Created on Skills Network Labs

exploratory-data-analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>\n",
    "    <img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/Logos/organization_logo/organization_logo.png\" width=\"300\" alt=\"cognitiveclass.ai logo\"  />\n",
    "</center>\n",
    "\n",
    "# Data Analysis with Python\n",
    "\n",
    "Estimated time needed: **30** minutes\n",
    "\n",
    "## Objectives\n",
    "\n",
    "After completing this lab you will be able to:\n",
    "\n",
    "-   Explore features or charecteristics to predict price of car\n"
   ]
  },
  {
   "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",
    "</div>\n",
    " \n",
    "<hr>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>What are the main characteristics which have the most impact on the car price?</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"import_data\">1. Import Data from Module 2</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Setup</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import libraries \n"
   ]
  },
  {
   "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:\n"
   ]
  },
  {
   "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\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To install seaborn we use the pip which is the python package manager.\n"
   ]
  },
  {
   "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.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "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": {},
   "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",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "float64\n",
    "\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\":\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>symboling</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.466264</td>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.365404</td>\n",
       "      <td>-0.242423</td>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.233118</td>\n",
       "      <td>-0.110581</td>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.008245</td>\n",
       "      <td>-0.182196</td>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.279740</td>\n",
       "      <td>-0.035527</td>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.066171</td>\n",
       "      <td>-0.196735</td>\n",
       "      <td>0.196735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>normalized-losses</th>\n",
       "      <td>0.466264</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.101546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wheel-base</th>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>-0.307237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>length</th>\n",
       "      <td>-0.365404</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>-0.211187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>width</th>\n",
       "      <td>-0.242423</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>-0.244356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>height</th>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>-0.281578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>curb-weight</th>\n",
       "      <td>-0.233118</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>-0.221046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>-0.110581</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>-0.070779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>-0.054458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.008245</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>-0.241303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>-0.182196</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.985231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>0.169053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>0.279740</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.475812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-mpg</th>\n",
       "      <td>-0.035527</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>-0.265676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>-0.198690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.110326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-L/100km</th>\n",
       "      <td>0.066171</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>0.241282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diesel</th>\n",
       "      <td>-0.196735</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gas</th>\n",
       "      <td>0.196735</td>\n",
       "      <td>0.101546</td>\n",
       "      <td>-0.307237</td>\n",
       "      <td>-0.211187</td>\n",
       "      <td>-0.244356</td>\n",
       "      <td>-0.281578</td>\n",
       "      <td>-0.221046</td>\n",
       "      <td>-0.070779</td>\n",
       "      <td>-0.054458</td>\n",
       "      <td>-0.241303</td>\n",
       "      <td>-0.985231</td>\n",
       "      <td>0.169053</td>\n",
       "      <td>0.475812</td>\n",
       "      <td>-0.265676</td>\n",
       "      <td>-0.198690</td>\n",
       "      <td>-0.110326</td>\n",
       "      <td>0.241282</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   symboling  normalized-losses  wheel-base    length  \\\n",
       "symboling           1.000000           0.466264   -0.535987 -0.365404   \n",
       "normalized-losses   0.466264           1.000000   -0.056661  0.019424   \n",
       "wheel-base         -0.535987          -0.056661    1.000000  0.876024   \n",
       "length             -0.365404           0.019424    0.876024  1.000000   \n",
       "width              -0.242423           0.086802    0.814507  0.857170   \n",
       "height             -0.550160          -0.373737    0.590742  0.492063   \n",
       "curb-weight        -0.233118           0.099404    0.782097  0.880665   \n",
       "engine-size        -0.110581           0.112360    0.572027  0.685025   \n",
       "bore               -0.140019          -0.029862    0.493244  0.608971   \n",
       "stroke             -0.008245           0.055563    0.158502  0.124139   \n",
       "compression-ratio  -0.182196          -0.114713    0.250313  0.159733   \n",
       "horsepower          0.075819           0.217299    0.371147  0.579821   \n",
       "peak-rpm            0.279740           0.239543   -0.360305 -0.285970   \n",
       "city-mpg           -0.035527          -0.225016   -0.470606 -0.665192   \n",
       "highway-mpg         0.036233          -0.181877   -0.543304 -0.698142   \n",
       "price              -0.082391           0.133999    0.584642  0.690628   \n",
       "city-L/100km        0.066171           0.238567    0.476153  0.657373   \n",
       "diesel             -0.196735          -0.101546    0.307237  0.211187   \n",
       "gas                 0.196735           0.101546   -0.307237 -0.211187   \n",
       "\n",
       "                      width    height  curb-weight  engine-size      bore  \\\n",
       "symboling         -0.242423 -0.550160    -0.233118    -0.110581 -0.140019   \n",
