKfpfD2x56bk75BwAJb6IQCfwHgUDIFQLpz81R2oPoouYoTSX0H1TSxF3tmCAxKs5DTx8mEpK0GSYIkS00rHK+8dDTh0l6HqdHxsNM2xoLDzMF2P5MrzNFSVqYeCnlu0/9itamaB7/wdT5B7niIfj+4pEzU86jtTFMR1OUk8Nx4slUlj9NFZa0NXDre9akhcIvjw3xjy8c5djgWFUm/E1m4q6lRMVSYILEqDhHB0bpaMq+FJuiId4cmDqibb7y+qlhBkcTSMgPfEh4KU4NpYglh/j5kTMF5R8Mu2hCL0dDiHnK137yWlHm2RwN8bF1K/xoo+ZIOszU/+w7lMMuGvBT33ma10+NpH1afvyI0t4Y4apzlwD+zfjb/36oIpppoeQTGEDFNOpqwQSJUXGWdTRzcjjbMTyWSLG0o7mCsyouU/kP0jkHMX/szKjTCHKEwMBYklsfem5O8xDgnMUt2eahptwQ1Gz/wafuf5qEl+L0SDLtb1nYEqExEubGAp3twwmPszoa6R9JpLWszpYGRjJ8I9WumT514BRbf7ifYddTpX84ztYfDtPZHK3qeZcDEyRGxdn0Dj9PZzThZTkxg6e9aiLXf5Bbqyi3fpFftiIxa/9BPgLzUEMkxNkLmlne2ZwjEKL87PVT7H7lhAu7Hu9I+H+96y0FR1oFnL2ghZPDMbraxotGjiY8Frc2FryP4GFhRUY2/GjCoztjH9WumW771wMMjCb8PK6woIr/244mWN3VmrVuNc27HJggMSpOJZyYM8s/KE39osB/kBt2+uSBkwzFEsRdkmAkJLQ0hOlojhJP+k/zgcAdTXh84KJlE87VB9++jJX/fojtz/QymvBojob52OU9MxYi4Av6rT/cz7HBMVIpJRQSWhsi3LLh3BntY7qHhWrXTA/3j6Tzq8BF34mSSPnzrNZ5lwMTJEZVMNs8nWqoX9SWWaYiIwu5zWkJxwfH+OeXjhENh2iOhkh4fpLpp99z3iSO28V5w0wjImg4VLAJ5ZP/YeWsBMekuHDl2QS3FfKwUEuaaSaRECRTWnPzLiYmSIyKk89/kN9kVLr6RZGQpCOHOpoitDmncUeeDOVM30Ih9Yt+53vPEwnB4FiCU8PTR2FNdtO9+7FXCAsc7o9l+BmiMzahhFyC53j1AT/ZM7NOXDrRE+Hvnu1lQXOUZQv8J2wBRhJJ/v5nR/jI5cuz9p0vvyYYu+7S5Vx76dnp8cxkShR+86KltDaGuf+J13nj9CjLFjTziXeewzvfupiUS84MStwHCaaaMZ6uAlEiVixs5vVTI5DSLHPhWxa1sHn9W+s6LNgEiVE0CvEfHDg+nC61ERYhGgkx5ooAFoOmaChLG0g7kXNKV3RkLi9x/kFuFFYypfQPJ0imhifdJp+G1vqvEV4/OeyXsHH7OTYQY+XiVpobwtl12EKSUZttbjXVjg6MERZ4/eRwumPjkrYGjp4ZpTESnnLbmTaE+9Aly/nQJcsnXV4IuRn/gXBJ5YyTIXzULccJB8Vtm9J00ujmX38rWx/dz3A8mTbxdTRE2bz+rXVR+WIqTJAYE/BSynBs3BSUz3+Q3Rxndv6DBMpYMn8Rscn8BxMS0pzQCD5XY/2ieDKVftoH/2naE01Xfc5HNBwiEhYioVBaIISDUjLqcjHUfyqPhiWtLZSC9sYIr/YN+fNwAuzI6THWdLdNuV0xGsLNBkmfq+I+GLxlcStLO5r4y3/5Jb39IyzvbOGmq1Zx1ZolfukaV8ImLZyC8jYpzdCYxrtRzidMkMxjZus/GI4li5HjneU/aGuMcOT0KPGkRzLl140KfABdbU38t/99DR1N476F8CyenKuVaFiIJf2n28AkAtAQFpqiYSJhoSEcIpp+SV7taDSZoqezebyXe8TXDIZnUIF6puze38ehk8MkU+OO/0AgTndDvO/xAyQ8j5NDybQm09Hsd1wMls+2dXWlKEYV50xNKeVqqKU/63iNtbSWxLhIDMx5AVk11xgXWOmSO8F3SivATJBUOZn+g8EcQZDbHnNwLJklHIrpPxhveJPtPwhMSB2ZeQjN+fsf/Kd7/51RzzcJhCP+RT4a9+gfjXPh2QuKMtdqIxoOsbqrjd5TIwzFxm+o7U1RVne1c/bCwjWJoNNibi/3hnCI67ftKfpNOdAoEp4SCflpLYmU0hQRli9omlaAvdo3yJmRRNrMlkwpJwbjDI2d5vd3PM/gWJJkKsWJwRi/v+N5vrjx4poQJnMl0JjCRdaYCiGVyjbl5fqXck2CgblvuqmaICkTM80/mGv9onw0RUIZNYryJ6RN6JpWRP/BbEw8tUIkFKIh4msT/nso3Tfi1nev4c6d+2hvjs6pO2a+TosDowkUiHupOZuPcv0Z/cMxEp6XvsGEBCJhXyhEwiG625um3F++3zslfh+Q0UQqvR9V6B9JsPXR/XUhSCpJKCSESiDATJDMkNz8gwkCIXOsRP2TWxvDWaUopvIfBI1x2qvAfzCViacWCLnggGhYiIZCRCMhIiHfLDWVE7tYHRLz7ScaEhIpLaiB1VTk82ccPDGcNrGA6+PuKalUYYIwGhZGExN/75T6IbOZAkZFOXBi8uADo7qpW0FSiP8g06FcyvyDTIdyfudytmO5Vv0HKxe30ds/zHBWz+sIPZ2t029cRgIHdkMkRGM4TEPE1zbmct6L1SExdz9Xb93FwuZo1jrN0TC9/SMz2m++joqZVo3MZyAF7rr2wmmP57yzOjh4wm9Pm2nSOzYYm3Sbe378St6+8UZ1U3eC5JfHh/jAPT8tif8gePJPF7Brym2SMy4UWhsjJeufXK0EGdKeezT1VPGUiiZuhUTSgqIhEqIhwyRVCwR+k0AAgF96pCejFEkhHO4fmSCQNOc9ICSFmc0CU9zSBZEsk97yBU28ORBDcvIxFjaF+equ13wTWsg/jq/u8gtMmjCpbkrZIfHbwAeBPlW9yI0tAr4HrMTvkPgxVe13y+4AbsLvz3erqv7QjV/OeIfEh4HbVFVFpBF4ALgcOAl8XFUPTTevIAM1l6ZIyHccT6IN5CakdZQh/2A+kvBSxJPjNo6GcPn8I+GQ0zIi4bTQqLS5b67k85vMxv+STyBNRjLlaw65N/d8OSMbL1s+QcN4e89Cbv2bZxmKe2nfS1tDmOG454SI/5uExO+B8s2fHqx6QTLTfJn5Rik1ku8AX8O/2QfcDjymql8Qkdvd98+IyAX4rXIvxO/Z/mMROc+1270X2AzswRck1+C3270J6FfVc0VkE7AV+Ph0k1ra0cTnrrtwQhe1Wr+h1ALb/vUAo3HPhbeOR21t+9cDRU/mijoh0ZihaUTC8+83Lpb/JZ9AmopcTSGfj+X3djyPAF3tjZzj9rnj2SMANETDNLiQ4nBIaIiGGRyK0xDJfigLCSUNby4GlcqXqSZKJkhU9XERWZkzfB1+H3eA+4HdwGfc+EOqGgMOuj7sV4jIIaBDVZ8AEJEHgA/jC5LrgM+6fe0AviYiotMESy9ojqb7HxjlZbKid4dnaM/PJJ9pajrndyUpxZNrMfwv+QRS38AYwzGP/DqjZmkKgY8l6SkHz/gZ8J4zXY3Evaw8km/+9CBd7Y1ZSZQj8ST9I4m0hhKQUmhtmDp7vtLk8y/NJuChlim3j+QsVT0KoKpHRSQ4y8vxNY6AXjeWcJ9zx4NtDrt9JUXkDLAYOJH7R0VkM75Ww/Ke+imkNt8IQmyzhEYNaZK79/dVdf5ErkC6ftseDp0c4uiZic5xL0VW4Mnh/hEGRmIMxHLEjvqhyZl5JJ4q5yzK9uE0R8O0OvNWMpUiJC5KTOFTV68q7oEWmcP9I4QFDhwfyiohM9OAh1qmWv4X5nt8nCwNJtA4plqWPai6TVXXqeq6RYtNG6kUKxY246UglkylX17KHw8Qp2G0NUbobGmgu6OJ5Z3NrFrSyjmLW1i6oIlFrQ20NUaqUojs3t/H9dv2cPXWXVy/bQ+79/ell219dD/9I37eRyQcQhnPn6hGtqxfTTQ8URvIzLJOk0pNFCIOL6UILiPeFVvMNZ2NJjwuPHsB1759KSmFWNLPXbn27Uur3j/S3hjhyOkxks5MF5SQaWusn1imcv9PPCYiywDce/C/rBfIVBV6gDfceE+e8axtRCQCLABOlWzmxpz59fO6JphJUsB/vOAslrQ3sryzmZWLW+jpbKG7o4lOJzAaI+GaCGgIbOV9g2NZtvJAmBw4MZw27QU31pBQtfkTG9Z2c9e1F064SQRPay3R8d/k1OjkYfHpbGmXSNUSFQZGE7x6bJCXj57h1WODDIwmeNfqRTzzqzOsXNzCRWd3sHJxC8/86kyWMK5G0tZ0zXhljtcB5RYkO4Eb3ecbge9njG8SkUYRWQWsAZ5yZrBBEblS/DvJDTnbBPvaCOyazj9iVI5oOMQLRwY4q72BlmiISMi3fS9b0MgLRwboaIrWjMCYjKC21JtnxvjFsUHePDNGwvPStaVqlbacroUhgYXNES5a3pkeG5nCIR4SP9Q7EhYWtzawfGGLf6912gni33sffvEo8WT2+Ysnq//8DcU9li9sIhKW9HEuXzh9CZn5RCnDf/8G37G+RER6gT8BvgBsF5GbgF8BHwVQ1X0ish14CUgCt7iILYCbGQ//fcS9AL4FPOgc86fwo76MKiAoDxKE2jZGfOf3scExutqb6O4YFxaqOm9syZPVlkp4gwCsWtzCa8eHJ+RPnLtkZjkf5WL3/j5u/ZtnGYhl3xAjISEaDhUcYqxOI/FclJaIZPU3Ad/Z/trxYb9HCn6146SnnByOk/QGinpcxWayGmjTlZCZT5Qyauv6SRa9Z5L1Pw98Ps/4XuCiPONjOEFkVI5oOERjdFxgTJXMV6zkuWolnkz5ZcM9HW/A5MYBbn/f+fzejucZiiXTYa8LG6Pc/r7zSz632USL/dE/vDhBiADEPZ1RdWglW/M4PhRjaUf2TbY5GvarC4fHe6aI+OVV4kWqNVcqipXLU8tUn7fSqEoioRDNrm/4kvZGzl7oO8BXLGqhu72JBc1RmqJTm6a2rF9NwlNG4klXxDI5r/7DpTSFl26M5L97Cqq+INmwtpsvbbyYS1d0srSjiUtXdPKlMkRsTee7mYwjZ8YmXRYNS5bJaaryMa0NYdYu7WBNdzsLXN/5fM72SFjSzab8xlL+iazGoIpMAl9Sd3sTZ0YTdLc3FVRCZj5RP2EFRsFEQoGWMW6eKkZ9rw1ru9nYe3pCpvN8+Q8XS+SPWhrLGC9Wza2ZMFVfkMy55GotU3kcj52JZVWljob8kOB8dLU3pj83R8M0hCX9QJH5BP/WJa30DcY4PTqeT7KwOcqa7vY5n4NSU4nftZowQVLnBOG2TZEQjdEwTZHSZYDv3t/Hg3teJ55MIfjl4x/c8zpv71k4L/4TTiJHJh0vF6/2DdI/HE9rSknPm9DeePf+viyz24mhyQsrgh9tNzg2HqnVEAkTS+ZviNbeNF7DazThseasDrasXz0hG/+F3tN8dddrhENC1OWRnBlL8q46bmFbK5ggqTMCR3hjJJzWOsoVKbX10f2cGIqnbzbJVIrYUNz6UMyR6SrmjsQ9Mt0Mim9yy4y0+sIjL3N6JOFa+gpagPCLZfSRaXAl9UOh8fI3CdePJJ/vIN8T/H2PH6CrrSGnWnCEJw6c4tZZnx2jHJggmadklUJ3jvBKlw555djghCdWdeNGNoU6x+/58SvTVswdmyQMNXP84ElXvibD0c0MolfXdLdz6OQQA6PjQmDRgkYWNEXpbG0sqA7Y4f4RlrQ10pUR7TSfovrmMyZI5gG59aYCoVFtORmTBd9UeVBOwYQgb12qmRoKZ1IE8Js/PThtxdzJlItiWNyCKsBB5FJ7k2/yiiVTnBpOcP07zik4M32+R/XNZ6o7HMKYQEiE5oYwC135kJ7OFlYuaeXshc0saWucF4l9tcryzvz91ycbn4zMIoAi/ntulFRAUHo9k9lUzF29pDXdpzsdMVUAf+nmtGFtN5efs4BjAzGG4x5eSmltCLPj2SMFZ6bP96i++YxpJFVOQyREU9Q3TTVFw0TnYSn0+cJoPH+ZkMnGJ+Nw/wjxhMfBE8Pp6KUlrQ15e9u3NoQZGEuSa4fqaJrZf+3PXLN2vKCklyISCrGgOUI84TGanFyoBH6W3fv7ePjnx9I93VVhKObRGA0VXAW3WCXxjfJjgqSKCIckS2hU2qdhzIyTw4kZjUN+X4gAfUNxBNfmVv3vK/JoNh2NgSCZOD4TNqzt5osbL55wEwf/xv7EgZNTbn/f4wf8hMKQX0dMBFIoZ0YS9IYK93HUexhtrWKCpEIEzvB60jY6miIMjmWHiArQPsOn52plsuf2ycYnKyt/ZjSRd7t8Ibm9eUq8544X6ruZ7Ca+YW03K2//p0mOwudw/wiNkRBJzy//Ar7DPualzMdRB8yP/8E1QK62UUt9wYvFp65elY4wqqV+E6UiKCsfDolfVl79svLJlE64+Ydg1qVCopEQ8WRqggCPziBjXMgvEIMreEVnC0kvxcnhOKR8IeKpEgkVXpPLqF3m9yNwhRARGqN+OZHujiZWLGrhLYtbOaujiYUtDdOWEpmv3Pre87jt3efSHA2TTPlZzre9+9yq7zdRKJP9Z5psfLKy8uALEWG8XlcKaJxlqZBVi1sIh4TGsEs8DYcIh4RViwvXFCa7XIPxLetX0xAJs7i1gUjYL1gZEuGWDW81U1UdYBpJEQhKijRVIMmv1rj1vefNG8GRSzGe/DPR9D8+i5pn99+1GMUi2xojDMd8s2RmQcpW17zJHOX1jQmSGRKUFMk0Uc1334ZRGEGZ+LCMZ3d7qqxa3JLXqT5ZWfloSFjYEuHk8HjNqcWtUSQ0u+tsw9pubrjyLX72u+fRHA5xw5VvmdFNPjBLhqcwS5qjvH6xO+A0RMMh2poiLG7zK96uXNzCcpez0dYYMSFipLn9fefTEg2RSKUYS6ZIpFK0REO8/9eW5a2++/5fW8bCligS8gWOhGBhS5Rzu9uIhEM0R8NEw0JzNEwkHMrrtI5Ocvllju/e38eOZ4/Q1d7I+Uvb6WpvnFF+B8x/s6QxNyqikYjIIWAQP/g9qarrRGQR8D1gJXAI+Jiq9rv17wBucuvfqqo/dOOXM9706mHgtrl0ScysepvZkKmWmE3fCaO0PPzi0XSCIUBLQ4SReJInDpziS3lCboPihUFQQtxL0TcY5/p3TCxeWEi1gMwEx8y/X2h+R8B8Nksac6OSpq3fUNUTGd9vBx5T1S+IyO3u+2dE5AL87ocXAmcDPxaR81wHxXuBzcAefEFyDeMdFKckHBIaI2GX8OeXFClV1dtyMZPSGkbx2frofkYSKaLhUNpUNZJI8csTw7ztrOxS6M3RML39I3MuXpiaRJBkjh/uH2FhczRrefD3DaMYVJOP5Dr81rwA9wO7gc+48YdUNQYcdK11r3BaTYeqPgEgIg8AH2YaQRIJCysWtcxLk1SxnjyN2ZEZhQW+Q1pFSXjKaMIruIbUTIoXhkPi2teSsW52oymrYWWUmkrdTRX4ZxF5RkQ2u7GzVPUogHsP7nzLgcMZ2/a6seXuc+74BERks4jsFZG9J0+cmJdCBPwbUHM0O6PZnjwrTyQkM6ohtaKzJW8HwXw3/mvfvhQI+qKTbkYVjIPVsDJKT6XuqFep6mXA+4BbRGT9FOvmc1LoFOMTB1W3qeo6VV3X1dU189nWCDO5ARnFZ9XiFj+aKaWoKqmUklJ4a1frjFqxzuTGf/emy/jIJcvSGkg4JHzkkmXcvemy9DrWCtYoNRUxbanqG+69T0T+F3AFcExElqnqURFZBgQhJb3AiozNe4A33HhPnvG6JSjlna+RkFF6psrXmElo7ExzMu7edBl3b5p+nyY4jFIhcwhymt0fFGkFQqo66D7/CLgLeA9wMsPZvkhV/0BELgS+iy9szgYeA9aoqiciTwP/FXgS39n+F6r68FR/f926dbp3796SHV+lCaK2LCmsMtj5N+YrIvKMqq7Lt6wSGslZwP9ymd8R4Luq+qgTCttF5CbgV8BHAVR1n4hsB14CksAtLmIL4GbGw38focCIrfmMPXlWFjv/Rj1Sdo2k0sx3jcQwDKMUTKWRzM/wJcMwDKNsmCAxDMMw5oQJEsMwDGNOmCAxDMMw5kTdOdtF5Djwep5FS4ATecYNHzs/U2PnZ2rs/ExPtZ+jt6hq3ozuuhMkkyEieyeLSDDs/EyHnZ+psfMzPbV8jsy0ZRiGYcwJEySGYRjGnDBBMs62Sk+gyrHzMzV2fqbGzs/01Ow5Mh+JYRiGMSdMIzEMwzDmhAkSwzAMY07UjSARkRUi8hMReVlE9onIbXnWERG5R0ReE5EXROSyfPuarxR4jjaIyBkRec697qzEXCuBiDSJyFMi8rw7P3+aZ526vYYKPD91e/0EiEhYRH4mIj/Is6wmr59q6tleapLA76rqsyLSDjwjIj9S1Zcy1nkfsMa93gnc697rhULOEcC/quoHKzC/ShMD3q2qQyISBX4qIo+o6p6Mder5Girk/ED9Xj8BtwEvAx15ltXk9VM3GomqHlXVZ93nQfwfMrfH+3XAA+qzB1joujXWBQWeo7rFXRdD7mvUvXKjVer2Girw/NQ1ItIDfAD45iSr1OT1UzeCJBMRWQlcit9ZMZPlwOGM773U6Y10inME8C5nvnjEdbCsG5xZ4jn8VtA/UlW7hjIo4PxAHV8/wJ8DfwCkJllek9dP3QkSEWkD/g74tKoO5C7Os0ndPVFNc46exa+5czHwF8A/lHt+lURVPVW9BOgBrhCRi3JWqetrqIDzU7fXj4h8EOhT1WemWi3PWNVfP3UlSJzd9u+Av1bVv8+zSi+wIuN7D/BGOeZWLUx3jlR1IDBfqOrDQFRElpR5mhVHVU8Du4FrchbV/TUEk5+fOr9+rgKuFZFDwEPAu0Xkr3LWqcnrp24EifhN4r8FvKyqX5lktZ3ADS5y4krgjKoeLdskK0wh50hElrr1EJEr8K+hk+WbZeUQkS4RWeg+NwPvBfbnrFa311Ah56eerx9VvUNVe1R1JbAJ2KWqn8hZrSavn3qK2roK+CTworPhAvwhcA6Aqv4l8DDwfuA1YAT4vyswz0pSyDnaCNwsIklgFNik9VMeYRlwv4iE8W+A21X1ByLy/4BdQxR2fur5+snLfLh+rESKYRiGMSfqxrRlGIZhlAYTJIZhGMacMEFiGIZhzAkTJIZhGMacMEFiGIZhzAkTJIZRBkTk0yLSMovtDtVRwp5Ro5ggMYzy8GkgryBxeReGUbOYIDGMIiMirSLyT64w4c9F5E+As4GfiMhP3DpDInKXiDyJX8TwPa5HxYsi8m0RaczZZ7OIPCoiv+W+f8L1/nhORO4zYWRUEhMkhlF8rgHeUNWLVfUi/IqvbwC/oaq/4dZpBX6uqu8E9gLfAT6uqr+GX3Hi5oz9tQH/CHxXVb8hIucDHweucgUSPeD/LMNxGUZeTJAYRvF5EXiviGwVkf9NVc/kWcfDL44J8DbgoKq+4r7fD6zPWPf7wP9U1Qfc9/cAlwNPu1I27wFWF/sgDKNQ6qnWlmGUBVV9RUQux6+Z9P+JyD/nWW1MVT33OV/p8Ez+DXifiHzX1aUS4H5VvaN4szaM2WMaiWEUGRE5GxhR1b8CvgRcBgwC7ZNssh9YKSLnuu+fBP4lY/md+BVyv+6+PwZsFJFu9/cWichbinsUhlE4JkgMo/j8GvCUMzv9v8B/B7YBjwTO9kxUdQy/yuvfisiL+N3zdpO9ZgAAAF9JREFU/jJntU8DTSLyZ6r6EvBHwD+LyAvAj/Ar7xpGRbDqv4ZhGMacMI3EMAzDmBMmSAzDMIw5YYLEMAzDmBMmSAzDMIw5YYLEMAzDmBMmSAzDMIw5YYLEMAzDmBP/P1iZV5Q9YqHXAAAAAElFTkSuQmCC\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": 