exploratory-data-analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>\n",
    "    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Module%203/images/IDSNlogo.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 Contents</h2>\n",
    "\n",
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "<ol>\n",
    "    <li><a href=\"https://#import_data\">Import Data from Module</a></li>\n",
    "    <li><a href=\"https://#pattern_visualization\">Analyzing Individual Feature Patterns using Visualization</a></li>\n",
    "    <li><a href=\"https://#discriptive_statistics\">Descriptive Statistical Analysis</a></li>\n",
    "    <li><a href=\"https://#basic_grouping\">Basics of Grouping</a></li>\n",
    "    <li><a href=\"https://#correlation_causation\">Correlation and Causation</a></li>\n",
    "    <li><a href=\"https://#anova\">ANOVA</a></li>\n",
    "</ol>\n",
    "\n",
    "</div>\n",
    "\n",
    "<hr>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>What are the main characteristics that 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": [
    "#install specific version of libraries used in lab\n",
    "#! mamba install pandas==1.3.3\n",
    "#! mamba install numpy=1.21.2\n",
    "#! mamba install scipy=1.7.1-y\n",
    "#!  mamba install seaborn=0.9.0-y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the data and store it 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?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\">HERE</a> for free storage.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path='https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Data%20files/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 pip, the Python package manager.\n"
   ]
  },
  {
   "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": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "#float64"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "float64\n",
    "```\n",
    "\n",
    "</details>\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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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>symboling</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.466264</td>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.365404</td>\n",
       "      <td>-0.242423</td>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.233118</td>\n",
       "      <td>-0.110581</td>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.008245</td>\n",
       "      <td>-0.182196</td>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.279740</td>\n",
       "      <td>-0.035527</td>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.066171</td>\n",
       "      <td>-0.196735</td>\n",
       "      <td>0.196735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>normalized-losses</th>\n",
       "      <td>0.466264</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.101546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wheel-base</th>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>-0.307237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>length</th>\n",
       "      <td>-0.365404</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>-0.211187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>width</th>\n",
       "      <td>-0.242423</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>-0.244356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>height</th>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>-0.281578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>curb-weight</th>\n",
       "      <td>-0.233118</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>-0.221046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>-0.110581</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>-0.070779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>-0.054458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.008245</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>-0.241303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>-0.182196</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.985231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>0.169053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>0.279740</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.475812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-mpg</th>\n",
       "      <td>-0.035527</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>-0.265676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>-0.198690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.110326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-L/100km</th>\n",
       "      <td>0.066171</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>0.241282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diesel</th>\n",
       "      <td>-0.196735</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gas</th>\n",
       "      <td>0.196735</td>\n",
       "      <td>0.101546</td>\n",
       "      <td>-0.307237</td>\n",
       "      <td>-0.211187</td>\n",
       "      <td>-0.244356</td>\n",
       "      <td>-0.281578</td>\n",
       "      <td>-0.221046</td>\n",
       "      <td>-0.070779</td>\n",
       "      <td>-0.054458</td>\n",
       "      <td>-0.241303</td>\n",
       "      <td>-0.985231</td>\n",
       "      <td>0.169053</td>\n",
       "      <td>0.475812</td>\n",
       "      <td>-0.265676</td>\n",
       "      <td>-0.198690</td>\n",