       "normalized-losses  0.086802 -0.373737     0.099404     0.112360 -0.029862   \n",
       "wheel-base         0.814507  0.590742     0.782097     0.572027  0.493244   \n",
       "length             0.857170  0.492063     0.880665     0.685025  0.608971   \n",
       "width              1.000000  0.306002     0.866201     0.729436  0.544885   \n",
       "height             0.306002  1.000000     0.307581     0.074694  0.180449   \n",
       "curb-weight        0.866201  0.307581     1.000000     0.849072  0.644060   \n",
       "engine-size        0.729436  0.074694     0.849072     1.000000  0.572609   \n",
       "bore               0.544885  0.180449     0.644060     0.572609  1.000000   \n",
       "stroke             0.188829 -0.062704     0.167562     0.209523 -0.055390   \n",
       "compression-ratio  0.189867  0.259737     0.156433     0.028889  0.001263   \n",
       "horsepower         0.615077 -0.087027     0.757976     0.822676  0.566936   \n",
       "peak-rpm          -0.245800 -0.309974    -0.279361    -0.256733 -0.267392   \n",
       "city-mpg          -0.633531 -0.049800    -0.749543    -0.650546 -0.582027   \n",
       "highway-mpg       -0.680635 -0.104812    -0.794889    -0.679571 -0.591309   \n",
       "price              0.751265  0.135486     0.834415     0.872335  0.543155   \n",
       "city-L/100km       0.673363  0.003811     0.785353     0.745059  0.554610   \n",
       "diesel             0.244356  0.281578     0.221046     0.070779  0.054458   \n",
       "gas               -0.244356 -0.281578    -0.221046    -0.070779 -0.054458   \n",
       "\n",
       "                     stroke  compression-ratio  horsepower  peak-rpm  \\\n",
       "symboling         -0.008245          -0.182196    0.075819  0.279740   \n",
       "normalized-losses  0.055563          -0.114713    0.217299  0.239543   \n",
       "wheel-base         0.158502           0.250313    0.371147 -0.360305   \n",
       "length             0.124139           0.159733    0.579821 -0.285970   \n",
       "width              0.188829           0.189867    0.615077 -0.245800   \n",
       "height            -0.062704           0.259737   -0.087027 -0.309974   \n",
       "curb-weight        0.167562           0.156433    0.757976 -0.279361   \n",
       "engine-size        0.209523           0.028889    0.822676 -0.256733   \n",
       "bore              -0.055390           0.001263    0.566936 -0.267392   \n",
       "stroke             1.000000           0.187923    0.098462 -0.065713   \n",
       "compression-ratio  0.187923           1.000000   -0.214514 -0.435780   \n",
       "horsepower         0.098462          -0.214514    1.000000  0.107885   \n",
       "peak-rpm          -0.065713          -0.435780    0.107885  1.000000   \n",
       "city-mpg          -0.034696           0.331425   -0.822214 -0.115413   \n",
       "highway-mpg       -0.035201           0.268465   -0.804575 -0.058598   \n",
       "price              0.082310           0.071107    0.809575 -0.101616   \n",
       "city-L/100km       0.037300          -0.299372    0.889488  0.115830   \n",
       "diesel             0.241303           0.985231   -0.169053 -0.475812   \n",
       "gas               -0.241303          -0.985231    0.169053  0.475812   \n",
       "\n",
       "                   city-mpg  highway-mpg     price  city-L/100km    diesel  \\\n",
       "symboling         -0.035527     0.036233 -0.082391      0.066171 -0.196735   \n",
       "normalized-losses -0.225016    -0.181877  0.133999      0.238567 -0.101546   \n",
       "wheel-base        -0.470606    -0.543304  0.584642      0.476153  0.307237   \n",
       "length            -0.665192    -0.698142  0.690628      0.657373  0.211187   \n",
       "width             -0.633531    -0.680635  0.751265      0.673363  0.244356   \n",
       "height            -0.049800    -0.104812  0.135486      0.003811  0.281578   \n",
       "curb-weight       -0.749543    -0.794889  0.834415      0.785353  0.221046   \n",
       "engine-size       -0.650546    -0.679571  0.872335      0.745059  0.070779   \n",
       "bore              -0.582027    -0.591309  0.543155      0.554610  0.054458   \n",
       "stroke            -0.034696    -0.035201  0.082310      0.037300  0.241303   \n",
       "compression-ratio  0.331425     0.268465  0.071107     -0.299372  0.985231   \n",
       "horsepower        -0.822214    -0.804575  0.809575      0.889488 -0.169053   \n",
       "peak-rpm          -0.115413    -0.058598 -0.101616      0.115830 -0.475812   \n",
       "city-mpg           1.000000     0.972044 -0.686571     -0.949713  0.265676   \n",
       "highway-mpg        0.972044     1.000000 -0.704692     -0.930028  0.198690   \n",
       "price             -0.686571    -0.704692  1.000000      0.789898  0.110326   \n",
       "city-L/100km      -0.949713    -0.930028  0.789898      1.000000 -0.241282   \n",
       "diesel             0.265676     0.198690  0.110326     -0.241282  1.000000   \n",
       "gas               -0.265676    -0.198690 -0.110326      0.241282 -1.000000   \n",
       "\n",
       "                        gas  \n",
       "symboling          0.196735  \n",
       "normalized-losses  0.101546  \n",
       "wheel-base        -0.307237  \n",
       "length            -0.211187  \n",
       "width             -0.244356  \n",
       "height            -0.281578  \n",
       "curb-weight       -0.221046  \n",
       "engine-size       -0.070779  \n",
       "bore              -0.054458  \n",
       "stroke            -0.241303  \n",
       "compression-ratio -0.985231  \n",
       "horsepower         0.169053  \n",
       "peak-rpm           0.475812  \n",
       "city-mpg          -0.265676  \n",
       "highway-mpg       -0.198690  \n",
       "price             -0.110326  \n",
       "city-L/100km       0.241282  \n",
       "diesel            -1.000000  \n",
       "gas                1.000000  "
      ]
     },
     "execution_count": 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.\n"
   ]
  },
  {
   "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>\n"
   ]
  },
  {
   "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",
    "df[['bore', 'stroke', 'compression-ratio', 'horsepower']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "df[['bore', 'stroke', 'compression-ratio', 'horsepower']].corr()  \n",
    "\n",
    "-->\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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's see several examples of different linear relationships:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Positive linear relationship</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's find the scatterplot of \"engine-size\" and \"price\" \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 55945.82820337018)"
      ]
     },
     "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": [