16,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f40944d2470>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"body-style\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We see that the distributions of price between the different body-style categories have a significant overlap, and so body-style would not be a good predictor of price. Let's examine engine \"engine-location\" and \"price\":</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f40944095f8>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZIAAAEGCAYAAABPdROvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAgAElEQVR4nO3df5BdZZ3n8feHDguNGgaaJhW7waAdVwOM0bSYXXRHJUDLKMFdWMKqaXeyxsUI0XFqJNbUgFOFJVOjDIkFGsWlw6gQGWeIVJIlgIhOQbCjSAg/iq4hQn5saBvEICHSne/+cZ4Ltzu3O50+OX26cz+vqlv3nO85z7nP6brV3/uc55znUURgZmY2VkeUXQEzM5vcnEjMzCwXJxIzM8vFicTMzHJxIjEzs1ymlF2B8XbCCSfEjBkzyq6GmdmksmnTpt9GRHOtbXWXSGbMmEF3d3fZ1TAzm1Qk/Wa4bb60ZWZmuTiRmJlZLk4kZmaWixOJmZnl4kRiY9bX18fll19OX19f2VUxsxI5kdiYdXV1sXnzZlatWlV2VcysRE4kNiZ9fX2sX7+eiGD9+vVulZjVscITiaQGSb+SdEdav0rSdkkPpdd5Vfsuk9Qj6QlJ51bF50janLYtl6QUP0rSrSm+UdKMos/HMl1dXezbtw+AgYEBt0rM6th4tEiWAo8NiV0bEbPTay2ApFnAAuBUoAO4XlJD2v8GYDEwM706UnwR8HxEtAHXAtcUeib2qrvuuov+/n4A+vv72bBhQ8k1MrOyFJpIJLUCfw58ZxS7zwduiYi9EfEU0AOcIWk6MDUi7o9sFq5VwAVVZbrS8m3AWZXWihVr3rx5TJmSDYwwZcoUzj777JJrZGZlKbpF8o/AXwP7hsQ/K+lhSd+VdFyKtQDPVO2zLcVa0vLQ+KAyEdEPvAA0Da2EpMWSuiV19/b25jwlA+js7OSII7KvT0NDAwsXLiy5RmZWlsISiaQPA89GxKYhm24A3gLMBnYCX6sUqXGYGCE+UpnBgYiVEdEeEe3NzTXHHLOD1NTUREdHB5Lo6OigqWm//G1mdaLIQRvPBM5PnelHA1Ml/VNEfLyyg6RvA3ek1W3ASVXlW4EdKd5aI15dZpukKcCxwHMFnIvV0NnZydatW90aMatzhbVIImJZRLRGxAyyTvR7IuLjqc+j4qPAI2l5DbAg3Yl1Clmn+oMRsRPYLWlu6v9YCNxeVaYzLV+YPmO/FokVo6mpieXLl7s1YlbnyhhG/u8lzSa7BLUV+DRARGyRtBp4FOgHlkTEQCpzKXAT0AisSy+AG4GbJfWQtUQWjNM5mJlZonr7Ad/e3h6ej8TM7OBI2hQR7bW2+cl2MzPLxYnEzMxycSIxM7NcnEjMzCwXJxIzM8vFicTMzHJxIjEzs1ycSMzMLBcnEhszz9luZuBEYjl4znYzAycSG6O+vj7WrVtHRLBu3Tq3SszqmBOJjUlXV9erU+2+8sorbpWY1TEnEhuTDRs2UBnwMyK48847S66RmZXFicTGZNq0aSOum1n9cCKxMdm1a9eI62ZWP5xIbEzOPvtssgkrQRLnnHNOyTUys7IUnkgkNUj6laQ70vrxkjZIejK9H1e17zJJPZKekHRuVXyOpM1p2/I05S5pWt5bU3yjpBlFn49lOjs7OfLIIwE48sgjPW+7WR0bjxbJUuCxqvUrgLsjYiZwd1pH0iyyqXJPBTqA6yU1pDI3AIvJ5nGfmbYDLAKej4g24FrgmmJPxSqampro6OhAEh/60Ic8b7tZHSs0kUhqBf4c+E5VeD7QlZa7gAuq4rdExN6IeAroAc6QNB2YGhH3R3ab0KohZSrHug04q9JaseJ1dnZy+umnuzViVueKbpH8I/DXwL6q2LSI2AmQ3k9M8Rbgmar9tqVYS1oeGh9UJiL6gReA/X4aS1osqVtSd29vb95zsqSpqYnly5e7NWJW5wpLJJI+DDwbEZtGW6RGLEaIj1RmcCBiZUS0R0R7c3PzKKtjZmajMaXAY58JnC/pPOBoYKqkfwJ2SZoeETvTZatn0/7bgJOqyrcCO1K8tUa8usw2SVOAY4HnijohMzPbX2EtkohYFhGtETGDrBP9noj4OLAG6Ey7dQK3p+U1wIJ0J9YpZJ3qD6bLX7slzU39HwuHlKkc68L0Gfu1SMzMrDhFtkiG81VgtaRFwNPARQARsUXSauBRoB9YEhEDqcylwE1AI7AuvQBuBG6W1EPWElkwXidhZmYZ1dsP+Pb29uju7i67GmZmk4qkTRHRXmubn2w3M7NcnEjMzCwXJxIzM8vFicTMzHJxIjEzs1ycSGzM+vr6uPzyyz1fu1mdcyKxMevq6mLz5s2er92szpXxQKIdBvr6+li/fj0Rwfr161m4cKEHbzQAVqxYQU9PT6l12L59OwAtLS0H2LN4bW1tXHbZZWVXo1BukdiYdHV1sW9fNqjzwMCAWyU2oezZs4c9e/aUXY264SfbbUzOO+88XnrppVfXjznmGNauXVtijcxes3TpUgCuu+66kmty+PCT7XbIzZs3b9Cc7WeffXbJNTKzsjiR2Jicf/75VFqzEcFHPvKRkmtkZmVxIrExWbNmzaAWyY9//OOSa2RmZXEisTG56667BrVINmzYUHKNzKwsTiQ2Ju973/tGXDez+lHYcySSjgbuA45Kn3NbRFwp6SrgU0Bv2vVLEbE2lVkGLAIGgMsj4v+m+Bxem9hqLbA0IkLSUcAqYA7QB1wcEVuLOid7Tb3d7TcZTITnNyaKyt+hcvdWvSv6WZYiH0jcC3wwIl6UdCTwc0mVmQ2vjYh/qN5Z0iyyGQ5PBd4I3CXprWmWxBuAxcADZImkg2yWxEXA8xHRJmkBcA1wcYHnZMnPfvazQev33Xcfy5YtK6k2Btk/zye3/IqTXz9w4J0Pc//hlexiy97f+Fb/p19sKPwzCkskae70F9Pqkek10s/Y+cAtEbEXeCpNn3uGpK3A1Ii4H0DSKuACskQyH7gqlb8N+IYked724k2bNo2tW7cOWrfynfz6Ab70rt+XXQ2bQL7yy6mFf0ahfSSSGiQ9BDwLbIiIjWnTZyU9LOm7ko5LsRbgmari21KsJS0PjQ8qExH9wAvAfuN0SFosqVtSd29v79DNNga7du0acd3M6kehiSQiBiJiNtBK1ro4jewy1VuA2cBO4Gtpd9U6xAjxkcoMrcfKiGiPiPbm5uaDPAurZegDiOecc05JNTGzso3LXVsR8TvgXqAjInalBLMP+DZwRtptG3BSVbFWYEeKt9aIDyojaQpwLPBcQadhVc4///xB634g0ax+FZZIJDVL+pO03AjMAx6XNL1qt48Cj6TlNcACSUdJOgWYCTwYETuB3ZLmKnsCbiFwe1WZzrR8IXCP+0fGhx9INLOKIu/amg50SWogS1irI+IOSTdLmk12CWor8GmAiNgiaTXwKNAPLEl3bAFcymu3/65LL4AbgZtTx/xzZHd92Tio9UDi5z//+ZJrVd+2b9/OH3Y3jEvnqk0ev9ndwOvSsPpFKfKurYeBd9aIf2KEMlcDV9eIdwOn1Yi/DFyUr6Y2FvPmzWPt2rX09/czZcoUD9poVsc8sZWNSWdnJ+vXrwegoaGBhQsXllwja2lpYW//Tt/+a4N85ZdTOargCb48RIqNSVNTEx0dHUiio6PDsyOa1TG3SGzMOjs72bp1q1sjE8jTL7qPBGDXS9lv5GnH7Cu5JuV7+sUGZhb8GU4kNmZNTU0sX7687GpY0tbWVnYVJow/prG2jnqT/yYzKf674URiY9bX18eXv/xlrrzySl/amgCKHJRvsvFUu+PLicTGrKuri82bN7Nq1Srf+muvmgijEE+k0X+LHnl3InBnu41JX18f69evJyJYv349fX19ZVfJ7FWNjY00NjaWXY264RaJjUlXVxcDA9nzov39/W6V2KsO91/ftj+3SGxM7rrrrlcTycDAgKfaNatjTiQ2Ju9973sHrXuqXbP65URiY1IZsNHMzInExmToVLtD182sfjiR2JjMmzdv0DDyHrTRrH45kdiYnH/++YOGkffEVmb1y4nExsQTW5lZhROJjUmtia3MrD4VOdXu0ZIelPRrSVskfTnFj5e0QdKT6f24qjLLJPVIekLSuVXxOZI2p23L05S7pGl5b03xjZJmFHU+Nti8efOYMiV7ntUTW5nVtyJbJHuBD0bEO4DZQIekucAVwN0RMRO4O60jaRbZVLmnAh3A9WmaXoAbgMVkA1nOTNsBFgHPR0QbcC1wTYHnY1U6Ozs54ojs6+OJrczqW2GJJDIvptUj0yuA+UBXincBF6Tl+cAtEbE3Ip4CeoAzJE0HpkbE/ZFdS1k1pEzlWLcBZ1VaK1YsT2xlZhWF9pFIapD0EPAssCEiNgLTImInQHo/Me3eAjxTVXxbirWk5aHxQWUioh94AdjvP5qkxZK6JXX39vYeqtOre52dnZx++ulujZjVuUITSUQMRMRsoJWsdXHaCLvXaknECPGRygytx8qIaI+I9ubm5gNV20apMrGVWyNm9W1c7tqKiN8B95L1bexKl6tI78+m3bYBJ1UVawV2pHhrjfigMpKmAMcCzxVyEmZmVlORd201S/qTtNwIzAMeB9YAnWm3TuD2tLwGWJDuxDqFrFP9wXT5a7ekuan/Y+GQMpVjXQjcE5V7Us3MbFwUOR/JdKAr3Xl1BLA6Iu6QdD+wWtIi4GngIoCI2CJpNfAo0A8siYiBdKxLgZuARmBdegHcCNwsqYesJbKgwPMxM7MaVG8/4Nvb26O7u7vsapiZTSqSNkVEe61tfrLdzMxy8VS7k9CKFSvo6ekpuxps374dgJaWlgPsWay2tjZP72pWIicSG7M9e/aUXQUzmwCcSCahifLre+nSpQBcd911JdfEzMrkPhIzM8vFicTMzHJxIjEzs1xGnUgkvUnSvLTcKOkNxVXLzMwmi1ElEkmfIhum/Vsp1Ar8a1GVMjOzyWO0LZIlwJnA7wEi4kleG/7dzMzq2GgTyd6I+GNlJY20W19jq5iZWU2jTSQ/lfQloFHS2cAPgR8XVy0zM5ssRptIrgB6gc3Ap4G1wN8UVSkzM5s8RvtkeyPw3Yj4NmRT6KbYS0VVzMzMJofRtkjuJkscFY3AXYe+OmZmNtmMNpEcHREvVlbS8jEjFZB0kqSfSHpM0hZJS1P8KknbJT2UXudVlVkmqUfSE5LOrYrPkbQ5bVueZkokzaZ4a4pvlDRj9KduZmaHwmgTyR8kvauyImkOcKChX/uBL0TE24G5wBJJs9K2ayNidnqtTcecRTbD4alkc7tfny6hAdwALCabfndm2g6wCHg+ItqAa4FrRnk+ZmZ2iIy2j+RzwA8l7Ujr04GLRyqQ5lrfmZZ3S3oMGGniivnALRGxF3gqTZ97hqStwNSIuB9A0irgArLpducDV6XytwHfkCTP225mNn5G1SKJiF8AbyObO/0zwNsjYtNoPyRdcnonsDGFPivpYUnflXRcirUAz1QV25ZiLWl5aHxQmYjoB14Ammp8/mJJ3ZK6e3t7R1ttMzMbhRETiaQPpvf/CnwEeCvZpaWPpNgBSXo98M/A5yLi92SXqd4CzCZrsXytsmuN4jFCfKQygwMRKyOiPSLam5ubR1NtMzMbpQNd2voz4B6yJDJUAD8aqbCkI8mSyPci4kcAEbGravu3gTvS6jbgpKrircCOFG+tEa8usy09bX8s8NwBzsnMzA6hERNJRFwp6QhgXUSsPpgDpzurbgQei4ivV8Wnp/4TgI8Cj6TlNcD3JX0deCNZy+fBiBiQtFvSXLJLYwuBFVVlOoH7gQuBe9w/YmY2vg7Y2R4R+yR9FjioREI2yOMngM2SHkqxLwGXSJpN1qLZSvakPBGxRdJq4FGyO76WRMRAKncpcBPZ8yvr0guyRHVz6ph/juyuLzMzG0ejvWtrg6S/Am4F/lAJRsSwl5Ei4ufU7sNYO0KZq4Gra8S7gdNqxF8GLhqx5mZmVqjRJpK/IGtBfGZI/M2HtjpmZjbZjDaRzCJLIu8lSyg/A75ZVKXMzGzyGG0i6SKb1Gp5Wr8kxf57EZUyM7PJY7SJ5D9GxDuq1n8i6ddFVMjMzCaX0Y619at0+y0Akt4D/FsxVTIzs8lktC2S9wALJT2d1k8GHpO0GYiI+NNCamdmZhPeaBNJx4F3MTOzejSqRBIRvym6ImZmNjmNto/EzMysJicSMzPLxYnEzMxycSIxM7NcnEjMzCwXJxIzM8vFicTMzHJxIjEzs1wKSySSTpL0E0mPSdoiaWmKHy9pg6Qn0/txVWWWSeqR9ISkc6vicyRtTtuWp2l8kXSUpFtTfKOkGUWdj5mZ1VZki6Qf+EJEvB2YCyyRNAu4Arg7ImYCd6d10rYFwKlkQ7JcL6khHesGYDHZPO4zeW3IlkXA8xHRBlwLXFPg+ZiZWQ2FJZKI2BkRv0zLu4HHgBZgPtlcJqT3C9LyfOCWiNgbEU8BPcAZkqYDUyPi/ogIYNWQMpVj3QacVWmtmJnZ+BiXPpJ0yemdwEZgWkTshCzZACem3VqAZ6qKbUuxlrQ8ND6oTET0Ay8ATTU+f7Gkbkndvb29h+akzMwMGIdEIun1wD8Dn4uI34+0a41YjBAfqczgQMTKiGiPiPbm5uYDVdnMzA5CoYlE0pFkSeR7EfGjFN6VLleR3p9N8W3ASVXFW4EdKd5aIz6ojKQpwLHAc4f+TMzMbDhF3rUl4EbgsYj4etWmNUBnWu4Ebq+KL0h3Yp1C1qn+YLr8tVvS3HTMhUPKVI51IXBP6kcxM7NxMtqJrcbiTOATwGZJD6XYl4CvAqslLQKeBi4CiIgtklYDj5Ld8bUkIgZSuUuBm4BGYF16QZaobpbUQ9YSWVDg+ZiZWQ2FJZKI+Dm1+zAAzhqmzNXA1TXi3cBpNeIvkxKRmZmVw0+2m5lZLk4kZmaWixOJmZnl4kRiZma5OJGYmVkuTiRmZpaLE4mZmeXiRGJmZrk4kZiZWS5OJGZmlosTiZmZ5VLkoI2HpRUrVtDT01N2NSaEyt9h6dKlJddkYmhra+Oyyy4ruxpm486J5CD19PTw0COPMXDM8WVXpXRH/DEbsX/Tv+8quSbla3jJ0+BY/XIiGYOBY45nz9vOK7saNoE0Pr627CqYlcZ9JGZmlkuRMyR+V9Kzkh6pil0labukh9LrvKptyyT1SHpC0rlV8TmSNqdty9MsiaSZFG9N8Y2SZhR1LmZmNrwiWyQ3AR014tdGxOz0WgsgaRbZ7IanpjLXS2pI+98ALCabendm1TEXAc9HRBtwLXBNUSdiZmbDKyyRRMR9ZNPfjsZ84JaI2BsRTwE9wBmSpgNTI+L+NBf7KuCCqjJdafk24KxKa8XMzMZPGX0kn5X0cLr0dVyKtQDPVO2zLcVa0vLQ+KAyEdEPvAA01fpASYsldUvq7u3tPXRnYmZm455IbgDeAswGdgJfS/FaLYkYIT5Smf2DESsjoj0i2pubmw+uxmZmNqJxTSQRsSsiBiJiH/Bt4Iy0aRtwUtWurcCOFG+tER9URtIU4FhGfynNzMwOkXFNJKnPo+KjQOWOrjXAgnQn1ilkneoPRsROYLekuan/YyFwe1WZzrR8IXBP6kcxM7NxVNgDiZJ+ALwfOEHSNuBK4P2SZpNdgtoKfBogIrZIWg08CvQDSyJiIB3qUrI7wBqBdekFcCNws6QespbIgqLOxczMhldYIomIS2qEbxxh/6uBq2vEu4HTasRfBi7KU0czM8vPT7abmVkuTiRmZpaLE4mZmeXiRGJmZrk4kZiZWS5OJGZmlosTiZmZ5eJEYmZmuTiRmJlZLk4kZmaWixOJmZnl4kRiZma5OJGYmVkuTiRmZpaLE4mZmeXiRGJmZrkUlkgkfVfSs5IeqYodL2mDpCfT+3FV25ZJ6pH0hKRzq+JzJG1O25anKXdJ0/LemuIbJc0o6lzMzGx4hc2QSDY97jeAVVWxK4C7I+Krkq5I