       "      <td>-0.110326</td>\n",
       "      <td>0.241282</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   symboling  normalized-losses  wheel-base    length  \\\n",
       "symboling           1.000000           0.466264   -0.535987 -0.365404   \n",
       "normalized-losses   0.466264           1.000000   -0.056661  0.019424   \n",
       "wheel-base         -0.535987          -0.056661    1.000000  0.876024   \n",
       "length             -0.365404           0.019424    0.876024  1.000000   \n",
       "width              -0.242423           0.086802    0.814507  0.857170   \n",
       "height             -0.550160          -0.373737    0.590742  0.492063   \n",
       "curb-weight        -0.233118           0.099404    0.782097  0.880665   \n",
       "engine-size        -0.110581           0.112360    0.572027  0.685025   \n",
       "bore               -0.140019          -0.029862    0.493244  0.608971   \n",
       "stroke             -0.008245           0.055563    0.158502  0.124139   \n",
       "compression-ratio  -0.182196          -0.114713    0.250313  0.159733   \n",
       "horsepower          0.075819           0.217299    0.371147  0.579821   \n",
       "peak-rpm            0.279740           0.239543   -0.360305 -0.285970   \n",
       "city-mpg           -0.035527          -0.225016   -0.470606 -0.665192   \n",
       "highway-mpg         0.036233          -0.181877   -0.543304 -0.698142   \n",
       "price              -0.082391           0.133999    0.584642  0.690628   \n",
       "city-L/100km        0.066171           0.238567    0.476153  0.657373   \n",
       "diesel             -0.196735          -0.101546    0.307237  0.211187   \n",
       "gas                 0.196735           0.101546   -0.307237 -0.211187   \n",
       "\n",
       "                      width    height  curb-weight  engine-size      bore  \\\n",
       "symboling         -0.242423 -0.550160    -0.233118    -0.110581 -0.140019   \n",
       "normalized-losses  0.086802 -0.373737     0.099404     0.112360 -0.029862   \n",
       "wheel-base         0.814507  0.590742     0.782097     0.572027  0.493244   \n",
       "length             0.857170  0.492063     0.880665     0.685025  0.608971   \n",
       "width              1.000000  0.306002     0.866201     0.729436  0.544885   \n",
       "height             0.306002  1.000000     0.307581     0.074694  0.180449   \n",
       "curb-weight        0.866201  0.307581     1.000000     0.849072  0.644060   \n",
       "engine-size        0.729436  0.074694     0.849072     1.000000  0.572609   \n",
       "bore               0.544885  0.180449     0.644060     0.572609  1.000000   \n",
       "stroke             0.188829 -0.062704     0.167562     0.209523 -0.055390   \n",
       "compression-ratio  0.189867  0.259737     0.156433     0.028889  0.001263   \n",
       "horsepower         0.615077 -0.087027     0.757976     0.822676  0.566936   \n",
       "peak-rpm          -0.245800 -0.309974    -0.279361    -0.256733 -0.267392   \n",
       "city-mpg          -0.633531 -0.049800    -0.749543    -0.650546 -0.582027   \n",
       "highway-mpg       -0.680635 -0.104812    -0.794889    -0.679571 -0.591309   \n",
       "price              0.751265  0.135486     0.834415     0.872335  0.543155   \n",
       "city-L/100km       0.673363  0.003811     0.785353     0.745059  0.554610   \n",
       "diesel             0.244356  0.281578     0.221046     0.070779  0.054458   \n",
       "gas               -0.244356 -0.281578    -0.221046    -0.070779 -0.054458   \n",
       "\n",
       "                     stroke  compression-ratio  horsepower  peak-rpm  \\\n",
       "symboling         -0.008245          -0.182196    0.075819  0.279740   \n",
       "normalized-losses  0.055563          -0.114713    0.217299  0.239543   \n",
       "wheel-base         0.158502           0.250313    0.371147 -0.360305   \n",
       "length             0.124139           0.159733    0.579821 -0.285970   \n",
       "width              0.188829           0.189867    0.615077 -0.245800   \n",
       "height            -0.062704           0.259737   -0.087027 -0.309974   \n",
       "curb-weight        0.167562           0.156433    0.757976 -0.279361   \n",
       "engine-size        0.209523           0.028889    0.822676 -0.256733   \n",
       "bore              -0.055390           0.001263    0.566936 -0.267392   \n",
       "stroke             1.000000           0.187923    0.098462 -0.065713   \n",
       "compression-ratio  0.187923           1.000000   -0.214514 -0.435780   \n",
       "horsepower         0.098462          -0.214514    1.000000  0.107885   \n",
       "peak-rpm          -0.065713          -0.435780    0.107885  1.000000   \n",
       "city-mpg          -0.034696           0.331425   -0.822214 -0.115413   \n",
       "highway-mpg       -0.035201           0.268465   -0.804575 -0.058598   \n",
       "price              0.082310           0.071107    0.809575 -0.101616   \n",
       "city-L/100km       0.037300          -0.299372    0.889488  0.115830   \n",
       "diesel             0.241303           0.985231   -0.169053 -0.475812   \n",
       "gas               -0.241303          -0.985231    0.169053  0.475812   \n",
       "\n",
       "                   city-mpg  highway-mpg     price  city-L/100km    diesel  \\\n",
       "symboling         -0.035527     0.036233 -0.082391      0.066171 -0.196735   \n",