    "# 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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can examine the correlation between 'engine-size' and 'price' and see it's approximately  0.87\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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>engine-size</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.872335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>0.872335</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             engine-size     price\n",
       "engine-size     1.000000  0.872335\n",
       "price           0.872335  1.000000"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[[\"engine-size\", \"price\"]].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Highway mpg is a potential predictor variable of price \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='highway-mpg', ylabel='price'>"
      ]
     },
     "execution_count": 14,
     "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'highway-mpg' and 'price' and see it's approximately  -0.704\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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>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": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['highway-mpg', 'price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Weak Linear Relationship</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see if \"Peak-rpm\" as a predictor variable of \"price\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='peak-rpm', ylabel='price'>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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NYEJSBXzu2dc4NxJHPQiLoB6cG4nzuWdfq/SpGYZhzIrl2qoCjp8ZISQQCvnRzCKgnnL8jOVXMgyj+rERiWEYhjEnTEiqgDXLF+EpeKooiqeKp77dMAyj2jEhqQLuvmkdbU1RBEgkPQRoa4py903rKn1qhmEYs2JCUgVsWtfBn2+5husubmPFkkauu7iNP99yjYX/GoZRE+TsbBeRS4C1qvqcW6keUdXB0p3awsIS9RmGUavkNCIRkd/GT9O+w5k6gX8q0TkZhmEYNUSuU1t3Au8EBgBU9Shgt8+GYRhGzkIyrqqx1AuXaXdh5VYxDMMwMpKrkPyLiPxnoFFEfhX4O+B/lu60DMMwjFohVyG5B+gDXgG2Ac8A/6VUJ2UYhmHUDrlGbTUCX1PVr8BECd1GwHJ4FAnL/msYRq2S64jkeXzhSNEIPFf801mY7DnSy327D9M7OEZrY5TewTHu233Ysv8ahlET5CokDao6lHrhtptmaiAiq0Tkn0XkNRE5LCJ3Ofv9IvKGiLzsHh8ItLlXRI6JyOsi8r6A/XoRecW995CrlIirpviks78kIqvz6HvVsGNvF9Gw0FQXQcR/joaFHXu7Kn1qhmEYs5KrkAyLyNtTL0TkemB0ljYJ4A9V9UrgRuBOEbnKvfegql7rHs+4z7wKv8Lhevza7l92U2gADwNb8cvvrnXvA9wB9Kvq5cCDwPYc+1NVdPeP0BgNT7E1RsP09NvMoWEY1U+uPpLfA/5ORN50r1cAH5mpgau1ftJtD4rIa8DKGZpsBp5Q1XHguCufe4OInABaVHUfgIg8DtyCX253M3C/a78L+JKISDXUbc/H57GqrYnewTGa6ia/jtF4ks62GQd9hmEYVUFOIxJV/R6wDr92+u8CV6rqwVwP4qacrgNecqZPiMgPReRrItLmbCuB7kCzHmdb6bbT7VPaqGoCOA8sy3D8rSJyQEQO9PX15XraBZOvz2PbxjXEk8pILIGq/xxPKts2rin5uRqGYcyVGYVERN7tnv8D8O+BK/Cnlv69s82KiCwG/h74PVUdwJ+mugy4Fn/E8hepXTM01xnsM7WZalDdqaobVHVDe3t7Lqc9J/L1eWxa18EDN6+no7mB86NxOpobeODm9Ra1ZRhGTTDb1NYvAy/gi0g6CvzDTI1FJIovIv9DVf8BQFVPBd7/CvC0e9kDrAo07wTedPbODPZgmx632n4JcHaWPpWc7v4RWhujU2yz+TwsaaNhGLXKjEKiqn8qIiHgWVV9Kp8PdpFVXwVeU9W/DNhXOP8JwIeAH7nt3cA3ROQvgYvwRz77VTUpIoMiciP+1NhtwF8F2twO7AO2AC9Ug3/EfB5GObE1SEalmdVHoqoe8IkCPvudwMeAd6eF+v6ZC+X9IfArwO+74xwGngJeBb4F3KmqSfdZHwceAY4BP8F3tIMvVMucY/4P8FfgVxzzeRjlwtYgGdWA5HIDLyKfxg/3fRIYTtlVteLTSPmyYcMGPXDgQMmPk7pL7OkfodPuEo0S8dGdL04b/Y7EEnQ0N/C3W2+s4JkZ8w0ROaiqGzK9l2v472/i+0R+N81ut9hZMJ+HUQ4K8ccZRrHJdUHiVcB/Bw4BL+P7KNaX6JwMw8iRVW1NjMaTU2zmjzPKTa5C8hhwJfAQvohc6WyGYVQQ88cZ1UCuU1tvU9VrAq//WUQOleKEDGOhk08U1qZ1HTwA5o8zKkquQvIDEblRVV8EEJFfBP536U7LmG9YiGpupKKwomGZEoX1AMwoJvZ/aVSSXKe2fhH4NxE54XJf7QN+ORDGaxhZsRDV3LFM0EYtkuuI5KbZdzGMzAQvjgBNdRFGYgl27O2yO+k0ConCstGeUWlyEhJV/WmpT8SYv1iIau7kmxWhkKkwwyg2uU5tGUbBWIhq7uQbhWVTYUY1YEJilBwLUc2dfDNBd/ePkEh6dPUNceStAbr6hkgkPRvtGWUlVx+JkSc2bz2JhajmRz5RWIvrwhzrGyYsQliERFJ549wYl7cvKvFZGsYkJiQlYM+RXv5o1yEGxxIkPI/Tg+P80a5D/PmWaxbsxdNCVEuDn2QbvzJPqjqPBuyGUQZsaqsEbP/WEfpH4igQCYdQoH8kzvZvHan0qRnzjMHxBCtbG4iEhKSnRELCytYGhsYTlT41YwFhI5IS0HV6mJBAyN0VioCK0nV6eJaWhpEfqSivNe2LJ2yp7L+GUS5sRGIYNYwFMhjVgAlJCbh0WROegucpqornKZ76dsMoJvlGeRlGKSjZ1JaIrAIeBy4EPGCnqn5RRJbiF8haDZwAfl1V+12be4E7gCTwSVX9trNfDzwKNALPAHepqopIvTvG9cAZ4COqeqJUfcqVe95/JZ/adYih8QRJTwmHhNb6KPe8/8pKn5oxD7FABqPSlHJEkgD+UFWvBG4E7hSRq/DL4T6vqmuB591r3Hu34tc5uQn4soiE3Wc9DGzFr+O+lsmULXcA/ap6OfAgsL2E/cmZTes6+PyWa7huVRsXtjRw3ao2Pr+AI7bmE3uO9PLRnS/yru0v8NGdL1q+MMOghCMSVT0JnHTbgyLyGrAS2Axscrs9BuwB7nb2J1R1HDju6rDf4JJEtqjqPgAReRy4Bb9u+2bgfvdZu4AviYhoLvWDS4zdJc4/LB2JYWSmLD4SEVkNXAe8BFzgRCYlNqlf4EqgO9Csx9lWuu10+5Q2qpoAzgPLMhx/q4gcEJEDfX19ReqVsdCwdCSGkZmSC4mILAb+Hvg9VR2YadcMNp3BPlObqQbVnaq6QVU3tLe3z3bKhpGR7v4RGqPhKTZLPmkYJV5HIiJRfBH5H6r6D858SkRWqOpJEVkBpCaZe4BVgeadwJvO3pnBHmzTIyIRYAlwtiSdMeYd+aaxyTczbyHHKEc/DKPYlGxEIn6Ohq8Cr6nqXwbe2g3c7rZvB74ZsN8qIvUicim+U32/m/4aFJEb3WfeltYm9VlbgBeqwT9iVD+FFNvKd81GOQp6WdEwoxoo5dTWO4GPAe8WkZfd4wPA54BfFZGjwK+616jqYeAp4FXgW8CdqprKPf5x4BHgGPATfEc7+EK1zDnm/wAXAWYYs1GIvyPfNRvl8Kns2NtFLJHkrfNjvH5qkLfOjxFLJM1vY5SVUkZtfZfMPgyA92Rp81ngsxnsB4CrM9jHgA/P4TTnjE0rVA/5fBfd/SOEBbr6hoglPerCIZYvrsvZ35HLsLccBb1+fGqAgbEEISaz/54ZjpFIzuSONIziYivb54BNK1QP+X4XzfUR3jg3RsItGE14fvr1xfXZ763yPUY5CnrFk37mhLjnMZ7wiHsenqfEktmlztbCGMVmwQlJIQ6UbD88CwetHvL9LiZcaRp4BO1FOEa58mAlFSa6o/7rbNjNj1EKFlz233jC48TpYaKREHVh94j4j3Bo+kzcTIvQrBZ57pR6CjDf72IolmRlawOnh2ITU1sXLq5nOJbMuH8hxyhXQa+QgKdTX2cjKIYATXURRmIJduztsilZo2AWnJAAeKqMx5OMp007hENCXSRENCUu4RB//S8/yfrDKyQcdCFSjhXh+X4XhaRfL+T7LnWGA1WdIiLgi0q2kZXd/BilYMFNbc1E0lNGY0kGRuOcHhznzXOjHD/jlzGNJz0SSY+kp9RHQnSfHbYU3jlSjinAfL+LQr67avy+s01jZbOXw29jLDxMSGZhRUsj/SPj/PTMMEd7Bzl+eoi+wTGWL27gso7F/P5719LWVEf/SIzli+sthXcGyrEiPN/Q3ELSr29a18GWt6+kb3Cc194apG9wnC1vX1nR7zuWyDwVl81ejWJo1D4LcmorH65btYRDPecmnPQJz2Ms7vHBn1tCPOlxzapWrlnVOrG/iNDTP0JdJER9OEw0ItSFQ0TCC1ezyzUFmO80Ur777znSy67vv0F7cz0XR8OMxpPs+v4b/Hxna1HFJB9/UjgUQtXz4wXUr8Ypzp6JcvltLCx+YWFCMgv/cvR0VvvHfmn1NLuqEksosYTHEJN1s0MiRCMhomEhGpp08EcXgMBs27iG+3YfZiSWoNFdgEtxF/zQcz/mke8eZziWZFFdmN9616V88r1XFO3zy+GoztefdOmyJo71DRMR8Us6KyRVZyyiVmq/jWVJXniYkMxCd/8IkRCEAnd4nufRnee0zKSDf6o9JTCpCLJoRIiG55fAlOMu+KHnfsyDzx2dGDkOjCV48LmjAEUTk7kuYsyFHXu7iCeTnBlKTByjpTGSVayqsYhavn0wah8TkgqTLYJMRIiG/WmxVBRZ6rkWKfVd8F/987Fpa4TU2YslJIvrwhzr84MvUqvI3zg3xuXti4ry+QBHewc5PxInFJKJhZKnB2PEk4MZ908VUSv1VFU+5NsHo/YxIZmFVa2N/PTsCHg6MXXgKVzS1ljS4wanyIKkC0w0EiIS8l+HZlpAMM+JZwlTymYvBD9nKL4TIvVfrQF7EYglPBB/pOofEzyZ/ncQpNqKqBXSB6O2MSGZha0bL2P7t48wHEvgeUooJLTURdm68bKKnE82gQF/HUw0HCISnnTwp3wyC1lkisXgeIK2pghnhuN46i/8W7YoytB4YvbGORINC8MxZSyenCjGEwpBXbh2vr9oWBiNgxe4+YLa6oORHyYks3DDmqXc/b51PPG9bt4aGOXClkZu/YVV3LBmaaVPbRpJT0l6SYhPfy8S8v0vkZAvLiYy+bO4LkxP/+jEa0+hbyjOugvqi3aMjuYG+ofjvoI4JVEP2mdYKFltXHFBC8dPDzE4NukjaW6IcunyxbM3zgOLDKseTEhy4IY1S6tSOPIh4XkkYgDT1xekRCaYLqYuHCrqlE2p+dC1K/jHl09mtBeLvsHxrPZiXdRU/VFvOC0Kq5bK7KSi9C5cEilZlJ5FhlUXJiTGhMiMBkRGRIiEhPrIVEd/tUaTbb62k2+/2stIIFdWU12Yzdd2ztAqP86OZhjqAWdH4kW7qBWSA6za7szLEaVnOcOqi5IJiYh8Dfgg0KuqVzvb/cBvA31ut/+sqs+49+4F7sC/Zf6kqn7b2a8HHgUagWeAu1RVRaQeeBy4HjgDfERVT5SqPwsNVSWeVOJJDwI34unrYSJh55cJSUUXXe7Y28WKJQ1TFj0W+8KSGhQEB2qq/gxUscJd880BVq135qUOALCcYdVFKX/5jwI3ZbA/qKrXukdKRK4CbgXWuzZfFpFUTo2Hga34pXfXBj7zDqBfVS8HHgS2l6ojxiSpcOWhsQT9IzH6XE6yn50d4cTpYXr6R+gdGOPscIzBsThj8SReelbBEtDdP0Ii6dHVN8SRtwbo6hsikfSKemFpqnN/kqnuBLp1ejA2pbbJ6cEYR3vzD3fNN4XJQi1lYDnDqotSVkjcKyKrc9x9M/CEqo4Dx13p3BtE5ATQoqr7AETkceAW/FK7m4H7XftdwJdERGar2X6sb4jbvrafxfURWhoiLG6I0lwfYXFDhOaGiNuOBrZ9e2M0XFM+g0rgzRBRlsnZHwlJ0UYyzfURjvYOEQ6sXXjj3BhrO4rn4P2djWv4wvNH/Wy77q8sJBB24cDFCHfNd1pood6ZlytbgpEblfCRfEJEbgMOAH+oqv3ASuDFwD49zhZ32+l23HM3gKomROQ8sAyYltNERLbij2qou/DyKZE3uRIOCYvrndgEBcdEKCdmcvan/DHhkBAJ+2ITCUydRUIy6/+fOod0LKGTYbMyc6GqfPnke6/g+Okhdv/wrYlV5Df//IXsPXqagbFE0cJd85kWWqilDMqVM8zIjXILycPAZ/Dv5z4D/AXwm2Su7a4z2JnlvalG1Z3AToDV635O73rPWobG4wyOJRgaSzA4nghsxxkaS0xzbiY95fxonPNZHK4zEQ5JZsGZRYRaGqI0RGsreqoQJv0xZAxdBpzIhPxV5RMjmUn/TN/QeMaV7aeHMkdaFcKeI70c/Nl5Vi9rmrgLPviz83Q0NxANx0oe7pqJhXxnXm0LMRcyZRUSVT2V2haRrwBPu5c9wKrArp3Am87emcEebNMjIhFgCXB2tnNoaYiy+dqLZj3XpKcMjScYHHOC48TG385fhM6NxjlXTBFyrxfXT7c110donmciNLFGJgtjcc+fZgqHJu4wEq6O+Wgs6RZrzj6ymYlskUKqSl0kXNJw12zYnbmRjuf5o3JP1QWDuGd1tsB7ZLApOll62n1maJbfTVmFRERWqGoq2P9DwI/c9m7gGyLyl8BF+E71/aqaFJFBEbkReAm4DfirQJvbgX3AFuCF2fwj+RAOCUsaoyxpjLK/6yxPfK+bkwOjrMhhQWLS0wlhySRCA6MJhsdLL0IAkZDQ2hSlvbl+xpGQ7y+qXRGqi4QYjyfxNDC9pBAJhzh5fnIqMxIKEQr5zyl/SuoRCQkhmXydTjZ/xPnROJ/ZfHXFL+a1s9LEAP+Cn34R91zFS08V9VKvJ/fBpWhS3H7e5MV/psqYc2W2sP9Shv/+LbAJWC4iPcCfAptE5Fr8v/kTwDYAVT0sIk8BrwIJ4E5VTV1RP85k+O+z7gHwVeDrzjF/Fj/qq+js7zrLF184SiQktDREODM8zhdfOMpdrM0qJuGQsKQpypKmaMb3Z2I2Eco0EhoYizM0npiyhiJFwlNOD8U4PRTL6zwizifkT7H5YjM5+kn5iqJOeCovQpcsXcQb54YZGk8ST3pEwyEWN0ZY2To1oWLC88CDGDM7wsUlZgyF/O8zLMKFLQ2cHhpP80ckWLGkkRsvW8Y7Ll9GSMQ9StLNaVRr+G85SF8/s/XfXcqmdR0TIdngfGdM+q3UvRO83k65aydwZ66TttTnBEn/zMk3gscPiIFOFYz5hNTSitli8PPXvl3/6Tt7c97/D548xJnh8SkV/kbjSZYtqucvP3JNKU6xYJKe8vtPvMzp4XGi4RCepyRVGU94NETC/Lsrlk8TpZRYZRKhQomEZHLazT2nRkLNjVN9RFNEqDFKQ6QwEdrfddbPiRZIp76oPsLd71tXtKwE+7vO8pmnDzMS9yYceE3REJ/+4Pqsxwi5FeqpqYFQyBeZoD0k4ueBFBCE7x7t49F9J3jj3CidrU38x3euZuMV7RPvizDR9mOPvETv4BiL6idvWlLrTv52643Tzif99x68UKaT6XtInWcmcv3egnfiwYtq0v29+u/7r1MX4eDdN8CLPznNg8/7N3gN0RBjcY+Ep9z17uw3eEbhRMMhLl626KCqbsj0vq1sn4WTA6OEBbr7xyfudNuaorw1kH/kV6kJh4S+4XFaGiJIIBZBUQbHEvzOL2dPNJk+EgqOhoIjoYEcRCjhKf0jcfpH8p+OC4rQ4gw+oXQRSo2MYgnPvxi6i2zGUIw58vpbAxMiAv4FeCTu8fpbA1kvXqnpiGSq1Sx6HRwBL6oLc/L8KA88/WrWC+TxM8OEBU6eH5vy93n89BDHTw9P7FfOG8aUoMgUG0W9E//G/m4iIZm4wUv5pp74XrcJSQUwIZmFRXURfnpm2L+TdOsTTg2Mc8my4tWgKCYrWhqnjaDG4h4Xtsyc9r4Y03GpKbZMPqF0USqFCAUR9YMltn/rCBvf1j5dhBonp+IWN0RyGgk9dbCHcGhqGduk5/HUwZ6M1TIL4Ynv5XeBXBQN89OzIxMjm0TS/X0ubapYfq7UcaccvcincnJglJaGqZevhmioKm/wFgImJLMxORGa9lydU4K3/sIqvvjCUUbjySlD/lt/YdXsjQtkLiKUSHoBkZkqQukRc0ERGhxLTFvZHETVr0XSPxrnmy+/mXW/FNOm4zIEJYzEkoRCk3fVKdkp5rRg3iPgLDVSss4/lYl8A1TypdAbJqM0mJDMwnA8yQUt9fSPxAM/7DpGZriIVZIb1izlLtbWRNp78KOqWpvqaG2qy7ttSoSGxhPc8dj3yPSVhAR+6bLl/sgoFaiQQYRyHQklvcA0VYD/8+F/yyhCwewJ6UEJmUZC+Y6Ah2OJ6X+fi+sYiRWvRkq+FBKgki+VuGEysmNCMgupO59VgZXCo/EkHYuKV4Oi2MyHtPe5EBShZDZdV3hg8/pp5vSRULYghIGx+ESU3KnzY1mz8BbDJ9TcEOHk+VE/jDOpEyMMVRgej3Oo59w0EarGv898p+cKodZumOY7JiSzYHc+tUG2YN5s9kJHQl//txM8eaCb0bhHQzTEe97WwbuuaOfln53ju8dO0z8aoyka4eKlTTTUhSZEKN+RkE7843NqMMbvP3loah9CQkM07BZF+jYRP8JmbUczf3ewZ1pQQkqw6guMjsuFcvkvFsoNUy1gQjILdudjBPnYL62e5ljf33WWfznaRyQkXLSkgbG4x5vnRzNGWs00EhoYS/D0oZMT01KeKkmFZFInFpxN+SyXfSGIKownPF54vZcXXu/N2o9oOJU7Ljolh1xweq4l8DofETL/xcLDhCQHCr3zkcD6gIzvM5ktNrW+IOwvFpi2X7o52w85kzV9V0GQUCqxoUysaZiyTiHDcaatQXDP6YutZjt+cJ9s/zfpMQ6p408sLks7TlggmeHYYYHWprrJ9Qje1AViqbUKc+GJ73WTSCY5NxJYDFkfzjiVM9tI6G0dzRP+hfT1EW+/pHWKCA2MxfnrPV2cH40TDsnEuqF40iMkwgVLGrKOhOLJwqPjZhKhloYonW2NHD8zzGjMH8XH3fqP/3DdSlS1aCOhUjv0jdxZcEIScqlPxK0+Dl5Up9hSwTDpr5kUiGCt8+BFtpZSi+RH4f166Lkf88h3jzMcS7KoLsxvvetSPvneK4p2Zhe1NtKdIavzRa2NLF008/SVqpLwdEJUkp4vOEnVKQIUTEuR2g/gp2eHGRyNIwEHef9wnIQ3PONxMzHbCDhdhL7w3FGa6kJpwSBRPIVHbptcO5YaCU0EHLiUPIOBqbegP2jyvThj8akThIWK0H3/83BWEWpOi5KbbSRUDoe+kTsLTkgiIWHZ4uI7IueveMydh577MV984RghgUjIdwZ/8YVjAEUTk0V1YcKSykM0mUZ+UV14tqaI+Akdo7PvOo1E0iOR9CA1msQ/eEL8kUFdJDQxWkumz01lIZ8RcK5RXnOJjosHp+MyiNBEmHYJRQimjoTODI2TVCXqcqaF3Hf/5T0/Ie55ZfUJGQtQSIpNtdXLrkYe+e5xf9olYBNnL5aQDMWSdLY1Tql1vnxx3Yy1zotBxNWyH0t4qE6u4BYRGiKhKXVBgiOfeNIjkfRfJ7zJ7bwXEZZhnVMq5L2tiCIUHBnNRYTG0sIpzo3G+fQ3D2fog0xMvU0d9eQ3EjIyY0IyBxZywrx8GBxLZKwVMjhWvLUOq9qaOHFmaIotlvRYvaz0NUGuuKCF46eHZq1HEhz5NGQZ/iSdsKSm1pKekkh6zq5OcCYvntW+zqnYIpQKTvi7Az2cH40RS3h4TsBT+cfCISn6SCiz4ExN3bMoIEIpW30hw9waxIRkDuzY20U8meTM0OQFpKUxwo69XfNCSIo12sp2b1zM3ADvWLOU/SfOuoSIvoj0Dsb46C+Ufr48VVyqGPVI/BT2M198UiObRFK5eGkTfYPjXLKsbmIQMhJLVPU6p1yZSYSGRuM89uJPJ6ZL1aVX/41fvJiP/dLqKSI0LUNCASOhs8Mxzg7nl0Hb78N0EcokSotrXIRMSObA0d5Bzo/ECQXqhJ8ejBFPDlb0vIohALU22trXdZb2xXVpo4II+7rO8skSH7vcxaWCI5s7N13OfbsPE096EyIG8IlfuYwLlzQQT/ojmkRgOm0+pDD/Qfd5ljZFGY5NRsotqgvzg+7zfIy5j4SmCU4uIjQWZyxRGhGayIoQEKGppb+jU9L5lFuETEjmQCzhO1lTKcJFwBP17RWiWAKQrRpgIaOtlCM0k71YdPePsHxxPe3NDRM2VaWnf6R4B5mBSpV93bSugy0956ZFxL13/YVZ26SEJZby0yQ94oEptFrg5MAobYvqWLpoapbrYix6jIZDLF1UN2u0XyayiZCfuHTydVCEUtFyJRGhQOnuCRGaUs5hqgi1NESpi8xcxCoTJiRzIBoWRuN+OOhEVT6gLlw5x1yxBCBbNcBCLsxtjRHOjEz3h7Q1Fu/Pb1VbE72DY2lFp5JTnN3FoNqCK/Yc6WXX99+gvbmei92IZNf33+DnO1uznlckHCKSxU+TCgTwH4WLzEJN2lhsEQouWA2OigYmRknFF6G6SCggMv7zksaZE7KWskLi14APAr2qerWzLQWeBFbjV0j8dVXtd+/dC9yBX7Hhk6r6bWe/nskKic8Ad6mqikg98DhwPXAG+IiqnihVfzJxxQUtHHnrPOdHE3jq32EvaYyw9oKWcp7GFIolAEW9MGdbPFnESJiUn2IklijIT5GLQOw50ssf7TrE4FiChOdxenCcP9p1iD/fck3FxGTH3i5OD44xEpjXb4qGCvbTpXw0mURGVYknXdSZ55FMizqLJ/1zsKSNhTEXEYolvImRTqqcw9TRT7owZRehWMLjTCLGmTxEqJQjkkeBL+Ff7FPcAzyvqp8TkXvc67tF5Cr8Urnr8Wu2PyciV7hyuw8DW4EX8YXkJvxyu3cA/ap6uYjcCmwHPlLC/kwj5eANh4Som74ZGEvyjgouiCqWAMz1whwkW5r1YobmzsVPket04PZvHaF/xF9FHgn760P6R+Js/9aRignJ9392hrQsKYzEPX7wszNFP5aIUBfxxb+R7EJzzw9eoT4SoiEaRhUa64TRmCVtLCV1kRBLI3MToWBQQvp03HAsyY4ZPqNkQqKqe0VkdZp5M34dd4DHgD3A3c7+hKqOA8ddHfYbROQE0KKq+wBE5HHgFnwh2Qzc7z5rF/AlEREtYzWfSjp4s7Ft4xo+tesQb5wbnSg5u7g+wqd/7aq8PqeYDuRElimRbPZCKdRPket0YNfpYcC/WKbWjIQkZa8M6SKSooiR1TmTEpo3z4/S6rJHpIiGhNNDY1zQ0uCPXjw3fZaYGs6cD5a0MXdmmmrMRYSi4VBlhCQLF6jqSQBVPSkiqV/pSvwRR4oeZ4u77XR7qk23+6yEiJwHlgGn0w8qIlvxRzVcfPHFRetMpR282RAAdWlbVApObFI0B3I54n/nQHf/CGGBrr6hKYsZ079HTxUXXwHOJ5ZQEKmSjlQJmUbFYwmPVUsXsah++iXHc47/lF8mlvC3C1qgaUxjf9dZtn/7CMPjCZKe0j8cY/u3h7n7feuKJsT5u+dLQ6Zrnc5gn6nNdKPqTlXdoKob2tvbCzzF6axqa5qWDK8UDt582LG3i5bGKGsvaObKFUtYe0EzLY1Rduztqtg5RbNEgWSzl5vm+ghvnBsj4UZwCU9549wYi9MuehEXZpZKHKlp9kqQ7ciVXIe9beMaBkbjHD01yGsnz3P01CADo/Gs06Ihlw6/uSHK0kV1XLikgVVLm1i9rInOtiYuXNLAskX1NDdEaYiGCVfw/7sW2fmvXQyMxlEgHBYUGBiNs/Nfi3dNKPeI5JSIrHCjkRVAKs91DxD0knUCbzp7ZwZ7sE2PiESAJcDZUp58Ots2ruGPdh3ijf5REp5HJORPbeU7jVRMihltVSyy3VUW+26z0MSQmiXNSPr5NdWFGYt7U+5WhNzyeZWKUJasx5W+1iqAuIAKKWzwmZoqqyMEabMumaLLYm7bRjFT6e4fcQt1J5cpIEp3Ea8J5b4l3A3c7rZvB74ZsN8qIvUicimwFtjvpsEGReRG8Sdcb0trk/qsLcAL5fSPpCjGD6aYVOMoKZbpSjeDvRBSiSFH48kpiSEfeu7Hs7YdiiVZ2dpAJCwkVYmEhZWtDdOCATqaG6aUBUil2w9ObZadrDUKKhuCHgnJRBLLsAiRkBR1VBxOG8V0tDTQ2dbEpcsXsWqpjWLKTSnDf/8W37G+XER6gD8FPgc8JSJ3AD8DPgygqodF5CngVSAB3OkitgA+zmT477PuAfBV4OvOMX8WP+qrrOzY28WSxigrlkzGrhe6aK9YFDPaqlhkW39QzMVvj3z3OLhCUAmdvMjnkhgyNae/pn0yN9ZILEFHmkCoqp/FwNVvUfXzYalqxdaXLKoLM+wqJKYCACTHrMel4senBhgYSxDC/79KJJUzwzESyYGyHD8aDhENTx/FpPtiUqOY+bLaPxurWhv56dkRCKx38xQuaSvemptSRm19NMtb78my/2eBz2awHwCuzmAfwwlRpajGaaRyp+uoFobG/bU8qftOVb/MbnoFwUzkKr6pkUsww/CFi+s5PTResXQy71nXzj++fHLidaro13vWFc8XmC9xN9JM1esRSV3EK3uxDoWEhixrZNJX+8eTHrHE/HD4b914me9sjyXwPP9mqKUuytaNlxXtGLayfQ6UazV1vlQqXUclEXerlf6Tz2XRY67imy3DcCypRCuUvPOtgRitjREGxiYXxbY0RHhrIP8VzcWiLhJiNJbE00DGB6Wg1BvlIttq/9TamJQ/JpbwGK8xgblhzVLuft+6kq65MSGZA9U4jQTVl8ajHERDkMywHCGa47UrF/F9x5qlvHT8zETesHgy6VZWh+kdGJ8oqpVIJhlzfwulprt/hGhaSp5oWCo6Kl7b0czrbw1wbjQ+IW6tjVHWdjRX7JwKZcLhn0EEU0kwY664WWIiAKD6RKbUa25MSOZAOaaR8hWFPUd6+dSuQwy5mPHTQ+N8atchPl/BNB7loC4SZjyRmBZRVRcpnq/g2R+9Na1elKo/ClVl0hGvfiRVthX9RUWVvqHJGhueQt9QnM7WyvlIMmV8OD+WqGjGh1Lg+2Iyr/IPRpTFA9Nl8Ux3O/MAE5I5UspppEJyO33u2dc4NxInLL6jUz04NxLnc8++Ns+FJETElZudcCh6WtTplGO9QxkLdE2ECwe2AWKJ0gtJ3+B4XvZyUI0ZH8rNhMM/jdRUWcLzV/XHvfkhMiYkVUwhuZ2On3Ex4wFHp3rK8TOVXW1fasoxnTJTSpewTC5UTEWMhUOl9wmMZ5k+y2YvB+XK+FDouqFKMtPamHSRmYwwq/70/iYkVUw15naqVsoxnTLTT1lEiKSFBV+6rLJBF5WiHEEoDz33Y77w/NEJf9XAWIIvPH8UoOrFJBu5LMCMJT3iztlfTVFl1RtGYUzkdlKXLEYVEh4zxryvWb4IT/19FD8+3lPfPp/Z13WW5vowSU8ZT/ipzpvrw+zrKk+yg9amKBLyBURC/ut73n9lWY5dbWzbuIZ4UhmJJVD1n4sdhPLXe7umFUvz1LfPR1ILMFsaoixbXM8FLX4amWpZgGlCUsUUktvp7pvW0dYURfBj4wVoa4py903rSn26FSW1CC51cfFT+ic4eqo8i+A+v+UarlvVxoUtDVy3qq1swQ1NWUqqZrOXg03rOnjg5vV0NDdwfjROR3MDD9y8vqj/H9kCGcoS4FBlRMMhmuoiLGmK0t5cz0WtjVyybBEXO4FZuqiOxfWRjD6bYmFTW1VMU12Y8YQ3ISKpqKCZVi1vWtfBn2+5ZgEuSExmvEMdHC/PhaWYQRf5ROpdvLSBI6emT3VevLSCaVtYmGuZqg1/bUyIYNl6VWU84U+RxRKTj7mu7DchqWKuuKCF46eHpkW/XLp88YztFuKPOJbIHPGSzV4IIfzV8pnsxSLfSL2jfZkd2NnsxsJGxJ8iS194GVxwmVp0mU8UmU1tVTHbNq6hLhLmwiUNvO2CZi5c0kBdJFzxBY/VSDlKnkQjoWnp2YXipsNPReop/h2lMhmpl4ly5DGrRhqzrDTNZjdmJjU91trkJ8BM+V8uam1keXP9tJIK6dj/ehVTjrnm+UJdOLPfKJu9EC5d1kQ4JNSHQzREQtSHQ4RDUtTorK7TwxMpvwUhJGKRehlYVB8hxNRMzCFnN4pDavTS0hClbZYSvva/XuXMh2kqt9g7o71YdCyuo+f89EV4HYvzr2GdjXvef+WUrAHhkNBav3CjsyrJ2o5mToSHGBidmt9s9bKZp32N0mAjEqPkrGzN7PjNZi+IUIj2xdGJgk4hgfbFUaSIiwI3revgthsvoS4cwlOoC4e47cZLiir0ly5r8sO33foAz/PDtxfqmpRsbNu4hmh46rRvNGzTvpXChMQoOf/tlp+jKW3uuika4r/d8nNFO8aqtiZaGutYf9ESfm7lEtZftISWxrqiLoLbc6SXXd9/g/bmeq68sJn25np2ff8N9hzpnb1xjtzz/ivzWpPSEMk8rstmny/YtG91UZGpLRE5AQwCSSChqhtEZCnwJLAaOAH8uqr2u/3vBe5w+39SVb/t7NczWfTqGeCuSlRJNGanqT6Cx+SUUNMsc9n5JqsspOxxvsfYsbeLaFgmVmw31UWKXshs07oOPp9H+Ha2oLQiBqtVLfNh2ne+UEkfya+o6unA63uA51X1cyJyj3t9t4hchV/9cD1wEfCciFzhKig+DGwFXsQXkpuYrKBoVAn5VpLcc6S3oEJR+ZQ9LuQY5Spkls8FMlv+r5nyghlGsammqa3NwGNu+zHgloD9CVUdV9XjwDHgBhFZAbSo6j43Cnk80MaoIrr7R2hMi1uf6QIcvPMX8Z+j4ZlrfqfEam1HM+subGFtRzNLGqNZ2xRyjFVtTYzGpy5wrIZCZoZRaSolJAr8LxE5KCJbne0CVT0J4J5Tt2Qrge5A2x5nW+m20+3TEJGtInJARA709fUVsRtGLuR7Ac5XeAppU8gxypFDKl/KEfZsGLNRKSF5p6q+HXg/cKeIbJxh30y/CJ3BPt2oulNVN6jqhvb2ytWyXqjkewEu5M4/3zaFHKMaHbyf+JXL87IbRimoiI9EVd90z70i8o/ADcApEVmhqifdtFUqFKYHWBVo3gm86eydGexGlZFvJclCShjn26bQMsnV5uBNpUyvtbocxvxCyh3kJCKLgJCqDrrt7wAPAO8BzgSc7UtV9Y9FZD3wDXyxuQh4HlirqkkR+R7wn4CX8J3tf6Wqz8x0/A0bNuiBAwdK1j+jOKQiqvJJPJlvm0KOYRgLFRE5qKobMr5XASFZA/yjexkBvqGqnxWRZcBTwMXAz4APq+pZ1+ZPgN8EEsDvqeqzzr6ByfDfZ4H/NFv4rwmJYRhG/lSVkFQaExLDMIz8mUlIqin81zAMw6hBTEgMwzCMOWFCYhiGYcwJExLDMAxjTiw4Z7uI9AE/rfR5lInlwOlZ95p/WL8XFtbv8nCJqmZc0b3ghGQhISIHskVZzGes3wsL63flsaktwzAMY06YkBiGYRhzwoRkfrOz0idQIazfCwvrd4UxH4lhGIYxJ2xEYhiGYcwJExLDMAxjTpiQ1BgiEhaRH4jI0+71/SLyhoi87B4fCOx7r4gcE5HXReR9Afv1IvKKe+8hEan6cnoicsKd88sicsDZlorId0TkqHtuC+w/L/qepd/z/jsXkVYR2SUiR0TkNRF5xwL5vjP1u/q/b1W1Rw09gD/Ar8/ytHt9P/CpDPtdBRwC6oFLgZ8AYffefuAd+FUmnwXeX+l+5dDvE8DyNNufAfe47XuA7fOt71n6Pe+/c+Ax4Lfcdh3QukC+70z9rvrv20YkNYSIdAK/BjySw+6bgSdUdVxVjwPHgBtc9ckWVd2n/l/c48AtpTrnErMZ/4eHe74lYJ/vfc/EvOi3iLQAG4GvAqhqTFXPMc+/7xn6nY2q6bcJSW3xBeCPAS/N/gkR+aGIfC0w3F8JdAf26XG2lW473V7tKPC/ROSgiGx1tgtU9SSAe06VN5xPfc/Ub5jf3/kaoA/4f9007iPiV1Od7993tn5DlX/fJiQ1goh8EOhV1YNpbz0MXAZcC5wE/iLVJMPH6Az2auedqvp24P3AnSKycYZ951PfM/V7vn/nEeDtwMOqeh0wjD+VlY353u+q/75NSGqHdwI3i8gJ4Ang3SLyN6p6SlWTquoBX8GvbQ/+XciqQPtO4E1n78xgr2pU9U333ItfqvkG4JQbxuOee93u86bvmfq9AL7zHqBHVV9yr3fhX2Dn+/edsd+18H2bkNQIqnqvqnaq6mrgVuAFVf2N1A/L8SHgR257N3CriNSLyKXAWmC/mxIYFJEbXSTHbcA3y9eT/BGRRSLSnNoG/g/8fu4Gbne73c5kP+ZF37P1e75/56r6FtAtIm9zpvcArzLPv+9s/a6J77vSUQr2yP8BbGIyauvrwCvAD90f1orAfn+CH8nxOoGoDWCD+2P8CfAlXIaDan3gzx0fco/DwJ84+zLgeeCoe146n/o+Q78Xwnd+LXDA9fGfgLb5/n3P0O+q/74tRYphGIYxJ2xqyzAMw5gTJiSGYRjGnDAhMQzDMOaECYlhGIYxJ0xIDMMwjDlhQmIYFUBEHhWRLZU+D8MoBiYkhlEDiEi40udgGNkwITGMPBCR1a5WxGMuid4uEWly9R/+xSVX/HYglcdvi8j3ROSQiPy9iDRl+MzPuBFKKM2+SUT+WUS+AbyS7dhu3xMi8v+IyD4ROSAib3fn8RMR+Z2y/OcYCxYTEsPIn7cBO1X154EB4E7gr4Atqno98DXgs27ff1DVX1DVa4DXgDuCHyQif4afxfY/qp9LKZ0b8Fe0X5Xl2L8b2LdbVd8B/CvwKLAFuBF4YI79NYwZMSExjPzpVtX/7bb/BngfcDXwHRF5GfgvTCbNu1pE/lVEXgH+L2B94HM+DbSq6jbNnmJiv/q1JrId+12B93a751eAl1R1UFX7gDERac27l4aRI5FKn4Bh1CDpF/1B4LAbDaTzKHCLqh4Skf8bP09aiu8B14vIUlU9KyK/COxw792HP+IYnuXYwdfj7tkLbKde22/dKBk2IjGM/LlYRFKi8VHgRaA9ZRORqIikRh7NwEkRieKPSIJ8C/gc8P+JSLOqvqSq17rHbjKTfuzvFqtThlEoJiSGkT+vAbeLyA+BpTj/CLBdRA4BLwO/5Pb9NPAS8B3gSPoHqerf4deY2C0ijQUc++G5dcUw5o5l/zWMPBCR1fgp/K9eSMc2jJmwEYlhGIYxJ2xEYhiGYcwJG5EYhmEYc8KExDAMw5gTJiSGYRjGnDAhMQzDMOaECYlhGIYxJ/5/aDvtD8inzMsAAAAASUVORK5CYII=\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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'peak-rpm' and 'price' and see it's approximately -0.101616 \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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>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": 17,
     "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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>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": 18,
     "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",
    "-->\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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='stroke', ylabel='price'>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 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",
    "-->\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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the relationship between \"body-style\" and \"price\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='body-style', ylabel='price'>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='engine-location', ylabel='price'>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's examine \"drive-wheels\" and \"price\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='drive-wheels', ylabel='price'>"
      ]
     },
     "execution_count": 22,
     "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"discriptive_statistics\">3. Descriptive Statistical Analysis</h2>\n"
   ]
  },
  {
   "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",
    "\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:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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>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": 23,
     "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:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "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": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe(include=['object'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Value Counts</h3>\n"
   ]
  },
  {
   "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fwd    118\n",
       "rwd     75\n",
       "4wd      8\n",
       "Name: drive-wheels, dtype: int64"
      ]
     },
     "execution_count": 25,
     "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 :\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "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",