61+UNItsqtxTgTcCd0l6a5pu9wZgMfAAsBboIJtudxHwfES0SVoAXANcXOD5ALB9+3YaXnqBxsfXFv1RNok0vNTH9u39ZVfDrBSFtUgi4j6yudSrzQe60nIXcEFV/JaI2BsRTwE9wBmSpgNTI+L+iAiypHRBjWPdBpxVaa2Ymdn4KbJFUsu0iNgJEBE7JZ2Y4i1kLY6KbSn2SloeGq+UeSYdq1/SC0AT8NuhHyppMVmrhpNPPjnXCbS0tPD/9k5hz9vOy3UcO7w0Pr6WlpZpZVfDrBQTpbO9VksiRoiPVGb/YMTKiGiPiPbm5uYxVtHMzGoZ70SyK12uIr0/m+LbgJOq9msFdqR4a434oDKSpgDHsv+lNDMzK9h4J5I1QGda7gRur4ovSHdinQLMBB5Ml8F2S5qb+j8WDilTOdaFwD2pH8XMzMZRYX0kkn4AvB84QdI24Ergq8BqSYuAp4GLACJii6TVwKNAP7Ak3bEFcCnZHWCNZHdrrUvxG4GbJfWQtUQWFHUuZmY2vMISSURcMsyms4bZ/2rg6hrxbuC0GvGXSYnIzMzKM1E6283MbJJyIjEzs1ycSMzMLBcnEjMzy2W8n2w/LDS89JzH2gKOePn3AOw7emrJNSlfw0vPAX6y3eqTE8lBamtrK7sKE0ZPz24A2t7sf6Awzd8Nq1tOJAfpsssuK7sKE8bSpUsBuO6660quiZmVyX0kZmaWixOJmZnl4kRiZma5OJGYmVkuTiRmZpaLE4mZmeXiRGJmZrk4kZiZWS6lJBJJWyVtlvSQpO4UO17SBklPpvfjqvZfJqlH0hOSzq2Kz0nH6ZG0PM2iaGZm46jMFskHImJ2RLSn9SuAuyNiJnB3WkfSLLLZD08FOoDrJTWkMjcAi8mm5p2ZtpuZ2TiaSEOkzCebmhegC7gX+GKK3xIRe4Gn0tS6Z0jaCkyNiPsBJK0CLuC1qXgPWytWrKCnp6fsarxah8pQKWVpa2vz0DVmJSqrRRLAnZI2SVqcYtMiYidAej8xxVuAZ6rKbkuxlrQ8NL4fSYsldUvq7u3tPYSnUd8aGxtpbGwsuxpmVrKyWiRnRsQOSScCGyQ9PsK+tfo9YoT4/sGIlcBKgPb29pr7TCb+9W1mE0kpLZKI2JHenwX+BTgD2CVpOkB6fzbtvg04qap4K7AjxVtrxM3MbByNeyKR9DpJb6gsA+cAjwBrgM60Wydwe1peAyyQdJSkU8g61R9Ml792S5qb7tZaWFXGzMzGSRmXtqYB/5Lu1J0CfD8i1kv6BbBa0iLgaeAigIjYImk18CjQDyyJiIF0rEuBm4BGsk72w76j3cxsolHEpO8yOCjt7e3R3d1ddjXMzCYVSZuqHtcYxE+2m5lZLk4kZmaWixOJmZnl4kRiZma51F1nu6Re4Ddl1+MwcgLw27IrYVaDv5uH1psiornWhrpLJHZoSeoe7k4OszL5uzl+fGnLzMxycSIxM7NcnEgsr5VlV8BsGP5ujhP3kZiZWS5ukZiZWS5OJGZmlosTie1H0uWSHpP0vUNwrC8dijqZ2cTlPhLbT5qx8kMR8VRVbEpE9I/hWC9GxOsPaQXNqqT5iBQR+8ZYfkzfbXuNWyQ2iKRvAm8G1kh6QdJKSXcCqyQdLen/SNos6VeSPpDKfFLSjyStl/SkpL9P8a8CjZIeOhStG7MKSTNSq/l64JfAJyTdL+mXkn4o6fVpv7+V9AtJj6TvslL8XklfkfRTYGmJp3JYcIvE9iNpK9AOfBb4CPDeiNgj6QvAaRHxPyW9DbgTeCuwAPhb4J3AXuCJVOYZt0isCJJmAP8O/GegB/gRWSv6D5K+CBwVEX8n6fiIeC6VuRlYHRE/lnQv8GhEfKaUEzjMuEViB7ImIvak5fcCNwNExONkY5a9NW27OyJeiIiXyWazfNO419TqzW8i4gFgLjAL+DdJD5FN1V35/n1A0kZJm4EPAqdWlb91XGt7GCtjql2bXP5QtawR9ttbtTyAv1tWvMp3U8CGiLikeqOko4HrgfbUOr4KOLpGecvJLRI7GPcBHwOQ9FbgZLLLWCN5RdKRRVfM6toDwJmS2gAkHZO+n5Wk8dvUZ3JhWRU83DmR2MG4HmhIlwluBT4ZEXsPUGYl8LA7260oEdELfBL4gaSHyRLL2yLid8C3gc3AvwK/KK2Shzl3tpuZWS5ukZiZWS5OJGZmlosTiZmZ5eJEYmZmuTiRmJlZLk4kZmMk6Y2SbjtEx5oh6ZFDcayqY35S0hur1r8jadah/Awz8NPHZmMWETuY2A+5fRJ4BNgBEBH/q9Ta2GHLLRKrS5I+LunBNDLxtyQ1SHpR0tWSfi3pAUnT0r5vSeu/kPR3kl5M8VdbEcONgJy2nVNrZNoR6jbcKMsNkv4hxR+WdFmK7zfCraQLyQbe/F46x8Y04m17KnNJOs4jkq6p+uyafwOzkTiRWN2R9HbgYuDMiJhNNjbYx4DXAQ9ExDvIhoP5VCpyHXBdRLyb9Ot+GLPTcU8HLpZ0kqQTgL8B5kXEu4Bu4C8PUMUlABFxOnAJ0JXGjVoMnAK8MyL+FKiMFvCNiHh3RJwGNAIfjojb0md9LCJmVw28SbrcdQ3ZIIazgXdLuiBtHu5vYDYsJxKrR2cBc4BfpNFizyKbg+WPwB1pn03AjLT8n4AfpuXvj3DcWiMgjzQy7XCGG2V5HvDNyiRMleHRGXmE21reDdwbEb3pWN8D/kvaNtzfwGxY7iOxeiSgKyKWDQpKfxWvjRk0lhGMa42APNzItO8BvpVW/xZ4eEj9hqv3oDGNRjHC7XDHGc4rOf8GVofcIrF6dDdwoaQTASQdL2mkVsIDwH9LywsO8rNqjkwbERvTJafZEbFmSJnhRlm+E/jfkqZU6s3II9zuBt5Qo04bgT+TdIKkBrLLZz89yPMye5UTidWdiHiUrN/izjRa7AZg+ghFPgf8paQH034vHMRn1RyZ9gDFhhtl+TvA02SjKf8a+B8HGOH2JuCblc72qjrtBJYBPwF+DfwyIm4f7TmZDeXRf80OQNIxwJ6ICEkLgEsiYn7Z9TKbKHz90+zA5gDfkCTgd8BflFwfswnFLRIzM8vFfSRmZpaLE4mZmeXiRGJmZrk4kZiZWS5OJGZmlsv/B/I9ZroA5YoAAAABSURBVLGUXv7yAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"engine-location\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Here we see that the distribution of price between these two engine-location categories, front and rear, are distinct enough to take engine-location as a potential good predictor of price.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's examine \"drive-wheels\" and \"price\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f409437a8d0>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# drive-wheels\n",
    "sns.boxplot(x=\"drive-wheels\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Here we see that the distribution of price between the different drive-wheels categories differs; as such drive-wheels could potentially be a predictor of price.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"discriptive_statistics\">3. Descriptive Statistical Analysis</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Let's first take a look at the variables by utilizing a description method.</p>\n",
    "\n",
    "<p>The <b>describe</b> function automatically computes basic statistics for all continuous variables. Any NaN values are automatically skipped in these statistics.</p>\n",
    "\n",
    "This will show:\n",
    "<ul>\n",
    "    <li>the count of that variable</li>\n",
    "    <li>the mean</li>\n",
    "    <li>the standard deviation (std)</li> \n",
    "    <li>the minimum value</li>\n",
    "    <li>the IQR (Interquartile Range: 25%, 50% and 75%)</li>\n",
    "    <li>the maximum value</li>\n",
    "<ul>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can apply the method \"describe\" as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.00000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>197.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.840796</td>\n",
       "      <td>122.00000</td>\n",
       "      <td>98.797015</td>\n",
       "      <td>0.837102</td>\n",
       "      <td>0.915126</td>\n",
       "      <td>53.766667</td>\n",
       "      <td>2555.666667</td>\n",
       "      <td>126.875622</td>\n",
       "      <td>3.330692</td>\n",
       "      <td>3.256904</td>\n",
       "      <td>10.164279</td>\n",
       "      <td>103.405534</td>\n",
       "      <td>5117.665368</td>\n",
       "      <td>25.179104</td>\n",
       "      <td>30.686567</td>\n",
       "      <td>13207.129353</td>\n",
       "      <td>9.944145</td>\n",
       "      <td>0.099502</td>\n",
       "      <td>0.900498</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.254802</td>\n",
       "      <td>31.99625</td>\n",
       "      <td>6.066366</td>\n",
       "      <td>0.059213</td>\n",
       "      <td>0.029187</td>\n",
       "      <td>2.447822</td>\n",
       "      <td>517.296727</td>\n",
       "      <td>41.546834</td>\n",
       "      <td>0.268072</td>\n",
       "      <td>0.319256</td>\n",
       "      <td>4.004965</td>\n",
       "      <td>37.365700</td>\n",
       "      <td>478.113805</td>\n",
       "      <td>6.423220</td>\n",
       "      <td>6.815150</td>\n",
       "      <td>7947.066342</td>\n",
       "      <td>2.534599</td>\n",
       "      <td>0.300083</td>\n",
       "      <td>0.300083</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-2.000000</td>\n",
       "      <td>65.00000</td>\n",
       "      <td>86.600000</td>\n",
       "      <td>0.678039</td>\n",
       "      <td>0.837500</td>\n",
       "      <td>47.800000</td>\n",
       "      <td>1488.000000</td>\n",
       "      <td>61.000000</td>\n",
       "      <td>2.540000</td>\n",
       "      <td>2.070000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>48.000000</td>\n",
       "      <td>4150.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>5118.000000</td>\n",
       "      <td>4.795918</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>101.00000</td>\n",
       "      <td>94.500000</td>\n",
       "      <td>0.801538</td>\n",
       "      <td>0.890278</td>\n",
       "      <td>52.000000</td>\n",
       "      <td>2169.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>3.150000</td>\n",
       "      <td>3.110000</td>\n",
       "      <td>8.600000</td>\n",
       "      <td>70.000000</td>\n",
       "      <td>4800.000000</td>\n",
       "      <td>19.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>7775.000000</td>\n",
       "      <td>7.833333</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>122.00000</td>\n",
       "      <td>97.000000</td>\n",
       "      <td>0.832292</td>\n",
       "      <td>0.909722</td>\n",
       "      <td>54.100000</td>\n",
       "      <td>2414.000000</td>\n",
       "      <td>120.000000</td>\n",
       "      <td>3.310000</td>\n",
       "      <td>3.290000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>95.000000</td>\n",
       "      <td>5125.369458</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>10295.000000</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2.000000</td>\n",
       "      <td>137.00000</td>\n",
       "      <td>102.400000</td>\n",
       "      <td>0.881788</td>\n",
       "      <td>0.925000</td>\n",
       "      <td>55.500000</td>\n",
       "      <td>2926.000000</td>\n",
       "      <td>141.000000</td>\n",
       "      <td>3.580000</td>\n",
       "      <td>3.410000</td>\n",
       "      <td>9.400000</td>\n",
       "      <td>116.000000</td>\n",
       "      <td>5500.000000</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>34.000000</td>\n",
       "      <td>16500.000000</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>256.00000</td>\n",
       "      <td>120.900000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>59.800000</td>\n",
       "      <td>4066.000000</td>\n",
       "      <td>326.000000</td>\n",
       "      <td>3.940000</td>\n",
       "      <td>4.170000</td>\n",
       "      <td>23.000000</td>\n",
       "      <td>262.000000</td>\n",
       "      <td>6600.000000</td>\n",
       "      <td>49.000000</td>\n",