       "normalized-losses -0.225016    -0.181877  0.133999      0.238567 -0.101546   \n",
       "wheel-base        -0.470606    -0.543304  0.584642      0.476153  0.307237   \n",
       "length            -0.665192    -0.698142  0.690628      0.657373  0.211187   \n",
       "width             -0.633531    -0.680635  0.751265      0.673363  0.244356   \n",
       "height            -0.049800    -0.104812  0.135486      0.003811  0.281578   \n",
       "curb-weight       -0.749543    -0.794889  0.834415      0.785353  0.221046   \n",
       "engine-size       -0.650546    -0.679571  0.872335      0.745059  0.070779   \n",
       "bore              -0.582027    -0.591309  0.543155      0.554610  0.054458   \n",
       "stroke            -0.034696    -0.035201  0.082310      0.037300  0.241303   \n",
       "compression-ratio  0.331425     0.268465  0.071107     -0.299372  0.985231   \n",
       "horsepower        -0.822214    -0.804575  0.809575      0.889488 -0.169053   \n",
       "peak-rpm          -0.115413    -0.058598 -0.101616      0.115830 -0.475812   \n",
       "city-mpg           1.000000     0.972044 -0.686571     -0.949713  0.265676   \n",
       "highway-mpg        0.972044     1.000000 -0.704692     -0.930028  0.198690   \n",
       "price             -0.686571    -0.704692  1.000000      0.789898  0.110326   \n",
       "city-L/100km      -0.949713    -0.930028  0.789898      1.000000 -0.241282   \n",
       "diesel             0.265676     0.198690  0.110326     -0.241282  1.000000   \n",
       "gas               -0.265676    -0.198690 -0.110326      0.241282 -1.000000   \n",
       "\n",
       "                        gas  \n",
       "symboling          0.196735  \n",
       "normalized-losses  0.101546  \n",
       "wheel-base        -0.307237  \n",
       "length            -0.211187  \n",
       "width             -0.244356  \n",
       "height            -0.281578  \n",
       "curb-weight       -0.221046  \n",
       "engine-size       -0.070779  \n",
       "bore              -0.054458  \n",
       "stroke            -0.241303  \n",
       "compression-ratio -0.985231  \n",
       "horsepower         0.169053  \n",
       "peak-rpm           0.475812  \n",
       "city-mpg          -0.265676  \n",
       "highway-mpg       -0.198690  \n",
       "price             -0.110326  \n",
       "city-L/100km       0.241282  \n",
       "diesel            -1.000000  \n",
       "gas                1.000000  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The diagonal elements are always one; we will study correlation more precisely Pearson correlation in-depth at the end of the notebook.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h3> Question  #2: </h3>\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": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "df[['bore', 'stroke', 'compression-ratio', 'horsepower']].corr()\n",
    "```\n",
    "\n",
    "</details>\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. They can be of 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 use \"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": [
    "<h3>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": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 55899.59573792229)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Engine size as potential predictor variable of price\n",
    "sns.regplot(x=\"engine-size\", y=\"price\", data=df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>As the engine-size goes up, the price goes up: this indicates a positive direct correlation between these two variables. Engine size seems like a pretty good predictor of price since the regression line is almost a perfect diagonal line.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'engine-size' and 'price' and see that it's approximately 0.87.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[[\"engine-size\", \"price\"]].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Highway mpg is a potential predictor variable of price. Let's find the scatterplot of \"highway-mpg\" and \"price\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='highway-mpg', ylabel='price'>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x=\"highway-mpg\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>As 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": 12,
   "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": 12,
     "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\" is a predictor variable of \"price\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='peak-rpm', ylabel='price'>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x=\"peak-rpm\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Peak rpm does not seem like a good predictor of the price at all since the regression line is close to horizontal. Also, the data points are very scattered and far from the fitted line, showing lots of variability. Therefore, it's 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": 14,
   "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": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['peak-rpm','price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " <div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  3 a): </h1>\n",
    "\n",
    "<p>Find the correlation  between x=\"stroke\" and 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": 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>stroke</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>1.00000</td>\n",