       "    </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": 26,
     "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'.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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>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": 27,
     "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':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "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>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": 28,
     "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'.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "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>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": 31,
     "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"basic_grouping\">4. Basics of Grouping</h2>\n"
   ]
  },
  {
   "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['rwd', 'fwd', '4wd'], dtype=object)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].unique()\n",
    "#df['drive-wheels'].value_counts()"
   ]
  },
  {
   "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "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.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "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>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": 36,
     "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "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>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": 37,
     "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
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       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>body-style</th>\n",
       "      <th>convertible</th>\n",
       "      <th>hardtop</th>\n",
       "      <th>hatchback</th>\n",
       "      <th>sedan</th>\n",
       "      <th>wagon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7603.000000</td>\n",
       "      <td>12647.333333</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>11595.0</td>\n",
       "      <td>8249.000000</td>\n",
       "      <td>8396.387755</td>\n",
       "      <td>9811.800000</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>23949.6</td>\n",
       "      <td>24202.714286</td>\n",
       "      <td>14337.777778</td>\n",
       "      <td>21711.833333</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   price                                            \\\n",
       "body-style   convertible       hardtop     hatchback         sedan   \n",
       "drive-wheels                                                         \n",
       "4wd                  NaN           NaN   7603.000000  12647.333333   \n",
       "fwd              11595.0   8249.000000   8396.387755   9811.800000   \n",
       "rwd              23949.6  24202.714286  14337.777778  21711.833333   \n",
       "\n",
       "                            \n",
       "body-style           wagon  \n",
       "drive-wheels                \n",
       "4wd            9095.750000  \n",
       "fwd            9997.333333  \n",
       "rwd           16994.222222  "
      ]
     },
     "execution_count": 39,
     "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "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",
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       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>body-style</th>\n",
       "      <th>convertible</th>\n",
       "      <th>hardtop</th>\n",
       "      <th>hatchback</th>\n",
       "      <th>sedan</th>\n",
       "      <th>wagon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>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": 40,
     "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "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>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": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df_grp_body= df[['body-style', 'price']]\n",
    "df_grp_body = df_grp_body.groupby(['body-style'], as_index=False).mean()\n",
    "df_grp_body"
   ]
  },
  {
   "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",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you did not import \"pyplot\" let's do it again. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use a heat map to visualize the relationship between Body Style vs Price.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"correlation_causation\">5. Correlation and Causation</h2>\n"
   ]
  },
  {
   "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p3>Pearson Correlation</p>\n",
    "\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>\n"
   ]
  },
  {
   "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>symboling</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.466264</td>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.365404</td>\n",
       "      <td>-0.242423</td>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.233118</td>\n",
       "      <td>-0.110581</td>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.008245</td>\n",
       "      <td>-0.182196</td>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.279740</td>\n",
       "      <td>-0.035527</td>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.066171</td>\n",
       "      <td>-0.196735</td>\n",
       "      <td>0.196735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>normalized-losses</th>\n",
       "      <td>0.466264</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.101546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wheel-base</th>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>-0.307237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>length</th>\n",
       "      <td>-0.365404</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>-0.211187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>width</th>\n",
       "      <td>-0.242423</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>-0.244356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>height</th>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>-0.281578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>curb-weight</th>\n",
       "      <td>-0.233118</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>-0.221046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>-0.110581</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>-0.070779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>-0.054458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.008245</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>-0.241303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>-0.182196</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.985231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>0.169053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>0.279740</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.475812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-mpg</th>\n",