       "      <td>54.000000</td>\n",
       "      <td>45400.000000</td>\n",
       "      <td>18.076923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        symboling  normalized-losses  wheel-base      length       width  \\\n",
       "count  201.000000          201.00000  201.000000  201.000000  201.000000   \n",
       "mean     0.840796          122.00000   98.797015    0.837102    0.915126   \n",
       "std      1.254802           31.99625    6.066366    0.059213    0.029187   \n",
       "min     -2.000000           65.00000   86.600000    0.678039    0.837500   \n",
       "25%      0.000000          101.00000   94.500000    0.801538    0.890278   \n",
       "50%      1.000000          122.00000   97.000000    0.832292    0.909722   \n",
       "75%      2.000000          137.00000  102.400000    0.881788    0.925000   \n",
       "max      3.000000          256.00000  120.900000    1.000000    1.000000   \n",
       "\n",
       "           height  curb-weight  engine-size        bore      stroke  \\\n",
       "count  201.000000   201.000000   201.000000  201.000000  197.000000   \n",
       "mean    53.766667  2555.666667   126.875622    3.330692    3.256904   \n",
       "std      2.447822   517.296727    41.546834    0.268072    0.319256   \n",
       "min     47.800000  1488.000000    61.000000    2.540000    2.070000   \n",
       "25%     52.000000  2169.000000    98.000000    3.150000    3.110000   \n",
       "50%     54.100000  2414.000000   120.000000    3.310000    3.290000   \n",
       "75%     55.500000  2926.000000   141.000000    3.580000    3.410000   \n",
       "max     59.800000  4066.000000   326.000000    3.940000    4.170000   \n",
       "\n",
       "       compression-ratio  horsepower     peak-rpm    city-mpg  highway-mpg  \\\n",
       "count         201.000000  201.000000   201.000000  201.000000   201.000000   \n",
       "mean           10.164279  103.405534  5117.665368   25.179104    30.686567   \n",
       "std             4.004965   37.365700   478.113805    6.423220     6.815150   \n",
       "min             7.000000   48.000000  4150.000000   13.000000    16.000000   \n",
       "25%             8.600000   70.000000  4800.000000   19.000000    25.000000   \n",
       "50%             9.000000   95.000000  5125.369458   24.000000    30.000000   \n",
       "75%             9.400000  116.000000  5500.000000   30.000000    34.000000   \n",
       "max            23.000000  262.000000  6600.000000   49.000000    54.000000   \n",
       "\n",
       "              price  city-L/100km      diesel         gas  \n",
       "count    201.000000    201.000000  201.000000  201.000000  \n",
       "mean   13207.129353      9.944145    0.099502    0.900498  \n",
       "std     7947.066342      2.534599    0.300083    0.300083  \n",
       "min     5118.000000      4.795918    0.000000    0.000000  \n",
       "25%     7775.000000      7.833333    0.000000    1.000000  \n",
       "50%    10295.000000      9.791667    0.000000    1.000000  \n",
       "75%    16500.000000     12.368421    0.000000    1.000000  \n",
       "max    45400.000000     18.076923    1.000000    1.000000  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The default setting of \"describe\" skips variables of type object. We can apply the method \"describe\" on the variables of type 'object' as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>make</th>\n",
       "      <th>aspiration</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>engine-type</th>\n",
       "      <th>num-of-cylinders</th>\n",
       "      <th>fuel-system</th>\n",
       "      <th>horsepower-binned</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>unique</th>\n",
       "      <td>22</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>top</th>\n",
       "      <td>toyota</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>ohc</td>\n",
       "      <td>four</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>Low</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>freq</th>\n",
       "      <td>32</td>\n",
       "      <td>165</td>\n",
       "      <td>115</td>\n",
       "      <td>94</td>\n",
       "      <td>118</td>\n",
       "      <td>198</td>\n",
       "      <td>145</td>\n",
       "      <td>157</td>\n",
       "      <td>92</td>\n",
       "      <td>115</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          make aspiration num-of-doors body-style drive-wheels  \\\n",
       "count      201        201          201        201          201   \n",
       "unique      22          2            2          5            3   \n",
       "top     toyota        std         four      sedan          fwd   \n",
       "freq        32        165          115         94          118   \n",
       "\n",
       "       engine-location engine-type num-of-cylinders fuel-system  \\\n",
       "count              201         201              201         201   \n",
       "unique               2           6                7           8   \n",
       "top              front         ohc             four        mpfi   \n",
       "freq               198         145              157          92   \n",
       "\n",
       "       horsepower-binned  \n",
       "count                200  \n",
       "unique                 3  \n",
       "top                  Low  \n",
       "freq                 115  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe(include=['object'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Value Counts</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Value-counts is a good way of understanding how many units of each characteristic/variable we have. We can apply the \"value_counts\" method on the column 'drive-wheels'. Don’t forget the method \"value_counts\" only works on Pandas series, not Pandas Dataframes. As a result, we only include one bracket \"df['drive-wheels']\" not two brackets \"df[['drive-wheels']]\".</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fwd    118\n",
       "rwd     75\n",
       "4wd      8\n",
       "Name: drive-wheels, dtype: int64"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can convert the series to a Dataframe as follows :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     drive-wheels\n",
       "fwd           118\n",
       "rwd            75\n",
       "4wd             8"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].value_counts().to_frame()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's repeat the above steps but save the results to the dataframe \"drive_wheels_counts\" and rename the column  'drive-wheels' to 'value_counts'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value_counts</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     value_counts\n",
       "fwd           118\n",
       "rwd            75\n",
       "4wd             8"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "drive_wheels_counts = df['drive-wheels'].value_counts().to_frame()\n",
    "drive_wheels_counts.rename(columns={'drive-wheels': 'value_counts'}, inplace=True)\n",
    "drive_wheels_counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Now let's rename the index to 'drive-wheels':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value_counts</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              value_counts\n",
       "drive-wheels              \n",
       "fwd                    118\n",
       "rwd                     75\n",
       "4wd                      8"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "drive_wheels_counts.index.name = 'drive-wheels'\n",
    "drive_wheels_counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can repeat the above process for the variable 'engine-location'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value_counts</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-location</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>front</th>\n",
       "      <td>198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rear</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 value_counts\n",
       "engine-location              \n",
       "front                     198\n",
       "rear                        3"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# engine-location as variable\n",
    "engine_loc_counts = df['engine-location'].value_counts().to_frame()\n",
    "engine_loc_counts.rename(columns={'engine-location': 'value_counts'}, inplace=True)\n",
    "engine_loc_counts.index.name = 'engine-location'\n",
    "engine_loc_counts.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Examining the value counts of the engine location would not be a good predictor variable for the price. This is because we only have three cars with a rear engine and 198 with an engine in the front, this result is skewed. Thus, we are not able to draw any conclusions about the engine location.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"basic_grouping\">4. Basics of Grouping</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The \"groupby\" method groups data by different categories. The data is grouped based on one or several variables and analysis is performed on the individual groups.</p>\n",