       "      <td>0.08231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>0.08231</td>\n",
       "      <td>1.00000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         stroke    price\n",
       "stroke  1.00000  0.08231\n",
       "price   0.08231  1.00000"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute\n",
    "df[[\"stroke\",\"price\"]].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "\n",
    "#The correlation is 0.0823, the non-diagonal elements of the table.\n",
    "\n",
    "df[[\"stroke\",\"price\"]].corr()\n",
    "\n",
    "```\n",
    "\n",
    "</details>\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": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='stroke', ylabel='price'>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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uUz2mqsOV2zXDMIzpWBHJ2qMoi0REfpOgTPtdTtQLfLtC+2QYhmHUEcVObd0IvBMYAlDVVwF7JDAMwzCKViQJVU2GH1yl3caqrWIYhmHkpVhF8m8i8odAq4j838DfA/9Uud0yDMMw6oViFcktwGHgReAG4CHg05XaKcMwDKN+KDZqqxX4hqr+NWRa6LYCVpfAMIwFxar/1h7FWiSPESiOkFbg0fLvjmEYRmF27Bngtgd2MzA8wbLWOAPDE9z2wG6r/ltlilUkLao6En5wy20zDRCR1SLyryLysojsFpGbnfwzIvK6iDzvXu/PGnOriOwVkZ+KyC9lyS8UkRfdd3e4Tom4bor3O/lTIrKmhGM3DKPOuGtnH/Go0NYUQyR4j0eFu3b2VXvXGppiFcmoiFwQfhCRC4HxWcakgd9V1bOAi4EbReRs992XVPV893rIbfNsgg6H5xD0dv+qm0IDuBPYTNB+d737HuB6YFBVzwC+BGwp8ngMw6hDDgyO0RqP5sha41H6B22WvZoU6yP5JPD3IvKG+7wS+OhMA1yv9YNueVhEXgZWzTDkCuA+VU0A+1z73ItEZD/QqapPAIjIPcCVBO12rwA+48ZvB74iImJ9243FSqP7B1Z3tTEwPEFb0+Stazzl0ds14wSJUWGKskhU9RlgA0Hv9P8OnKWqzxb7R9yU09uBp5zoEyLyYxH5hoh0Odkq4EDWsH4nW+WWp8pzxqhqGjgBLM/z9zeLyC4R2XX48OFid9swagrzD8ANl6wj5SljyTSqwXvKU264ZF21d62hmVGRiMil7v0/A78MnEkwtfTLTjYrItIO/APwSVUdIpimOh04n8Bi+fNw1TzDdQb5TGNyBapbVXWjqm7s7u4uZrcNo+Yw/0BQZ+v2y8+hp6OFE+MpejpauP3ycxrKKqtFZpva+kXgcQIlMhUF/nGmwSISJ1Aif6uq/wigqoeyvv9r4EH3sR9YnTW8F3jDyXvzyLPH9Lts+6XAsVmOyTDqkgODYyxrjefIGtE/YEUba48ZFYmq/rGIRICHVXVbKRt2kVVfB15W1S9myVc6/wnAh4CX3PIDwN+JyBeBUwksn6dV1RORYRG5mGBq7FrgL7PGXAc8AVwFPG7+EWOxUk3/QKP7ZoyZmdVHoqo+8Ik5bPudwMeAS6eE+v4vF8r7Y+DdwP/r/s5uYBvwE+AR4EZV9dy2Pg58DdgL/AeBox0CRbXcOeZ/hyAD3zAWJdXyD5hvxpgNKeYBXkT+iCDc935gNJSrat1NI23cuFF37dpV7d0wjDkRWgb9g2P0LpBlcM3WJ6dZQmPJND0dLXxr88UV/dtG7SAiz6rqxnzfFRv+++sEPpH/PkVuoRKGsYBUwz9gvhljNopNSDwb+N/AC8DzBD6Kcyq0T4Zh1BCru9oYT3k5MsvdMLIpVpHcDZwF3EGgRM5yMsMwFjmWu2HMRrFTW29V1fOyPv+riLxQiR0yDKO2oqQ2bejhdlhw34xRPxRrkfzIhd8CICI/D/x7ZXbJMBqbWo6Ssth6Ix/FKpKfB34oIvtd7asngF/MCuM1DKNM1FoGey0rNqM2KHZq67LZVzEMo1TyTWHVWpRUtmIDaGuKMZZMc9fOPpveMoAiFYmqvlbpHTGMRiN80o9HJedJv6M5xnjKq5kKt7Wm2Izao9ipLcMwykyhKSxVrakoKQv/NWbDFInRcOzYM8A1W5/kXVse55qtT1Ztrr9Qk6bRpFdTFW4t/NeYjWJ9JIaxKCg0nXQ7LPiNeqYijIUy2KsRFmzhv8ZsmCIxGopachzfcMk6bntgN2PJNK3xKOMpb8Yn/R17Bvj97S8wPJEm7fscGU7w+9tf4PNXnbcgysQUh1EIm9oyGopa6vldapOmLY/sYXAshQKxaAQFBsdSbHlkz4Lut2FMxSwSo6GotZ7fpTzp9x0ZJSIQkaAxqAioKH1HRmcZaRiVxSwSo6Ewx7FhlB9TJEZDUc89v9cub8NX8H1FVfF9xddAbhjVpGJTWyKyGrgHOAXwga2q+mUROYmgQdYaYD/wEVUddGNuBa4HPOAmVf2uk18IfBNoBR4CblZVFZFm9zcuBI4CH1XV/ZU6JmNxUK+O41vedxa/t/0FRhJpPF+JRoRlzXFued9Z1d41o8GppEWSBn5XVc8CLgZuFJGzCdrhPqaq64HH3Gfcd1cT9Dm5DPiqiIRe0TuBzQR93NczWbLlemBQVc8AvgRsqeDxGEZV2bShhy9cdR5vX93FKZ0tvH11F1+YIWKrVvJljMVPxSwSVT0IHHTLwyLyMrAKuALY5Fa7G9gBfMrJ71PVBLDP9WG/yBWJ7FTVJwBE5B7gSoK+7VcAn3Hb2g58RUREi+kfbBh1SLHWVC3lyxiLnwXxkYjIGuDtwFPAyU7JhMomvKpXAQeyhvU72Sq3PFWeM0ZV08AJYHmev79ZRHaJyK7Dhw+X6agMo3aptQrCxuKm4opERNqBfwA+qapDM62aR6YzyGcakytQ3aqqG1V1Y3d392y7bBh1Ty3lyxj1T8rzZ/y+onkkIhInUCJ/q6r/6MSHRGSlqh4UkZVAOHHbD6zOGt4LvOHkvXnk2WP6RSQGLAWOVeRgDGMBuePRV/jaD/YxmvRY0hTlN961lpvee2bR48udL1NLHRuNypJM+yTSnnv3SaZ9opF8z+yTVMwiEREBvg68rKpfzPrqAeA6t3wd8J0s+dUi0iwiawmc6k+76a9hEbnYbfPaKWPCbV0FPG7+EaPeuePRV/jy43sZT3nEIoEC+PLje7nj0VeK3kY582WssdXiRFVJpD2GJ1IcHUnwxvFx9h8ZpX9wjMPDCU6Mp5hIefhF3FIraZG8E/gY8KKIPO9kfwh8DtgmItcDPwM+DKCqu0VkG/ATgoivG1U1rF39cSbDfx92LwgU1b3OMX+MIOrLMGqOUp7ov/aDfUQEYpHgOS8ikPZ9vvaDfUVbJeUstFhL9cmMuZH2fJJeYF0k08FyygvykcpBJaO2fkB+HwbAewqM+Szw2TzyXcC5eeQTOEVkGLVKqRFUo0mPCMpEystx+Hl+ek5/f763ilprbGXTbIXxfQ0URrbSSPtFWRXzwWptGUaFuWtnHynP4+hImqTn0xSN0NkaK/hE3xyLMJb0pslVg5toOGamG2o5w39rqT6ZhTVPEloWobJIef6sTvFKYSVSDKPCvDowzJHhJGmXjZ72lSPDSV4dGM67/kmt+Z/vBDLhu7P5LcoZ/lsuf0s5EiQbNazZ84PzPjia5M0TE7x2NPBlDAxNcHws6X6T6igRMIvEMCpOMu3DlKq9vmggz0dk+vNdBIhGJTOdNJvfopzTUZs29HBV//FpUWTFWgA79gyw5ZE9vDIwQjwqnNzRPGdLotam2SpB4AT3SaSC6KlEunqWRrGYRWIYFSYeDRRIdrFFgKZofhfi6q42WmIRmmMRWuNRWuNR4tEI0YhkppNmyxMpZ5/1HXsGuPfJ10imfYRAAd775GtFWRSh5bTvyChRAfXhjRMTpD2dkyWxGPvHJ9M+wxMpDg8n6B8cY//RMd44Ps7R0QQjiepaGsViisQwKsyZJ3eyfEkTsajgqRKLCsuXNLH+5M68699wyTo6WmJ4vuL5fvBSpb05lplOmu2GWs7w3/k01AotJ0+VSESCF8KRkcScLIl6bwPg+cpoIs2x0SQHT+SG2w5PpEim/bJFUi0kpkgMo8LccMk6mmJRTlnawltP7uCUpS00xaIFb36bNvTw+avOY31POyKCiHBG95KcAo2z3VA3bejhqgtWcXg4wctvDnN4OMFVF6yak0M6u6GWIEREiAhFNdQKLaemaATPD/IWEp7PWNLj6GiiZEuintoAeL4ynvQ4PpZkYGiCA8fGeO3oKIecX2M8WVyORj1gPhJj0VCrYaFzzelY1tZEd0c677HMts0dewbY/tzrdHc0c5rrB7/9udd5W++yBT0nYcRXe3OMQ8OJjFyBQ0MJrnnHaSVvsxbbAGSUZGoyGzzt1/6UVLkwRbKA1OqNbjFQ62Ghpdz8ZjoWoKhrqJxJhGuXt7H38Cjia9DeV8FXOGPF7NbEDZes47YHdjM4lpz+pcLDL71ZUumXWiCR9kh5mgm5TdaBM7zSmCJZIGr9Rldt5qtkS83VqCWmHvvxsWTeY9nyyB5Gk15R19BcopsK/QalNNTKt43bLz+HX7v7GSDI0o+KEItG8Hy/pvvNe76S8iYtjDBnox59GJXGfCQLRKPGvxdDOWo5lZqrUSvkO/afHhpmYCgx7Vj2uvDZYq6hUqObZvoNim2oVWgbAE3RCE1RoTkWJRatvdtOyvMzNacOnhjnZ0cDf8Ybx8c5OhI4whMpz5RIAcwiWSAaIf59rpRjGqbkXI0aId+xA3gKTVOOJe1r0aXhwymlsWSaVucjmSm6abbfoJipuZm2MZ/psUowkQr8GRPOr9FI/oxKUHuPBouUxRj/Xi7K0Tuj1FyNWiHfsYdMpDzGU16mAmtUKPoaKjW66cDgGGnPp+/wCHveHKLv8Ahpzy/pN5jpd7zlfWexrC2ORMBTRSKwrG1