       "      <td>-0.035527</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>-0.265676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>-0.198690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.110326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-L/100km</th>\n",
       "      <td>0.066171</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>0.241282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diesel</th>\n",
       "      <td>-0.196735</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gas</th>\n",
       "      <td>0.196735</td>\n",
       "      <td>0.101546</td>\n",
       "      <td>-0.307237</td>\n",
       "      <td>-0.211187</td>\n",
       "      <td>-0.244356</td>\n",
       "      <td>-0.281578</td>\n",
       "      <td>-0.221046</td>\n",
       "      <td>-0.070779</td>\n",
       "      <td>-0.054458</td>\n",
       "      <td>-0.241303</td>\n",
       "      <td>-0.985231</td>\n",
       "      <td>0.169053</td>\n",
       "      <td>0.475812</td>\n",
       "      <td>-0.265676</td>\n",
       "      <td>-0.198690</td>\n",
       "      <td>-0.110326</td>\n",
       "      <td>0.241282</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   symboling  normalized-losses  wheel-base    length  \\\n",
       "symboling           1.000000           0.466264   -0.535987 -0.365404   \n",
       "normalized-losses   0.466264           1.000000   -0.056661  0.019424   \n",
       "wheel-base         -0.535987          -0.056661    1.000000  0.876024   \n",
       "length             -0.365404           0.019424    0.876024  1.000000   \n",
       "width              -0.242423           0.086802    0.814507  0.857170   \n",
       "height             -0.550160          -0.373737    0.590742  0.492063   \n",
       "curb-weight        -0.233118           0.099404    0.782097  0.880665   \n",
       "engine-size        -0.110581           0.112360    0.572027  0.685025   \n",
       "bore               -0.140019          -0.029862    0.493244  0.608971   \n",
       "stroke             -0.008245           0.055563    0.158502  0.124139   \n",
       "compression-ratio  -0.182196          -0.114713    0.250313  0.159733   \n",
       "horsepower          0.075819           0.217299    0.371147  0.579821   \n",
       "peak-rpm            0.279740           0.239543   -0.360305 -0.285970   \n",
       "city-mpg           -0.035527          -0.225016   -0.470606 -0.665192   \n",
       "highway-mpg         0.036233          -0.181877   -0.543304 -0.698142   \n",
       "price              -0.082391           0.133999    0.584642  0.690628   \n",
       "city-L/100km        0.066171           0.238567    0.476153  0.657373   \n",
       "diesel             -0.196735          -0.101546    0.307237  0.211187   \n",
       "gas                 0.196735           0.101546   -0.307237 -0.211187   \n",
       "\n",
       "                      width    height  curb-weight  engine-size      bore  \\\n",
       "symboling         -0.242423 -0.550160    -0.233118    -0.110581 -0.140019   \n",
       "normalized-losses  0.086802 -0.373737     0.099404     0.112360 -0.029862   \n",
       "wheel-base         0.814507  0.590742     0.782097     0.572027  0.493244   \n",
       "length             0.857170  0.492063     0.880665     0.685025  0.608971   \n",
       "width              1.000000  0.306002     0.866201     0.729436  0.544885   \n",
       "height             0.306002  1.000000     0.307581     0.074694  0.180449   \n",
       "curb-weight        0.866201  0.307581     1.000000     0.849072  0.644060   \n",
       "engine-size        0.729436  0.074694     0.849072     1.000000  0.572609   \n",
       "bore               0.544885  0.180449     0.644060     0.572609  1.000000   \n",
       "stroke             0.188829 -0.062704     0.167562     0.209523 -0.055390   \n",
       "compression-ratio  0.189867  0.259737     0.156433     0.028889  0.001263   \n",
       "horsepower         0.615077 -0.087027     0.757976     0.822676  0.566936   \n",
       "peak-rpm          -0.245800 -0.309974    -0.279361    -0.256733 -0.267392   \n",
       "city-mpg          -0.633531 -0.049800    -0.749543    -0.650546 -0.582027   \n",
       "highway-mpg       -0.680635 -0.104812    -0.794889    -0.679571 -0.591309   \n",
       "price              0.751265  0.135486     0.834415     0.872335  0.543155   \n",
       "city-L/100km       0.673363  0.003811     0.785353     0.745059  0.554610   \n",
       "diesel             0.244356  0.281578     0.221046     0.070779  0.054458   \n",
       "gas               -0.244356 -0.281578    -0.221046    -0.070779 -0.054458   \n",
       "\n",
       "                     stroke  compression-ratio  horsepower  peak-rpm  \\\n",
       "symboling         -0.008245          -0.182196    0.075819  0.279740   \n",
       "normalized-losses  0.055563          -0.114713    0.217299  0.239543   \n",
       "wheel-base         0.158502           0.250313    0.371147 -0.360305   \n",
       "length             0.124139           0.159733    0.579821 -0.285970   \n",
       "width              0.188829           0.189867    0.615077 -0.245800   \n",
       "height            -0.062704           0.259737   -0.087027 -0.309974   \n",
       "curb-weight        0.167562           0.156433    0.757976 -0.279361   \n",
       "engine-size        0.209523           0.028889    0.822676 -0.256733   \n",
       "bore              -0.055390           0.001263    0.566936 -0.267392   \n",
       "stroke             1.000000           0.187923    0.098462 -0.065713   \n",
       "compression-ratio  0.187923           1.000000   -0.214514 -0.435780   \n",
       "horsepower         0.098462          -0.214514    1.000000  0.107885   \n",
       "peak-rpm          -0.065713          -0.435780    0.107885  1.000000   \n",
       "city-mpg          -0.034696           0.331425   -0.822214 -0.115413   \n",
       "highway-mpg       -0.035201           0.268465   -0.804575 -0.058598   \n",
       "price              0.082310           0.071107    0.809575 -0.101616   \n",
       "city-L/100km       0.037300          -0.299372    0.889488  0.115830   \n",
       "diesel             0.241303           0.985231   -0.169053 -0.475812   \n",
       "gas               -0.241303          -0.985231    0.169053  0.475812   \n",
       "\n",
       "                   city-mpg  highway-mpg     price  city-L/100km    diesel  \\\n",
       "symboling         -0.035527     0.036233 -0.082391      0.066171 -0.196735   \n",
       "normalized-losses -0.225016    -0.181877  0.133999      0.238567 -0.101546   \n",
       "wheel-base        -0.470606    -0.543304  0.584642      0.476153  0.307237   \n",
       "length            -0.665192    -0.698142  0.690628      0.657373  0.211187   \n",
       "width             -0.633531    -0.680635  0.751265      0.673363  0.244356   \n",
       "height            -0.049800    -0.104812  0.135486      0.003811  0.281578   \n",
       "curb-weight       -0.749543    -0.794889  0.834415      0.785353  0.221046   \n",