    "\n",
    "<p>For example, let's group by the variable \"drive-wheels\". We see that there are 3 different categories of drive wheels.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['rwd', 'fwd', '4wd'], dtype=object)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>If we want to know, on average, which type of drive wheel is most valuable, we can group \"drive-wheels\" and then average them.</p>\n",
    "\n",
    "<p>We can select the columns 'drive-wheels', 'body-style' and 'price', then assign it to the variable \"df_group_one\".</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_group_one = df[['drive-wheels','body-style','price']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then calculate the average price for each of the different categories of data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4wd</td>\n",
       "      <td>10241.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>fwd</td>\n",
       "      <td>9244.779661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>rwd</td>\n",
       "      <td>19757.613333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  drive-wheels         price\n",
       "0          4wd  10241.000000\n",
       "1          fwd   9244.779661\n",
       "2          rwd  19757.613333"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# grouping results\n",
    "df_group_one = df_group_one.groupby(['drive-wheels'],as_index=False).mean()\n",
    "df_group_one"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>From our data, it seems rear-wheel drive vehicles are, on average, the most expensive, while 4-wheel and front-wheel are approximately the same in price.</p>\n",
    "\n",
    "<p>You can also group with multiple variables. For example, let's group by both 'drive-wheels' and 'body-style'. This groups the dataframe by the unique combinations 'drive-wheels' and 'body-style'. We can store the results in the variable 'grouped_test1'.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>body-style</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4wd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7603.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4wd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>12647.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4wd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>fwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>11595.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>8249.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>8396.387755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9811.800000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>23949.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>24202.714286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>14337.777778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>21711.833333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   drive-wheels   body-style         price\n",
       "0           4wd    hatchback   7603.000000\n",
       "1           4wd        sedan  12647.333333\n",
       "2           4wd        wagon   9095.750000\n",
       "3           fwd  convertible  11595.000000\n",
       "4           fwd      hardtop   8249.000000\n",
       "5           fwd    hatchback   8396.387755\n",
       "6           fwd        sedan   9811.800000\n",
       "7           fwd        wagon   9997.333333\n",
       "8           rwd  convertible  23949.600000\n",
       "9           rwd      hardtop  24202.714286\n",
       "10          rwd    hatchback  14337.777778\n",
       "11          rwd        sedan  21711.833333\n",
       "12          rwd        wagon  16994.222222"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# grouping results\n",
    "df_gptest = df[['drive-wheels','body-style','price']]\n",
    "grouped_test1 = df_gptest.groupby(['drive-wheels','body-style'],as_index=False).mean()\n",
    "grouped_test1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>This grouped data is much easier to visualize when it is made into a pivot table. A pivot table is like an Excel spreadsheet, with one variable along the column and another along the row. We can convert the dataframe to a pivot table using the method \"pivot \" to create a pivot table from the groups.</p>\n",
    "\n",
    "<p>In this case, we will leave the drive-wheel variable as the rows of the table, and pivot body-style to become the columns of the table:</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>body-style</th>\n",
       "      <th>convertible</th>\n",
       "      <th>hardtop</th>\n",
       "      <th>hatchback</th>\n",
       "      <th>sedan</th>\n",
       "      <th>wagon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7603.000000</td>\n",
       "      <td>12647.333333</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>11595.0</td>\n",
       "      <td>8249.000000</td>\n",
       "      <td>8396.387755</td>\n",
       "      <td>9811.800000</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>23949.6</td>\n",
       "      <td>24202.714286</td>\n",
       "      <td>14337.777778</td>\n",
       "      <td>21711.833333</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   price                                            \\\n",
       "body-style   convertible       hardtop     hatchback         sedan   \n",
       "drive-wheels                                                         \n",
       "4wd                  NaN           NaN   7603.000000  12647.333333   \n",
       "fwd              11595.0   8249.000000   8396.387755   9811.800000   \n",
       "rwd              23949.6  24202.714286  14337.777778  21711.833333   \n",
       "\n",
       "                            \n",
       "body-style           wagon  \n",
       "drive-wheels                \n",
       "4wd            9095.750000  \n",
       "fwd            9997.333333  \n",
       "rwd           16994.222222  "
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_pivot = grouped_test1.pivot(index='drive-wheels',columns='body-style')\n",
    "grouped_pivot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Often, we won't have data for some of the pivot cells. We can fill these missing cells with the value 0, but any other value could potentially be used as well. It should be mentioned that missing data is quite a complex subject and is an entire course on its own.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>body-style</th>\n",
       "      <th>convertible</th>\n",
       "      <th>hardtop</th>\n",
       "      <th>hatchback</th>\n",
       "      <th>sedan</th>\n",
       "      <th>wagon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7603.000000</td>\n",
       "      <td>12647.333333</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>11595.0</td>\n",
       "      <td>8249.000000</td>\n",
       "      <td>8396.387755</td>\n",
       "      <td>9811.800000</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>23949.6</td>\n",
       "      <td>24202.714286</td>\n",
       "      <td>14337.777778</td>\n",
       "      <td>21711.833333</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   price                                            \\\n",
       "body-style   convertible       hardtop     hatchback         sedan   \n",
       "drive-wheels                                                         \n",
       "4wd                  0.0      0.000000   7603.000000  12647.333333   \n",
       "fwd              11595.0   8249.000000   8396.387755   9811.800000   \n",
       "rwd              23949.6  24202.714286  14337.777778  21711.833333   \n",
       "\n",
       "                            \n",
       "body-style           wagon  \n",
       "drive-wheels                \n",
       "4wd            9095.750000  \n",
       "fwd            9997.333333  \n",
       "rwd           16994.222222  "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_pivot = grouped_pivot.fillna(0) #fill missing values with 0\n",
    "grouped_pivot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question 4:</h1>\n",
    "\n",
    "<p>Use the \"groupby\" function to find the average \"price\" of each car based on \"body-style\" ? </p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .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": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df_group_one = df[['body-style','price']]\n",
    "\n",
    "df_group_one = df_group_one.groupby(['body-style'],as_index=False).mean()\n",
    "df_group_one"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "# grouping results\n",
    "df_gptest2 = df[['body-style','price']]\n",
    "grouped_test_bodystyle = df_gptest2.groupby(['body-style'],as_index= False).mean()\n",
    "grouped_test_bodystyle\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you did not import \"pyplot\" let's do it again. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Variables: Drive Wheels and Body Style vs Price</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use a heat map to visualize the relationship between Body Style vs Price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#use the grouped results\n",