h+s1nZ4WHIbdhnsZoIm1KpAyYRbJAlPqE2EiUo5bTmSd3su/ICMMTk36FjpY4a1e0V2KXy0a+Y49FhKSnQU0U19pNfTi1qzUT8lvMNVSKg7+9KcqeQyOZzynPY/TYOBtOLv78zfQ7htNj5ahGXIi0q2ib9CbrTiXTPp5v01GVxhTJAjHfMhOLmXIo2XAbpyyN1aSiLuTIznfsofURi0Qy00CeKkuaotzyvrMqcjM+nBWaW4w8H7P9juUK201NKVRY7pLoRumYIlkgaiWuvxYpR++McvbfKDezRexN3e8T4ymWNEU5MpLMWFentDczmvQqlkNxbDw1o7yYqLpy/waer1m9MyYVh1kYtYdUSouLyDeADwIDqnquk30G+E3gsFvtD1X1IffdrcD1gAfcpKrfdfILmWxq9RBws6qqiDQD9wAXAkeBj6rq/tn26+0XXqg7//1JIiJEI4I4B21UgvIN+ShH/sc1W5+cZvaPJdP0dLTwrc0Xl7Qto74o9bevxrWy5pZ/BgLHfkh4a/jmf3tHRhFmWxrlyijPVhjZ5dBNYVSXsAbY0ESa8aTHL5+/6llV3Zhv3UpaJN8EvkJws8/mS6r6hWyBiJxN0N3wHOBU4FEROdN1SLwT2Aw8SaBILiPokHg9MKiqZ4jI1cAW4KOz7ZTn6YzmelD+QYhEguWn/uMoX/jeK8SiQntTlIMnxvn0t1/if3zgLDa9tSejiCKCU0z5lZFFbTUupf721fCntTVFgx4ozicTdsNqa4qWLblRVTPTUCmnOOoxYurpvmPc98wBDg6Ns7KzlavfsZqL1p1U7d3Ki6oykfIZmkgxMpFmaCLF8ESaoYk0w5nl4D1UGsPjwfJECRGPleyQuFNE1hS5+hXAfaqaAPa51rkXich+oFNVnwAQkXuAKwkUyRXAZ9z47cBXRETm27PdVw3q37hzePcTrxERaI5G8BVXM8jjrn/r462ndOTdRqiMRCASCaydkztaODKaoC0ezSib8VSalUtbSaS9SQUmFFRGRn1SajBBNabpfuuSdfzFY6/iKxklEpFAvu3Z/pIUYT6ndyqtdacw8vF03zG+/PirxCJCZ0uMo6MJvvz4q9zM+ooqE1+VsYSXpQim3PxD+fjk8nAiWE55lbfsquEj+YSIXAvsAn5XVQeBVQQWR0i/k6Xc8lQ57v0AgKqmReQEsBw4MvUPishmAquGVb2rS9rZg0PjdLbknqaWeIQ3h8YLjskoIwgm6oAPX9jLlx9/Fd9XWuIRJlI+aV/5z29fxeuD07c1VRlFZFIWDT87JRVO0U0umyKqJeZiYZTDF1LKlGxYpmRqMMhN7z2TJ/qO5VWEq5a1MpHyFrytazW575kDpNIex5MeKc8nHo2wpCnKfc8cKEqReL4GN//xQBmMJLKsg/F8CiJYHkmkKcdMnwDtLTE6WmJ0tMTpaI7R2RqnoyVGZygLv2+O09kayE5a0sTpWwpvd6EVyZ3AnxI88/wp8OfAr5O/t7vOIGeW73KFqluBrQBvO/+Ckn6OlZ2tHB1N5MTHT6R8TulsLWUzXLTuJG5mPfc9c4A3h8Y5ZRaTOJ8yKhZxPh9x023Zlk62Egrl2daQKaLyUw0LYy4leW5675nT6l75vvLr71zDnzz4Ezw/RXMs4pSHcuX5q3jjeOEHqsXI/qMjjCTSoIE/KZX2GUz7jKeGePjFg1OmjKZbDPlaKM+FaEToaJ5UCJ2tMdqdUggVwlTF0NkSZ0lzjGgBX/BMxGepRrCgikRVD4XLIvLXwIPuYz+QbSr0Am84eW8eefaYfhGJAUuBY+Xe56vfsZovP/4q4ykvx5K4+h2lWTYQKJOFmEtVVdJOCaXmcN1KtoLJsoZCqyc7e1wI/EmTCit3rBGw0BVri/FrBP1OggeWtFtOOyd3Kmv59J52PrHpjKIfguoFVWU85Tm/QK4FMJzjTwithDQnxtOTT6tZj6SjSZ/P/8srJe9DcyySucl35Lnxd+QohUml0Zo1RV4LLKgiEZGVqnrQffwQ8JJbfgD4OxH5IoGzfT3wtKp6IjIsIhcDTwHXAn+ZNeY64AngKuDx+fpH8lGqJbEYUFU8BQ8t2RqaSnixz3bJh0ELECilWFSIRSLEokI8fK/BGk21hO8rKd8n7SmvHRtlaUs88EtocM+LRYT9R0Z47egovlJS3sVP3xzi1YFhxlMewxNpfvrmUMn/ByrlpPZ8ZSSR5RuYYglkK4jQhxBOKZUzMuzkzuac6aCcm3+oJFoDBdHeHEwlNReoalBvVEyRiMi3gE3AChHpB/4Y2CQi5xNc1/uBGwBUdbeIbAN+AqSBG13EFsDHmQz/fdi9AL4O3Osc88cIor4qwkJZEouR8GY163/XUHHhrKg8aQ1TlVK+B7Lse2NoMeVjtoc51enriJselKxtFzK6so833Cd10nCffA0k4TnKp3SnnjdVdXWqFF9z1832TfS0t0ybkh1PeZzc2VryzfPeH+7n7idfc1OfQRn1u598DYCP/ac1RW2jGCd1UDgxn0WQz4cwuTySSJd0PIWICJnpocBHMMVCaI3zT88f5Ph4golUYK3Fo0J7c5Terna++NHzyrIf9UjF8khqlbedf4F++3s7q70bxhTqKaRyIZjv+Xi67xh/+uBuxlJ+xtnYFo/wRx88p+Tz+st/+QMSaY9oZNIi9Hyf5liUf/rtd+Wsq6ok0r6LIEplbvZf/8E+hiZSRETwfcVTJeUFBRw7W+IMTaSYSJUnqisWkRxl0N4SY2lrfJoPIXv6qLMlTltzNGMVFyJbIWZPdd98aWWjtqpNPBrhtOVLqpJHYhhFUa2QylqlHOfjp28OZZQIBJbNWMovekpKVRlNegxPpBhLegjkhO8KMJr0+PS3X5o2fVRquOlEKn9eV0s8Ms1P0J7jO8hVBO3OamiJRSrmP2jEqe5iMEViVJ37njlALCKZaZgwRLbYkMrFRjnOx7Zn+4lGJv1OSuBD+btnDnDKstbpvoOcXITp4abTptjc+w//4+is+9LeHGMi5ZH2NTMtCMGUX9eSJn7jXWsnlULr5JRSU6w2fWKFprob2ao2RWJUnbnk6ixmDg6NExU4MJjI5Cosa43x+vEx9h0ZnRZemvEXjE8qhdFMmGmuCvDSPv/z4T1l2c+WWIT3/9zKjJUQOJmzLIbmwEqIRoTf+OYzvHZsLBP9F+T8KstaYlx27imZbT7dd4w7ntlb0zfjfAoDaGir2hSJUXXKlatT60wNNw2VwUgilZuRPCXfIO37jKeCnufX371r3vuxvL0p62Y/3aE81Ydw8/0/IpX2ODHuZfwty9piNMeifOLSM4r6m6Mpj5M7mxkcS2WUY1dbE2NZ8en1MMX5dN8xtnx3D6Ou7fDgaJIt3x2lqzXe0Fa1KRKj6pQzV2ch8HxlNDEZOTSSyC1NkS//ILQUyhVuKkAsKnS3N3PK0pYgWzkr9HR3/3F+2HfMJaJOdiT8b7/wlqIjrUJWLW3j6GiCno7cCLDlS5qL3kb4sLA6qyzMeMqjJ2sb9TDFufX7fQyNp4KqElFBlSCoYDzFuu4lOes2klVtisSoOtVyYKY9P6hH5MJK89348/kQRibSs4czF4EAHdMcyHGe+I8jRCNCIuXjqWae0JOe0hKP0hQVWpuiGYX7kQvznKt3rObeH+5n27P9jKc8WuNRPnJhb8lKBAJFv+W7ezg0PIHvK5GIsKQpxo2birNGwm3M9rBQD1OcBwbHMgm34Pw9oqT8wIpe7FZ1IUyRGDXBXHN1csJNsyyBkUIVTsfTDCfKW64iFpHpmchhyYqWOMdGk/zbK4eJRYXWeIS0F+SA3Pye9Vx8+vJp2/ud+1/ImwMyPpqkORYp+on9Y/9pzZwUR0HU5cTMQYsW87BQz1OcsQikfa0bq7rcmCIxagJVZSzp5SqE8VxLIG+EURmrm+YrVzG1NMXUQncdLbOXq/id+18gHoWRRJrjY4F/oL05yrZd/XkVSaGn93hU8Hw/xwnf1RavyBN7JKsUzv27DtDREqOnoyUTcTWeTPP3z/Zz6Vk9kJWcGTrTM4mgEiZvwgfOW8kHzz81J3IrzLBXYPMla/n/HtpD0vMzSlIVfvP/WsvydjcFppN16IJkziDRU5WsRM3Jz+F35SokuXpZK68dGwNfc6YM33JSG5svOb1hw4JNkRhlxfM1p+9B+PQf+hBeHRjh5YNDjCY9YhGhrSlKygsqoparWsWS5mieUhXZVU2zFcHk95UKN33t2CjD4ykkEtQfS/vK4GiKtD+ad/1CT+9bv9/Ha0dHg/pnEcHzlUNDCdauWEJbUyzIsg9v5kzPwg++my7P7qmTr0ba4ZEEUYH+wbFMx8YV7U0MDE/Q09ky6/EXW4X4/W87lbamWMWKW6qrBuBrUFcsbGHsq6J+bqWBUElN5ab3nMntD+5mNBn4uyIRobMpzuZLTm/oChimSIy8ZHdHy28R5LcORhPFTxcloeD0UkTIihyanomcv7hdIJ9LddNKkkz7mRs8BDdwT4KugPmIRyNc8tZuLj2rx9UdixCLCN/4975gvAbbUretWEQ4ZensN/S50tEc49WBEaKRoHp02ldePz7B+p72WceWWoW4ksUtg6rYEEWYa4mrKy9YxbK2+DRl94tv7Q6KYE6xhkLF5fvBclgo03Oy7PWgtPpntYQpkkVM2B2tYO2iMnVHm4l4VDI3+sPDiUwLVV+D4owtcWH5khZufPfpdGaVsWhrmr1cRb0QjwqJdJAQKFndB5ujQldbU06BytgMZfzHUj69Xa15e7lXkuGJFGlfMwmFoaIu5qZ3184+Up7H0ZF0Zp87W2N87uGX592+uloUUnaxqJT1hpqpU6eTbqmgoGpuvbXAupq+HCqo7PpslWpfbIqkDphLd7RwnXSZLpzWeDTnqT/XSpisbNqRqWcUJKNll6v4lTt/SCLluYZcwX+QiaTPUDTFxjWLZ0pAJFAI8WigHNb3dPDasVFGJoKbaXMsOJdrV7TTtaSp6O2GnRbXdU9aAmPJNE3RCNdsfbIiN+UdewY4OBRMbSlkblYr2uNFKbBXB4Y5MebCZZ01c+hEwk3JadG9UhoRyY4Mm5TO+6Yd1joLLCWnYNz03qTcKSa3PFtLCFMkC0ja83M7ohWsbFq57mhLmqdPB3VOUQL5ppDKUcK91CmeWiZUFqE10RSNEI8FymPqubrx3Wdw2wO76WiJz6sHe75Oi0PjKRRIen5Fbsp37ewjKhDWUwybnw1PeJzR0znr+Hy/eeh/ePPERI6VUmoPeGNuRCJCZNbGDqVhimQOJNN+rnUwns9fUNnuaNMcyFOsg3J2RysXU6d4wpmRpmjtTmFFI5PKoSkaoSkWIR4N/BbFUq4Oifm2E48IKV9nbGBVLPmc4q8ODJPyNGtqBXxP8aQ4RRiPCuOp3N883Fba14yVcmQ4ScobLml/jdqhYRVJoXIVM2Unh/kJiTI9QYfhptk3/s4