       "engine-size       -0.650546    -0.679571  0.872335      0.745059  0.070779   \n",
       "bore              -0.582027    -0.591309  0.543155      0.554610  0.054458   \n",
       "stroke            -0.034696    -0.035201  0.082310      0.037300  0.241303   \n",
       "compression-ratio  0.331425     0.268465  0.071107     -0.299372  0.985231   \n",
       "horsepower        -0.822214    -0.804575  0.809575      0.889488 -0.169053   \n",
       "peak-rpm          -0.115413    -0.058598 -0.101616      0.115830 -0.475812   \n",
       "city-mpg           1.000000     0.972044 -0.686571     -0.949713  0.265676   \n",
       "highway-mpg        0.972044     1.000000 -0.704692     -0.930028  0.198690   \n",
       "price             -0.686571    -0.704692  1.000000      0.789898  0.110326   \n",
       "city-L/100km      -0.949713    -0.930028  0.789898      1.000000 -0.241282   \n",
       "diesel             0.265676     0.198690  0.110326     -0.241282  1.000000   \n",
       "gas               -0.265676    -0.198690 -0.110326      0.241282 -1.000000   \n",
       "\n",
       "                        gas  \n",
       "symboling          0.196735  \n",
       "normalized-losses  0.101546  \n",
       "wheel-base        -0.307237  \n",
       "length            -0.211187  \n",
       "width             -0.244356  \n",
       "height            -0.281578  \n",
       "curb-weight       -0.221046  \n",
       "engine-size       -0.070779  \n",
       "bore              -0.054458  \n",
       "stroke            -0.241303  \n",
       "compression-ratio -0.985231  \n",
       "horsepower         0.169053  \n",
       "peak-rpm           0.475812  \n",
       "city-mpg          -0.265676  \n",
       "highway-mpg       -0.198690  \n",
       "price             -0.110326  \n",
       "city-L/100km       0.241282  \n",
       "diesel            -1.000000  \n",
       "gas                1.000000  "
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " sometimes we would like to know the significant of the correlation estimate. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>P-value</b>: \n",
    "\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",
    "\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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can obtain this information using  \"stats\" module in the \"scipy\"  library.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Wheel-base vs Price</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the  Pearson Correlation Coefficient and P-value of 'wheel-base' and 'price'. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Horsepower vs Price</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the  Pearson Correlation Coefficient and P-value of 'horsepower' and 'price'.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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>\n"
   ]
  },
  {
   "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'.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Width vs Price</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the Pearson Correlation Coefficient and P-value of 'width' and 'price':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "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 &lt; 0.001, the correlation between width and price is statistically significant, and the linear relationship is quite strong (~0.751).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Curb-weight vs Price\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the Pearson Correlation Coefficient and P-value of 'curb-weight' and 'price':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "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>\n"
   ]
  },
  {
   "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':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Bore vs Price</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the  Pearson Correlation Coefficient and P-value of 'bore' and 'price':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can relate the process for each 'City-mpg'  and 'Highway-mpg':\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>City-mpg vs Price</h3>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Highway-mpg vs Price</h3>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "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",
    "\n",
    "Since the p-value is &lt; 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.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"anova\">6. ANOVA</h2>\n"
   ]
  },
  {
   "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Drive Wheels</h3>\n"
   ]
  },
  {
   "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's see if different types 'drive-wheels' impact  'price', we group the data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "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>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": 58,
     "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": 59,
   "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": 59,
     "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\".  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "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": 60,
     "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>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "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? \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Separately: fwd and rwd\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "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 \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4wd and rwd\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "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>\n"
   ]
  },
  {
   "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",
    "\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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Thank you for completing this lab!\n",
    "\n",
    "## Author\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>\n",
    "\n",
    "### Other Contributors\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/\" target=\"_blank\">Mahdi Noorian PhD</a>\n",
    "\n",
    "Bahare Talayian\n",
    "\n",
    "Eric Xiao\n",
    "\n",
    "Steven Dong\n",
    "\n",
    "Parizad\n",
    "\n",
    "Hima Vasudevan\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/fiorellawever/\" target=\"_blank\">Fiorella Wenver</a>\n",
    "\n",
    "<a href=\" https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n",
    "\n",
    "## Change Log\n",
    "\n",
    "| Date (YYYY-MM-DD) | Version | Changed By | Change Description                 |\n",
    "| ----------------- | ------- | ---------- | ---------------------------------- |\n",
    "| 2020-08-27        | 2.0     | Lavanya    | Moved lab to course repo in GitLab |\n",
    "\n",
    "<hr>\n",
    "\n",
    "## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n"
   ]
  }
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