    "plt.pcolor(grouped_pivot, cmap='RdBu')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The heatmap plots the target variable (price) proportional to colour with respect to the variables 'drive-wheel' and 'body-style' in the vertical and horizontal axis respectively. This allows us to visualize how the price is related to 'drive-wheel' and 'body-style'.</p>\n",
    "\n",
    "<p>The default labels convey no useful information to us. Let's change that:</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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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": 36,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>symboling</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.466264</td>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.365404</td>\n",
       "      <td>-0.242423</td>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.233118</td>\n",
       "      <td>-0.110581</td>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.008245</td>\n",
       "      <td>-0.182196</td>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.279740</td>\n",
       "      <td>-0.035527</td>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.066171</td>\n",
       "      <td>-0.196735</td>\n",
       "      <td>0.196735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>normalized-losses</th>\n",
       "      <td>0.466264</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.101546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wheel-base</th>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>-0.307237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>length</th>\n",
       "      <td>-0.365404</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>-0.211187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>width</th>\n",
       "      <td>-0.242423</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>-0.244356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>height</th>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>-0.281578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>curb-weight</th>\n",
       "      <td>-0.233118</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>-0.221046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>-0.110581</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>-0.070779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>-0.054458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.008245</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>-0.241303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>-0.182196</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.985231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>0.169053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>0.279740</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.475812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-mpg</th>\n",
       "      <td>-0.035527</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>-0.265676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>-0.198690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.110326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-L/100km</th>\n",
       "      <td>0.066171</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>0.241282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diesel</th>\n",
       "      <td>-0.196735</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gas</th>\n",
       "      <td>0.196735</td>\n",
       "      <td>0.101546</td>\n",
       "      <td>-0.307237</td>\n",
       "      <td>-0.211187</td>\n",
       "      <td>-0.244356</td>\n",
       "      <td>-0.281578</td>\n",
       "      <td>-0.221046</td>\n",
       "      <td>-0.070779</td>\n",
       "      <td>-0.054458</td>\n",
       "      <td>-0.241303</td>\n",
       "      <td>-0.985231</td>\n",
       "      <td>0.169053</td>\n",
       "      <td>0.475812</td>\n",
       "      <td>-0.265676</td>\n",
       "      <td>-0.198690</td>\n",
       "      <td>-0.110326</td>\n",
       "      <td>0.241282</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   symboling  normalized-losses  wheel-base    length  \\\n",
       "symboling           1.000000           0.466264   -0.535987 -0.365404   \n",
       "normalized-losses   0.466264           1.000000   -0.056661  0.019424   \n",
       "wheel-base         -0.535987          -0.056661    1.000000  0.876024   \n",
       "length             -0.365404           0.019424    0.876024  1.000000   \n",
       "width              -0.242423           0.086802    0.814507  0.857170   \n",
       "height             -0.550160          -0.373737    0.590742  0.492063   \n",
       "curb-weight        -0.233118           0.099404    0.782097  0.880665   \n",
       "engine-size        -0.110581           0.112360    0.572027  0.685025   \n",
       "bore               -0.140019          -0.029862    0.493244  0.608971   \n",
       "stroke             -0.008245           0.055563    0.158502  0.124139   \n",
       "compression-ratio  -0.182196          -0.114713    0.250313  0.159733   \n",
       "horsepower          0.075819           0.217299    0.371147  0.579821   \n",
       "peak-rpm            0.279740           0.239543   -0.360305 -0.285970   \n",
       "city-mpg           -0.035527          -0.225016   -0.470606 -0.665192   \n",
       "highway-mpg         0.036233          -0.181877   -0.543304 -0.698142   \n",
       "price              -0.082391           0.133999    0.584642  0.690628   \n",
       "city-L/100km        0.066171           0.238567    0.476153  0.657373   \n",
       "diesel             -0.196735          -0.101546    0.307237  0.211187   \n",
       "gas                 0.196735           0.101546   -0.307237 -0.211187   \n",
       "\n",
       "                      width    height  curb-weight  engine-size      bore  \\\n",
       "symboling         -0.242423 -0.550160    -0.233118    -0.110581 -0.140019   \n",
       "normalized-losses  0.086802 -0.373737     0.099404     0.112360 -0.029862   \n",
       "wheel-base         0.814507  0.590742     0.782097     0.572027  0.493244   \n",
       "length             0.857170  0.492063     0.880665     0.685025  0.608971   \n",
       "width              1.000000  0.306002     0.866201     0.729436  0.544885   \n",
       "height             0.306002  1.000000     0.307581     0.074694  0.180449   \n",
       "curb-weight        0.866201  0.307581     1.000000     0.849072  0.644060   \n",
       "engine-size        0.729436  0.074694     0.849072     1.000000  0.572609   \n",
       "bore               0.544885  0.180449     0.644060     0.572609  1.000000   \n",
       "stroke             0.188829 -0.062704     0.167562     0.209523 -0.055390   \n",
       "compression-ratio  0.189867  0.259737     0.156433     0.028889  0.001263   \n",
       "horsepower         0.615077 -0.087027     0.757976     0.822676  0.566936   \n",
       "peak-rpm          -0.245800 -0.309974    -0.279361    -0.256733 -0.267392   \n",
       "city-mpg          -0.633531 -0.049800    -0.749543    -0.650546 -0.582027   \n",
       "highway-mpg       -0.680635 -0.104812    -0.794889    -0.679571 -0.591309   \n",
       "price              0.751265  0.135486     0.834415     0.872335  0.543155   \n",
       "city-L/100km       0.673363  0.003811     0.785353     0.745059  0.554610   \n",
       "diesel             0.244356  0.281578     0.221046     0.070779  0.054458   \n",
       "gas               -0.244356 -0.281578    -0.221046    -0.070779 -0.054458   \n",
       "\n",
       "                     stroke  compression-ratio  horsepower  peak-rpm  \\\n",
       "symboling         -0.008245          -0.182196    0.075819  0.279740   \n",
       "normalized-losses  0.055563          -0.114713    0.217299  0.239543   \n",
       "wheel-base         0.158502           0.250313    0.371147 -0.360305   \n",
       "length             0.124139           0.159733    0.579821 -0.285970   \n",
       "width              0.188829           0.189867    0.615077 -0.245800   \n",
       "height            -0.062704           0.259737   -0.087027 -0.309974   \n",
       "curb-weight        0.167562           0.156433    0.757976 -0.279361   \n",
       "engine-size        0.209523           0.028889    0.822676 -0.256733   \n",
       "bore              -0.055390           0.001263    0.566936 -0.267392   \n",
       "stroke             1.000000           0.187923    0.098462 -0.065713   \n",
       "compression-ratio  0.187923           1.000000   -0.214514 -0.435780   \n",
       "horsepower         0.098462          -0.214514    1.000000  0.107885   \n",
       "peak-rpm          -0.065713          -0.435780    0.107885  1.000000   \n",
       "city-mpg          -0.034696           0.331425   -0.822214 -0.115413   \n",
       "highway-mpg       -0.035201           0.268465   -0.804575 -0.058598   \n",
       "price              0.082310           0.071107    0.809575 -0.101616   \n",
       "city-L/100km       0.037300          -0.299372    0.889488  0.115830   \n",