piiFffkKtdUcrljXL2+kfHGU0p991jN6uJbMPriChdREoiUBRhMqjXIq3XE7kqdt515bHWdYaz1mnNR6lf3CspO0WcoqHFs9UYhEp6njOPLmTfUdGGJ6Y9JEkvUCZZFspvrNMS+kzb9QODadI9h0Z5Vfu/GFZy1W0NUWnWAUFrINF2h2tWMIMac+ZIp7rxLhQSVsikrEomqKRjLKIR+u3T33oNwktEgiSF3uzSpEUQ6HWvIVydIrNywin405ZGstMx/UdHiUamW6Zqiq/v/0F59vzOTKc4Pe3v8DnrzrPlEmNU8kOid8APggMqOq5TnYScD+whqBD4kdUddB9dytwPUFz15tU9btOfiGTHRIfAm5WVRWRZuAe4ELgKPBRVd0/234lPZ/Bsent96Z1R3OJZ9nF7DI9EbIa5LQ3x0qa5mh0Up5PMu3uHL7SFK2MfyQWCaahmmORjKVRq2XJ50M+v8lc/C8HBsfyWjaF1EU+o7yQNXFV/3G+9oN9jCY9ljRF6e1qZSSR4sR44PuLCCxtjZFIK4NjqUzIsyoMjqXY8sieulAkjWxNVdIi+SbwFYKbfcgtwGOq+jkRucV9/pSInE3QKvccgp7tj4rIma7d7p3AZuBJAkVyGUG73euBQVU9Q0SuBrYAH51tp3o6mvn0B87K8S0sLbI7mjE/tn6/j/Gk5yyA4El0POmx9ft9c07kiogQdwojHp18r7VckkpRLv9LIcsmIhQM9Ljj0Ve46b1nAoWnxq7qP872516nu6OZ05yiGxiaYDTpBf4nt/2hCQ/1lVhUch3zovQdyZ+4WUuUmi+z2KiYIlHVnSKyZor4CoI+7gB3AzuATzn5faqaAPa5PuwXich+oFNVnwAQkXuAKwkUyRXAZ9y2tgNfERHRWYLbu9qauLQBfthapFDBuwNFzudnnN7OymiqQyujEk+t5fC/FLJsljRFGS6QZPq1H+zLKJJwaiztKftOjJL0fKIR4a/+rY+lbbGcPJKU5xMVnL8kkHW0xDg0nL9TYj1QaGqwUSLRFtpHcrKqHgRQ1YMiEp7hVQQWR0i/k6Xc8lR5OOaA21ZaRE4Ay4EjU/+oiGwmsGpY1dsYRdTqmWzfRWZaKhqZNZa91tmxZ6BmfQCFLJu7dvbxRF/+LogjiXRm+cDgGENjCYYSk3NeQb4CJIY8Ys5KTPtK0lOiQk4+jKpydCSJryBT6lidsaI0f081ODA4RlSg7/BIThmZUoMe6pVacbbnu0PoDPKZxkwXqm4FtgK87fwL6rMGwSJg9bJW9h8dI5XV+zsCrOtuo7ujOTM1Va+Ob5jZ4tjyyJ6a9gEUsmwKKZKc38n3c5QIQOin9xSasqxQYfp02XjK44yedl4fHGMk6WV8J+1NUW5531lzPqaFYj5lZBYDCz0vcEhEVgK49wEn7weyTYVe4A0n780jzxkjIjFgKXCsYntuzJmICC3xKP/POSeTfasJq4Vcft6pdLTEaanTsOaQcJ58YHgiZ558x57gMu87MjpZIRfJFEqsZR/Apg09tMTy/yZt8Un5sfF03nVC/LB0R1gmBnj10DAvHzzBq4eGGRpP8b5zT6EpHp2MrItFaKqTyMbMjLpmvbLli5yFViQPANe55euA72TJrxaRZhFZC6wHnnbTYMMicrEEd5hrp4wJt3UV8Phs/hGjsoThte0tMU5a0sQpS1s47aQ21qxYwqnLWnmhf4iVS5tZ0hR188lRTlnazBN9i0P/h3Wl3jwxwU8PDfPmiQlSnsddO/uqvWvzYu2K9pwbRURgWWuMc1d1ZWQzJdtGJahD5WngTO9siRGN4ErMByaKAg+9eJBYRIg6TRN1+T31cP5Gkh6rlrXkHOeqZS0Vr4NWK1Qy/PdbBI71FSLSD/wx8Dlgm4hcD/wM+DCAqu4WkW3AT4A0cKOL2AL4OJPhvw+7F8DXgXudY/4YQdSXsUBknN7RCPEiHd8HBsdYvqSZFe2TlWpVddHMI+erK5Wdsb12eRt7D4/WlQ9gx54B9h8ZybEkfZedXmyIccRVJw6d+P2D43R35F4HY8l0cG4EIgTKJO0pR0eTpL2h8h5UBShUB62no3JVmWuJSkZtXVPgq/cUWP+zwGfzyHcB5+aRT+AUkVE5QisjVBTNsbk7vsuVPFerJNN+UADPC6qthv6AsJbYLe87i9/b/gIjiSAZNhoRljXHa9oH8Olvv8h4erqhPzTLVFY2LTHh8HAik0fSHItM6/feGo/iheG/kayMd+ecr3XKlc9Tr9SKs92oEcLQ2uZY8B++nM7vxf6fzVef7HveZMZ2oEg2bejhC1edV7HGTTMx17Dj109M5JUr5IS2Rl2jrXwkPejtmswj6R8c5+hoIsciGU95xFyJYV+zMt6VugjxLlc+T71iiqSBCaOkmmNRmuOVD7HNl+X8G+9au2j+syVS+bP0J7LklWzcVIhiw47zKZuZvI6vDkwWWYxHwCtQpOCkJfGc/IqutjjHRlO0NcVyHihOX7GEgeEEx8dTmaitZa1x1vd0lOU8VJpq/La1gimSBiEWidAcz1IcsYXPy9ixZ4B7n3yNZNpHCIr03fvka7ytd9mi+A9YQI8UlC8UWx7Zw7HRZMa34fk+qdFkTtjxjj0DOdNuR0YS/N72F4gAhXZ/eGJyeqspFiWRTk+LvxeYNo21or2ZtOfT09GS8/T+4/7jfPnxvTkZ7ycm0vxCg7avrSdMkSxCohGhORaEUbY4S6MW6oFteWQPR0aSWWXEfRIjyZrJo6hX7nj0lWlWXphxDrB3YCR3yo0gt2PvwEhG9rmHX+b4WIqoBI5u9eH4WKqgEgFyqmA3xYJ2wJHIZPkb31eQYNpqql9s/cmdfGvzxTnbu2tnH93tTTmVgjtaYjzRd4yb5nx2jIXAFEmdExHJTEs1x6OZWlO1yCuHhqc9saqTG7kU69O449FX+PLje4kIxCLBTfrLj+8FyCiTQl0ys+X7jrryNVmObi2iOnZYb2t9Twf7j44wNJ7VUndJUMduLOUX5Rc7MDjGivZmujsWZ1TfYqY27zhGXkSE5niUztY43R3N9HYFORorl7ayvL2Z9ubydDKsFIWCb+ogKKcoCp35Un+R2RIbs/naD/Y5JRIhIhH3HshDCp3ecpz2v3jsVe549BVuuGQd8WjQTqEpGiGR9jk2muL9P7eS2y8/h56OFk6Mp+jpaOH2y8/JqxRXd7UxnsrNu1hMUX2LGbNIapimLEd4GHZbz5nfi51VXa0cGBzPKy+FUgoAjiY9pgY1RYSSE+HWrVjCqwMjiObmuMRcPkwhfIW/2tnHT26/jAuf7+fbzx/M1DbqbImx/bnXeVvvsmnTWPlY7FF9i5nafXxtMOLRICN8eXszpy5rZe2KJfR2BTWoOlviNMfqu3xIIzCezJ9bUUheiAODYwyPp9j9xglefP0Eu984wfB4Ku8Uz5KmKIl00O0zfCXSQdXeUvjUZRvoaosjQNrzEaCrLc5Nl55Ba4ESKSFjSY8dewZ46KVDxKIS+OViEUYSXkmZ/Zs29BRtvRi1hVkkVaAWIqiM8nN0dHrDtJnkkN8XIsDASBLB1SPT4PPqPJZNZ3OUoYnpiqqzuTRFsmlDD58vkOPytt5lfO7hl9lzaKTg+Lt29gUJhZGgjpgI+CgnxlL0R4r3cTRyCG09Y4qkwoRKI3CGB4qjUZouTaWzJcbwRG6IqAAdLYvjMizVF1Eov+PEeCrvuCMj0/t19J/I38MjW14ohHfqdEShm3goX3PLPxc4ksCKao5FSHuTRRlFIOH55uNoABbH/+AaITvBL8wQb1SlkY/feNfaTIRR2HnP10DeiBQqK5/2ddrNPwJzLhUSj0VIpv1pCjxeYsZ4WK05n3x1Vxtpz+foaBL8QIl4qsQiEfNxNACmSOZAJKw/ldWpr977aCwEYTjqTDkP9UyxT/4h2WXlYbK1LG47Apm7tw+0zbFUSFgsMiqTOR6eKmuXl2YpZMqW5JGHjvLlS4I8kEQ66JB446bTbaqqATBFMgtT8zTqsb1rLXHTe89cNIpjKuV68g/RzD8BJ7XO7b9ruYpFtjfHGE0EU5PZRSmXNMcavtZUo2OKJIvQ0miOmdIwSqfUJ/9CZeXjEWFZW4yjo5M1p5YviSORuV2Lmzb0cO3FbwksQc+jNRrh2ovfUvJNPpyajBaYmjRHeePSsIrElIZRbm5531nc9K3n8raKzRedVchS6G5vJun5nLJ0UgEV6m3REhMm8pR5z+5quGPPANufe53ujskKvGF+Ryk3/sU+NWnMnaooEhHZDwwDHpBW1Y0ichJwP7AG2A98RFUH3fq3Ate79W9S1e86+YVMNr16CLh5ti6JsajQ29W2KJXGXEuFG5Xlx/3H2f7c68SjkpOpfvvl5+QtKw/w+9tf4PXBcdK+TywS1Jz6ow+cPW3bha72bHkpCY6zsZinJo25U02L5N2qeiTr8y3AY6r6ORG5xX3+lIicTdD98BzgVOBRETnTdVC8E9gMPEmgSC5jsoNiXkJLZLERltWYdrMCUyYLxJZH9jCW8olHI5mpqrGUz1/t7GPl0pa8N/Jvbb542u+zY89A4BqZ0oo2H4kCkVzZ8gODYyxrjed83xqPWg0ro2zU0h31CuBut3w3cGWW/D5VTajqPmAvcJGIrAQ6VfUJZ4XckzWm4ch+6hQJ3uPR+uh3vVjIjsIShIgIEQkyv1vjuQmCM93I79rZx1LXh2PDKZ2s7+lgaWs872+ZnbMRvrLlYDWsjMpTLUWiwL+IyLMistnJTlbVgwDuPXxMWwUcyBrb72Sr3PJU+TREZLOI7BKRXYcPHy7jYdQOBwbHSrpZGQuHuFLq2cx0Iy/lt1y1NPCbqE6+suUQhOamPGUsmUY1eLcaVkY5qZYieaeqXgC8D7hRRC6ZYd18yRk6g3y6UHWrqm5U1Y3d3d2l720dYE+d1Wft8rYgkslXVBXfV3yFVZ3NJd3IS/kt/+zKn6OzOUqY9xqRoDzKn135c5l1rIaVUWmq4iNR1Tfc+4CI/B/gIuCQiKxU1YNu2iqsmd0PrM4a3gu84eS9eeQNiVVOrT6ForD+7ENvA4rPsSjlt9y0oYc7rrlg1m1baK5RSWSWIKfy/0GRJUBEVYfd8veA24H3AEeznO0nqeofiMg5wN8RKJtTgceA9arqicgzwG8DTxE42/9SVR+a6e9v3LhRd+3aVbHjqyZh1JYlhFWPcv0G9lsatYaIPKuqG/N+VwVFsg74P+5jDPg7Vf2siCwHtgGnAT8DPqyqx9yY/wH8OpAGPqmqDzv5RibDfx8Gfnu28N/FrEgMwzAqRU0pkmpjisQwDKN0ZlIktRT+axiGYdQhpkgMwzCMeWGKxDAMw5gXpkgMwzCMedFwznYROQy8NkW8AjiSZ3VjEjtHM2PnZ3bsHM1MrZ+ft6hq3ozuhlMk+RCRXYWiEYwAO0czY+dnduwczUw9nx+b2jIMwzDmhSkSwzAMY16YIgnYWu0dqAPsHM2MnZ/ZsXM0M3V7fsxHYhiGYcwLs0gMwzCMeWGKxDAMw5gXDaNIRGS1iPyriLwsIrtF5OY864iI3CEie0XkxyJyQTX2tRoUeX42icgJEXnevW6rxr5WCxFpEZGnReQFd47+JM86jXwNFXN+GvoaAhCRqIj8SEQezPNdXV4/VWlsVSXSwO+q6nMi0gE8KyLfU9WfZK3zPmC9e/08cKd7bwSKOT8A31fVD1Zh/2qBBHCpqo6ISBz4gYg8rKpPZq3TyNdQMecHGvsaArgZeBnozPNdXV4/DWORqOpBVX3OLQ8T/JBTe7xfAdyjAU8Cy1y3xkVPkeenoXHXxYj7GHevqdEqjXwNFXN+GhoR6QU+AHytwCp1ef00jCLJRkTWAG8n6KyYzSrgQNbnfhrwZjrD+QH4BTd18bDrXtlQuGmJ5wlaQX9PVe0ayqKI8wONfQ39BfAHgF/g+7q8fhpOkYhIO/APBJ0Wh6Z+nWdIQz1RzXJ+niOot3Me8JfAtxd496qOqnqqej7QC1wkIudOWaWhr6Eizk/DXkMi8kFgQFWfnWm1PLKav34aSpG4edt/AP5WVf8xzyr9wOqsz73AGwuxb7XAbOdHVYfCqQtVfQiIi8iKBd7NmkBVjwM7gMumfNXQ11BIofPT4NfQO4HLRWQ/cB9wqYj8zZR16vL6aRhFIiICfB14WVW/WGC1B4BrXeTExcAJVT24YDtZRYo5PyJyilsPEbmI4Po5unB7WV1EpFtElrnlVuC9wJ4pqzXyNTTr+Wnka0hVb1XVXlVdA1wNPK6qvzpltbq8fhopauudwMeAF90cLsAfAqcBqOpfAQ8B7wf2AmPAry38blaNYs7PVcDHRSQNjANXa2OVRlgJ3C0iUYIb4DZVfVBEfgvsGqK489Po19A0FsP1YyVSDMMwjHnRMFNbhmEYRmUwRWIYhmHMC1MkhmEYxrwwRWIYhmHMC1MkhmEYxrwwRWIYC4CIfFJE2kocs0ZEXqrUPhlGuTBFYhgLwyeBvIrE5V0YRt1iisQwyoyILBGRf3aFCV8SkT8GTgX+VUT+1a0zIiK3i8hTBEUMf8et+5KIfDLPNte5HhbvEJHTReQREXlWRL4vIhsW9ggNI5dGymw3jIXiMuANVf0AgIgsJchQfreqHnHrLAFeUtXbRORC9/3PExTte0pE/g0YdOPfSlCb6ddU9XkReQz4LVV9VUR+HvgqcOkCHp9h5GCZ7YZRZkTkTOC7wDbgQVX9vivUtzFUJK5ESLOqehJ0o1yuqre57/4UOExQd+kpAoXyK6q621VnPgz8NOtPNqvqWQt0eIYxDbNIDKPMqOorzsp4P/A/ReRf8qw2oaqeW85XOjzkBEF/incCuwmmo4+7Uu2GUROYj8QwyoyInAqMqerfAF8ALgCGgY4CQ3YCV4pIm4gsAT4EfN99lwSuJKgI+19cj5h9IvJh97dERM6r3NEYxuyYRWIY5efngM+LiA+kgI8DvwA8LCIHVfXd2Sur6nMi8k3gaSf6mqr+yHWqRFVHXVOk74nIKPBfgTtF5NME7WzvA15YgOMyjLyYj8QwDMOYFza1ZRiGYcwLUySGYRjGvDBFYhiGYcwLUySGYRjGvDBFYhiGYcwLUySGYRjGvDBFYhiGYcyL/x8miZLl4rruWwAAAABJRU5ErkJggg==\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": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "\n",
    "#There is a weak correlation between the variable 'stroke' and 'price.' as such regression will not work well. We can see this using \"regplot\" to demonstrate this.\n",
    "\n",
    "#Code: \n",
    "sns.regplot(x=\"stroke\", y=\"price\", data=df)\n",
    "\n",
    "```\n",
    "\n",
    "</details>\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": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='body-style', ylabel='price'>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"body-style\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We see that the distributions of price between the different body-style categories have a significant overlap, 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": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='engine-location', ylabel='price'>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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IE8m+iPhVZSWNtFtfY6uYmVlNI00k/yLp00CjpPOBbwLfLa5aZmY2UYw0kVwD9AJbgI8Ba4C/KqpSZmY2cYz0yfZG4KsR8WXIptBNsVeKqpiZmU0MI22RbCBLHBWNwH1HvjpmZjbRjDSRHB8RL1dW0vIJwxWQNE3S9yQ9LmmrpCUpfp2kHZIeTq+LqsosldQj6UlJF1bFZ0vakrYtSzMlkmZTvCvFN0mafhjnbmZmR8BIE8kvJf1OZUXSbOBQQ7/2A38WEe8A5gCLJc1M226MiFnptSYdcybZDIdnkM3tfnO6hAZwC7CIbPrdGWk7wELgxYhoA24Ebhjh+ZiZ2REy0j6STwLflLQzrU8FLh+uQJprfVda3iPpcWC4iSvmAXdGxD7g6TR97tmStgGTI2IjgKQVwCVk0+3OA65L5VcBX5Qkz9tuZjZ2RtQiiYgfAW8nmzv948A7ImLzSD8kXXJ6J7AphT4h6RFJX5V0Uoq1AM9VFdueYi1peWh8UJmI6AdeAppqfP4iSd2Sunt7e0dabTMzG4FhE4mk96X3/wJ8AHgb2aWlD6TYIUl6I/At4JMR8Quyy1RvBWaRtVg+X9m1RvEYJj5cmcGBiFsjoj0i2pubm0dSbTMzG6FDXdr6feB+siQyVADfHq6wpGPJksjXIuLbABGxu2r7l4F70up2YFpV8VZgZ4q31ohXl9menrY/EXjhEOdkZmZH0LCJJCKulXQMsDYiVh7OgdOdVbcBj0fEF6riU1P/CcAHgUfT8mrg65K+ALyJrOXzUEQMSNojaQ7ZpbEFwPKqMp3ARuBS4H73j5iZja1DdrZHxH5JnwAOK5GQDfL4EWCLpIdT7NPAFZJmkbVotpE9KU9EbJW0EniM7I6vxRExkMpdCdxO9vzK2vSCLFHdkTrmXyC768vMzMbQSO/aWi/pz4G7gF9WghFx0MtIEfFDavdhrBmmzPXA9TXi3cCZNeKvApcNW3MzMyvUSBPJR8laEB8fEn/Lka2OmZlNNCNNJDPJksi5ZAnlB8CXiqqUmZlNHCNNJF1kk1otS+tXpNh/K6JSZmY2cYw0kfzHiPjtqvXvSfppERUyM7OJZaRjbf0k3X4LgKTfBf61mCqZmdlEMtIWye8CCyQ9m9ZPAx6XtAWIiPitQmpnZmbj3kgTScehdzEzs3o0okQSEc8UXREzM5uYRtpHYmZmVpMTiZmZ5eJEYmZmuTiRmJlZLk4kZmaWixOJmZnl4kRiZma5OJGYmVkuhSUSSdMkfU/S45K2SlqS4idLWi/pqfR+UlWZpZJ6JD0p6cKq+GxJW9K2ZWkaXyQdJ+muFN8kaXpR52NmZrUV2SLpB/4sIt4BzAEWS5oJXANsiIgZwIa0Tto2HziDbEiWmyU1pGPdAiwim8d9Bq8P2bIQeDEi2oAbgRsKPB8zM6uhsEQSEbsi4sdpeQ/wONACzCOby4T0fklangfcGRH7IuJpoAc4W9JUYHJEbIyIAFYMKVM51irgvEprxczMxsaY9JGkS07vBDYBUyJiF2TJBjg17dYCPFdVbHuKtaTlofFBZSKiH3gJaKrx+YskdUvq7u3tPUJnZWZmMAaJRNIbgW8Bn4yIXwy3a41YDBMfrszgQMStEdEeEe3Nzc2HqrKZmR2GQhOJpGPJksjXIuLbKbw7Xa4ivT+f4tuBaVXFW4GdKd5aIz6ojKRJwInAC0f+TMzM7GCKvGtLwG3A4xHxhapNq4HOtNwJ3F0Vn5/uxDqdrFP9oXT5a4+kOemYC4aUqRzrUuD+1I9iZmZjZKQTW43GOcBHgC2SHk6xTwOfBVZKWgg8C1wGEBFbJa0EHiO742txRAykclcCtwONwNr0gixR3SGph6wlMr/A8zEzsxoKSyQR8UNq92EAnHeQMtcD19eIdwNn1oi/SkpEZmZWDj/ZbmZmuTiRmJlZLk4kZmaWixOJmZnl4kRiZma5OJGYmVkuTiRmZpaLE4mZmeXiRGJmZrk4kZiZWS5OJGZmlkuRgzYelZYvX05PT0/Z1RgXKn+HJUuWlFyT8aGtrY2rrrqq7GqYjTknksPU09PDw48+zsAJJ5ddldId86tsxP7N/7675JqUr+EVT4Nj9cuJZBQGTjiZvW+/qOxq2DjS+MSasqtgVhr3kZiZWS5FzpD4VUnPS3q0KnadpB2SHk6vi6q2LZXUI+lJSRdWxWdL2pK2LUuzJJJmUrwrxTdJml7UuZiZ2cEV2SK5HeioEb8xImal1xoASTPJZjc8I5W5WVJD2v8WYBHZ1Lszqo65EHgxItqAG4EbijoRMzM7uMISSUQ8QDb97UjMA+6MiH0R8TTQA5wtaSowOSI2prnYVwCXVJXpSsurgPMqrRUzMxs7ZfSRfELSI+nS10kp1gI8V7XP9hRrSctD44PKREQ/8BLQVOsDJS2S1C2pu7e398idiZmZjXkiuQV4KzAL2AV8PsVrtSRimPhwZQ4MRtwaEe0R0d7c3HxYFTYzs+GNaSKJiN0RMRAR+4EvA2enTduBaVW7tgI7U7y1RnxQGUmTgBMZ+aU0MzM7QsY0kaQ+j4oPApU7ulYD89OdWKeTdao/FBG7gD2S5qT+jwXA3VVlOtPypcD9qR/FzMzGUGEPJEr6BvAe4BRJ24FrgfdImkV2CWob8DGAiNgqaSXwGNAPLI6IgXSoK8nuAGsE1qYXwG3AHZJ6yFoi84s6FzMzO7jCEklEXFEjfNsw+18PXF8j3g2cWSP+