       "diesel             0.241303           0.985231   -0.169053 -0.475812   \n",
       "gas               -0.241303          -0.985231    0.169053  0.475812   \n",
       "\n",
       "                   city-mpg  highway-mpg     price  city-L/100km    diesel  \\\n",
       "symboling         -0.035527     0.036233 -0.082391      0.066171 -0.196735   \n",
       "normalized-losses -0.225016    -0.181877  0.133999      0.238567 -0.101546   \n",
       "wheel-base        -0.470606    -0.543304  0.584642      0.476153  0.307237   \n",
       "length            -0.665192    -0.698142  0.690628      0.657373  0.211187   \n",
       "width             -0.633531    -0.680635  0.751265      0.673363  0.244356   \n",
       "height            -0.049800    -0.104812  0.135486      0.003811  0.281578   \n",
       "curb-weight       -0.749543    -0.794889  0.834415      0.785353  0.221046   \n",
       "engine-size       -0.650546    -0.679571  0.872335      0.745059  0.070779   \n",
       "bore              -0.582027    -0.591309  0.543155      0.554610  0.054458   \n",
       "stroke            -0.034696    -0.035201  0.082310      0.037300  0.241303   \n",
       "compression-ratio  0.331425     0.268465  0.071107     -0.299372  0.985231   \n",
       "horsepower        -0.822214    -0.804575  0.809575      0.889488 -0.169053   \n",
       "peak-rpm          -0.115413    -0.058598 -0.101616      0.115830 -0.475812   \n",
       "city-mpg           1.000000     0.972044 -0.686571     -0.949713  0.265676   \n",
       "highway-mpg        0.972044     1.000000 -0.704692     -0.930028  0.198690   \n",
       "price             -0.686571    -0.704692  1.000000      0.789898  0.110326   \n",
       "city-L/100km      -0.949713    -0.930028  0.789898      1.000000 -0.241282   \n",
       "diesel             0.265676     0.198690  0.110326     -0.241282  1.000000   \n",
       "gas               -0.265676    -0.198690 -0.110326      0.241282 -1.000000   \n",
       "\n",
       "                        gas  \n",
       "symboling          0.196735  \n",
       "normalized-losses  0.101546  \n",
       "wheel-base        -0.307237  \n",
       "length            -0.211187  \n",
       "width             -0.244356  \n",
       "height            -0.281578  \n",
       "curb-weight       -0.221046  \n",
       "engine-size       -0.070779  \n",
       "bore              -0.054458  \n",
       "stroke            -0.241303  \n",
       "compression-ratio -0.985231  \n",
       "horsepower         0.169053  \n",
       "peak-rpm           0.475812  \n",
       "city-mpg          -0.265676  \n",
       "highway-mpg       -0.198690  \n",
       "price             -0.110326  \n",
       "city-L/100km       0.241282  \n",
       "diesel            -1.000000  \n",
       "gas                1.000000  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " sometimes we would like to know the significant of the correlation estimate. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>P-value</b>: \n",
    "<p>What is this P-value? The P-value is the probability value that the correlation between these two variables is statistically significant. Normally, we choose a significance level of 0.05, which means that we are 95% confident that the correlation between the variables is significant.</p>\n",
    "\n",
    "By convention, when the\n",
    "<ul>\n",
    "    <li>p-value is $<$ 0.001: we say there is strong evidence that the correlation is significant.</li>\n",
    "    <li>the p-value is $<$ 0.05: there is moderate evidence that the correlation is significant.</li>\n",
    "    <li>the p-value is $<$ 0.1: there is weak evidence that the correlation is significant.</li>\n",
    "    <li>the p-value is $>$ 0.1: there is no evidence that the correlation is significant.</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can obtain this information using  \"stats\" module in the \"scipy\"  library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Wheel-base vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the  Pearson Correlation Coefficient and P-value of 'wheel-base' and 'price'. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.584641822265508  with a P-value of P = 8.076488270733218e-20\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['wheel-base'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between wheel-base and price is statistically significant, although the linear relationship isn't extremely strong (~0.585)</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Horsepower vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the  Pearson Correlation Coefficient and P-value of 'horsepower' and 'price'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8095745670036559  with a P-value of P =  6.369057428260101e-48\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['horsepower'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between horsepower and price is statistically significant, and the linear relationship is quite strong (~0.809, close to 1)</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Length vs Price</h3>\n",
    "\n",
    "Let's calculate the  Pearson Correlation Coefficient and P-value of 'length' and 'price'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.6906283804483638  with a P-value of P =  8.016477466159556e-30\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['length'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between length and price is statistically significant, and the linear relationship is moderately strong (~0.691).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Width vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the Pearson Correlation Coefficient and P-value of 'width' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.7512653440522673  with a P-value of P = 9.200335510481646e-38\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['width'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Conclusion:\n",
    "\n",
    "Since the p-value is < 0.001, the correlation between width and price is statistically significant, and the linear relationship is quite strong (~0.751)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Curb-weight vs Price"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the Pearson Correlation Coefficient and P-value of 'curb-weight' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8344145257702843  with a P-value of P =  2.189577238894065e-53\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['curb-weight'], df['price'])\n",
    "print( \"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between curb-weight and price is statistically significant, and the linear relationship is quite strong (~0.834).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Engine-size vs Price</h3>\n",
    "\n",
    "Let's calculate the Pearson Correlation Coefficient and P-value of 'engine-size' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8723351674455185  with a P-value of P = 9.265491622198389e-64\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['engine-size'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between engine-size and price is statistically significant, and the linear relationship is very strong (~0.872).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Bore vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the  Pearson Correlation Coefficient and P-value of 'bore' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.5431553832626602  with a P-value of P =   8.049189483935489e-17\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['bore'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =  \", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between bore and price is statistically significant, but the linear relationship is only moderate (~0.521).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can relate the process for each 'City-mpg'  and 'Highway-mpg':"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>City-mpg vs Price</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.6865710067844678  with a P-value of P =  2.321132065567641e-29\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['city-mpg'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between city-mpg and price is statistically significant, and the coefficient of ~ -0.687 shows that the relationship is negative and moderately strong.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Highway-mpg vs Price</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.704692265058953  with a P-value of P =  1.7495471144476358e-31\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['highway-mpg'], df['price'])\n",
    "print( \"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Conclusion:\n",
    "Since the p-value is < 0.001, the correlation between highway-mpg and price is statistically significant, and the coefficient of ~ -0.705 shows that the relationship is negative and moderately strong."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"anova\">6. ANOVA</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>ANOVA: Analysis of Variance</h3>\n",
    "<p>The Analysis of Variance  (ANOVA) is a statistical method used to test whether there are significant differences between the means of two or more groups. ANOVA returns two parameters:</p>\n",
    "\n",
    "<p><b>F-test score</b>: ANOVA assumes the means of all groups are the same, calculates how much the actual means deviate from the assumption, and reports it as the F-test score. A larger score means there is a larger difference between the means.</p>\n",
    "\n",
    "<p><b>P-value</b>:  P-value tells how statistically significant is our calculated score value.</p>\n",
    "\n",
    "<p>If our price variable is strongly correlated with the variable we are analyzing, expect ANOVA to return a sizeable F-test score and a small p-value.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Drive Wheels</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Since ANOVA analyzes the difference between different groups of the same variable, the groupby function will come in handy. Because the ANOVA algorithm averages the data automatically, we do not need to take the average before hand.</p>\n",
    "\n",
    "<p>Let's see if different types 'drive-wheels' impact  'price', we group the data.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's see if different types 'drive-wheels' impact  'price', we group the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>rwd</td>\n",
       "      <td>13495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>rwd</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>fwd</td>\n",
       "      <td>13950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4wd</td>\n",
       "      <td>17450.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>fwd</td>\n",
       "      <td>15250.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>136</th>\n",
       "      <td>4wd</td>\n",
       "      <td>7603.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    drive-wheels    price\n",
       "0            rwd  13495.0\n",
       "1            rwd  16500.0\n",
       "3            fwd  13950.0\n",
       "4            4wd  17450.0\n",
       "5            fwd  15250.0\n",
       "136          4wd   7603.0"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_test2=df_gptest[['drive-wheels', 'price']].groupby(['drive-wheels'])\n",
    "grouped_test2.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>body-style</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>13495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>13950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4wd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>17450.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>196</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>16845.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>197</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>19045.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>21485.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>199</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>22470.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>200</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>22625.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>201 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    drive-wheels   body-style    price\n",
       "0            rwd  convertible  13495.0\n",
       "1            rwd  convertible  16500.0\n",
       "2            rwd    hatchback  16500.0\n",
       "3            fwd        sedan  13950.0\n",
       "4            4wd        sedan  17450.0\n",
       "..           ...          ...      ...\n",
       "196          rwd        sedan  16845.0\n",
       "197          rwd        sedan  19045.0\n",
       "198          rwd        sedan  21485.0\n",
       "199          rwd        sedan  22470.0\n",
       "200          rwd        sedan  22625.0\n",
       "\n",
       "[201 rows x 3 columns]"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_gptest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can obtain the values of the method group using the method \"get_group\".  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4      17450.0\n",
       "136     7603.0\n",
       "140     9233.0\n",
       "141    11259.0\n",
       "144     8013.0\n",
       "145    11694.0\n",
       "150     7898.0\n",
       "151     8778.0\n",
       "Name: price, dtype: float64"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_test2.get_group('4wd')['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can use the function 'f_oneway' in the module 'stats'  to obtain the <b>F-test score</b> and <b>P-value</b>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 67.95406500780399 , P = 3.3945443577151245e-23\n"
     ]
    }
   ],
   "source": [
    "# ANOVA\n",
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('fwd')['price'], grouped_test2.get_group('rwd')['price'], grouped_test2.get_group('4wd')['price'])  \n",
    " \n",
    "print( \"ANOVA results: F=\", f_val, \", P =\", p_val)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a great result, with a large F test score showing a strong correlation and a P value of almost 0 implying almost certain statistical significance. But does this mean all three tested groups are all this highly correlated? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Separately: fwd and rwd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 130.5533160959111 , P = 2.2355306355677845e-23\n"
     ]
    }
   ],
   "source": [
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('fwd')['price'], grouped_test2.get_group('rwd')['price'])  \n",
    " \n",
    "print( \"ANOVA results: F=\", f_val, \", P =\", p_val )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's examine the other groups "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4wd and rwd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 8.580681368924756 , P = 0.004411492211225333\n"
     ]
    }
   ],
   "source": [
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('4wd')['price'], grouped_test2.get_group('rwd')['price'])  \n",
    "   \n",
    "print( \"ANOVA results: F=\", f_val, \", P =\", p_val)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>4wd and fwd</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 0.665465750252303 , P = 0.41620116697845666\n"
     ]
    }
   ],
   "source": [
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('4wd')['price'], grouped_test2.get_group('fwd')['price'])  \n",
    " \n",
    "print(\"ANOVA results: F=\", f_val, \", P =\", p_val)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Conclusion: Important Variables</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We now have a better idea of what our data looks like and which variables are important to take into account when predicting the car price. We have narrowed it down to the following variables:</p>\n",
    "\n",
    "Continuous numerical variables:\n",
    "<ul>\n",
    "    <li>Length</li>\n",
    "    <li>Width</li>\n",
    "    <li>Curb-weight</li>\n",
    "    <li>Engine-size</li>\n",
    "    <li>Horsepower</li>\n",
    "    <li>City-mpg</li>\n",
    "    <li>Highway-mpg</li>\n",
    "    <li>Wheel-base</li>\n",
    "    <li>Bore</li>\n",
    "</ul>\n",
    "    \n",
    "Categorical variables:\n",
    "<ul>\n",
    "    <li>Drive-wheels</li>\n",
    "</ul>\n",
    "\n",
    "<p>As we now move into building machine learning models to automate our analysis, feeding the model with variables that meaningfully affect our target variable will improve our model's prediction performance.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Thank you for completing this notebook</h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "\n",
    "    <p><a href=\"https://cocl.us/corsera_da0101en_notebook_bottom\"><img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/BottomAd.png\" width=\"750\" align=\"center\"></a></p>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>About the Authors:</h3>\n",
    "\n",
    "This notebook was written by <a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/\" target=\"_blank\">Mahdi Noorian PhD</a>, <a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>, Bahare Talayian, Eric Xiao, Steven Dong, Parizad, Hima Vsudevan and <a href=\"https://www.linkedin.com/in/fiorellawever/\" target=\"_blank\">Fiorella Wenver</a> and <a href=\" https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n",
    "\n",
    "<p><a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a> is a Data Scientist at IBM, and holds a PhD in Electrical Engineering. His research focused on using Machine Learning, Signal Processing, and Computer Vision to determine how videos impact human cognition. Joseph has been working for IBM since he completed his PhD.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "<p>Copyright &copy; 2018 IBM Developer Skills Network. This notebook and its source code are released under the terms of the <a href=\"https://cognitiveclass.ai/mit-license/\">MIT License</a>.</p>"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python",
   "language": "python",
   "name": "conda-env-python-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}