KnBZnjqamVl+frLdzMxycSIxM7NcnEjMzCwXJxIzM8vFicTMzHJxIjEzs1ycSMzMLBcnEjMzy8WJxMzMcnEiMTOzXJxIzMwsFycSMzPLxYnEzMxycSIxM7NcnEjMzCwXJxIzM8ulsEQi6auSnpf0aFXsZEnrJT2V3k+q2rZUUo+kJyVdWBWfLWlL2rYsTblLmpb3rhTfJGl6UediZmYHV9gMiWTT434RWFEVuwbYEBGflXRNWv9LSTPJpso9A3gTcJ+kt6Xpdm8BFgEPAmuADrLpdhcCL0ZEm6T5wA3A5QWeDwA7duyg4ZWXaHxiTdEfZRNIwyt97NjRX3Y1zEpRWIskIh4gm0u92jygKy13AZdUxe+MiH0R8TTQA5wtaSowOSI2RkSQJaVLahxrFXBepbViZmZjp8gWSS1TImIXQETsknRqireQtTgqtqfYr9Py0HilzHPpWP2SXgKagJ8N/VBJi8haNZx22mm5TqClpYX/t28Se99+Ua7j2NGl8Yk1tLRMKbsaZqUYL53ttVoSMUx8uDIHBiNujYj2iGhvbm4eZRXNzKyWsU4ku9PlKtL78ym+HZhWtV8rsDPFW2vEB5WRNAk4kQMvpZmZWcHGOpGsBjrTcidwd1V8froT63RgBvBQugy2R9Kc1P+xYEiZyrEuBe5P/ShmZjaGCusjkfQN4D3AKZK2A9cCnwVWSloIPAtcBhARWyWtBB4D+oHF6Y4tgCvJ7gBrJLtba22K3wbcIamHrCUyv6hzMTOzgysskUTEFQfZdN5B9r8euL5GvBs4s0b8VVIiMjOz8oyXznYzM5ugnEjMzCwXJxIzM8vFicTMzHIZ6yfbjwoNr7zgsbaAY179BQD7j59cck3K1/DKC4CfbLf65ERymNra2squwrjR07MHgLa3+D9QmOLvhtUtJ5LDdNVVV5VdhXFjyZIlANx0000l18TMyuQ+EjMzy8WJxMzMcnEiMTOzXJxIzMwsFycSMzPLxYnEzMxycSIxM7NcnEjMzCyXUhKJpG2Stkh6WFJ3ip0sab2kp9L7SVX7L5XUI+lJSRdWxWen4/RIWpZmUTQzszFUZovkvRExKyLa0/o1wIaImAFsSOtImkk2++EZQAdws6SGVOYWYBHZ1Lwz0nYzMxtD42mIlHlkU/MCdAHfB/4yxe+MiH3A02lq3bMlbQMmR8RGAEkrgEt4fSreo9by5cvp6ekpuxqv1aEyVEpZ2traPHSNWYnKapEEcK+kzZIWpdiUiNgFkN5PTfEW4LmqsttTrCUtD40fQNIiSd2Sunt7e4/gadS3xsZGGhsby66GmZWsrBbJORGxU9KpwHpJTwyzb61+jxgmfmAw4lbgVoD29vaa+0wk/vVtZuNJKS2SiNiZ3p8H/gk4G9gtaSpAen8+7b4dmFZVvBXYmeKtNeJmZjaGxjyRSHqDpN+oLAMXAI8Cq4HOtFsncHdaXg3Ml3ScpNPJOtUfSpe/9kiak+7WWlBVxszMxkgZl7amAP+U7tSdBHw9ItZJ+hGwUtJC4FngMoCI2CppJfAY0A8sjoiBdKwrgduBRrJO9qO+o93MbLxRxITvMjgs7e3t0d3dXXY1zMwmFEmbqx7XGMRPtpuZWS5OJGZmlosTiZmZ5eJEYmZmudRdZ7ukXuCZsutxFDkF+FnZlTCrwd/NI+vNEdFca0PdJRI7siR1H+xODrMy+bs5dnxpy8zMcnEiMTOzXJxILK9by66A2UH4uzlG3EdiZma5uEViZma5OJGYmVkuTiR2AElXS3pc0tdyHme6pD86UvUys/HJicRq+ThwUUR8qBKQNJopB6YDTiRWKGVG/X+ZpIYjWZ965ERig0j6EvAWYLWklyTdKuleYIWkN0vaIOmR9H5aKnO7pGWS/k3Sv0u6NB3us8C7JT0s6VMlnZIdhVJr93FJNwM/Bv6XpB+l7+Znqvb7jqTNkrZKWlQVf1nS30jaBPxeCadwVPFdW3YASduAduATwAeAcyNir6TvAqsiokvSR4GLI+ISSbcDbwAuB94OrI6INknvAf48It5fwmnYUUzSdODfgf8ETAYuBT4GiGxW1c9FxAOSTo6IFyQ1Aj8Cfj8i+iQFcHlErCznDI4ubpHYoayOiL1p+feAr6flO4Bzq/b7TkTsj4jHyGbBNCvaMxHxINl03RcAPyFrnbydbEpugKsl/RR4EJhWFR8AvjW21T16lTHVrk0svxxmW3Vzdl/Vsgqqi1m1yndTwP+JiH+o3phaxHOB34uIVyR9Hzg+bX61aspuy8ktEjsc/wbMT8sfAn54iP33AL9RaI3M4J+Bj0p6I4CkFkmnAicCL6Yk8nZgTpmVPJo5kdjhuBr475IeAT4CLDnE/o8A/ZJ+6s52K0pE3Et2yXWjpC3AKrIfMOuASen7+r/JLm9ZAdzZbmZmubhFYmZmuTiRmJlZLk4kZmaWixOJmZnl4kRiZma5OJGYjZKkN0ladYSONV3So0fiWFXH/GNJb6pa/4qkmUfyM8zAT7abjVpE7CQb42m8+mPgUWAnQET8j1JrY0ctt0isLkn6sKSH0sjE/yCpIY0Ie316gPJBSVPSvm9N6z9KI8a+nOKvtSLSr/9vS1on6SlJn6v6rAskbZT0Y0nfrDyBPUzdjpf0fyVtkfQTSe9N8QZJf5fij0i6KsX/OtXt0TRas9IIzO3A19I5Nkr6vqT2VOaKdJxHJd1Q9dk1/wZmw3Eisboj6R1kIxWfExGzyAbw+xDZCMYPRsRvAw8Af5KK3ATcFBHvIv26P4hZ6bhnAZdLmibpFOCvgLkR8TtAN/Cnh6jiYoCIOAu4AuiSdDywCDgdeGdE/BZQmXjsixHxrog4E2gE3h8Rq9JnfSgiZlUNvEm63HUD8L5U53dJuiRtPtjfwOygnEisHp0HzAZ+JOnhtP4W4FfAPWmfzWQTc0E26vE30/LXObgNEfFSRLwKPAa8mWx8p5nAv6bP6kzx4ZxLNroyEfEE8AzwNrIBCL8UEf1p2wtp//dK2pSGB3kfcMYhjv8u4PsR0ZuO9TXgP6dtB/sbmB2U+0isHgnoioilg4LSn8frYwYNcPj/PqpHQK6UF7A+Iq4Y8lm/C1RGq/1rsnHJqut3sHoPGtMotVRuBtoj4jlJ1/H6CLcHM9zozL/O+TewOuQWidWjDcClaYRYJJ0sabhWwoPAf03L84fZ72Blz5HUlj7rBElvi4hN6ZLTrIhYPaTMA2SX2pD0NuA04EngXuB/Kk17LOlkXk8aP0t9L9Wd/wcbfXkT8PuSTlE2zewVwL8c5nmZvcaJxOpOmnzrr4B708iw64GpwxT5JPCnkh5K+710GJ/VS3b31DfSZz1INvHScG4GGtKlqruAP46IfcBXgGeBR9JkTX8UET8HvgxsAb5DNgtgxe3Alyqd7VV12gUsBb4H/BT4cUTcPdJzMhvKo/+aHYKkE4C9ERGS5gNXRMS8sutlNl74+qfZoc0GvihJwM+Bj5ZbHbPxxS0SMzPLxX0kZmaWixOJmZnl4kRiZma5OJGYmVkuTiRmZpbL/wdpj06ENSSTagAAAABJRU5ErkJggg==\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": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='drive-wheels', ylabel='price'>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Q2XRn1W3A8xHxV0XxyUW7fRJ4Li2vBZamO7HOJmv5PJH6WvZKmpuOeTlwX1GZlrR8KfCQ+0esFrW1tbFlyxba2tqqXRWz43bMPpLUcvjsOzj2hcBvAx/rd6vvX6ZbebcAvwr8t/Q5W4E1wDbgX4AVEXEwHetK4FagE/ghWUc7ZIlqYuqYv5rsCXyzmtLT00N7ezsRQXt7u1slVnMGe9fWBkmfB+4BflYIRsRRLyNFxHcp3YexboAyq4HVJeIdwHkl4vuAywasudkw19bWRqEh3dfXR1tbG1dffXWVa2U2eIN9juR3ye7W+g7QUfQyszJt2LCBAwcOAHDgwAHWr19f5RqZHZ/BJpKZwP8GngGeBm4ge3DQzMo0b9486uvrAaivr2f+/PlVrpHZ8RlsImkD3ge0kiWR96WYmZWppaWFNOoPdXV1tLS0HKOE2fAy2ETy3oj4rxHxr+m1HHhvnhUzGy0aGhpYtGgRkli0aBETJx7xTK3ZsDbYRPKUpLmFFUn/CfhePlUyG31aWlo4//zz3RqxmqTBPHaRxsl6L/BSCp0FPA/0ARER5+dWwyHW3NwcHR3Hvk+gtbWVzs7OCtRo6Gzfvh2AGTNmVLkmx2f69OmsWrWq2tUwswFI2hwRzaW2Dfb234XH3mVk6ezs5Klnt9F34unVrsqg6e3sR8HmH/6kyjUZvLq3PBCBWa0bVCKJiB/lXZHhqO/E09k385gjwVgZxm27v9pVMLMyDbaPxMzMrCQnEjMzK4sTiZmZlcWJxMzMyuJEYmZmZXEiMTOzsjiRmJlZWZxIzMysLLklEklTJf2rpOclbZV0VYqfLmmDpO3p/bSiMtdI6pT0gqQFRfHZaVbFTkmtacpd0rS896T445Km5XU+ZmZWWp4tkl7gDyPifcBcYIWkmWTT4W6MiBnAxrRO2raUbJ6ThcCNksakY90ELCebx30Gh4ZsWQa8FhHTgeuB63I8HzMzKyG3RBIROyPi+2l5L9kgj1OAJRyay6QNuCQtLwHujoj9EfEi2fzscyRNBiZExKbIRpi8s1+ZwrHuBS4qtFbMzKwyKtJHki45XQA8DkyKiJ2QJRvgjLTbFODlomJdKTYlLfePH1YmInqBN4AjJnOQtFxSh6SO7u7uITorMzODCiQSSScD3wI+FxE/HWjXErEYID5QmcMDEbdERHNENDc2Nh6rymYV19PTw8qVK9mzZ0+1q2J23HJNJJLqyZLI30bEt1N4V7pcRXrfneJdwNSi4k3AKyneVCJ+WBlJY4FTAI9LbjWnra2NLVu20NbmGayt9uR515aA24DnI+KvijatBQrTwLUA9xXFl6Y7sc4m61R/Il3+2itpbjrm5f3KFI51KfBQDGamLrNhpKenh3Xr1hERrFu3zq0Sqzl5tkguBH4b+Jikp9NrMfAVYJ6k7cC8tE5EbAXWANuAfwFWRMTBdKwrgVvJOuB/CLSn+G3AREmdwNWkO8DMaklbWxu9vb0AHDhwwK0SqzmDnSHxuEXEdyndhwFw0VHKrAZWl4h3AOeViO8DLiujmmZVt379egoN6YjggQce4Oqrr65yrcwGz0+2m1XZpEmTBlw3G+6cSMyq7Cc/+cmA62bDnROJWZWdeeaZA67b8Dfab992IjGrMrdIat9ov33bicSsytwiqW09PT20t7cTEbS3t4/KVokTiVmV7dq1a8B1G97a2tr+/a67vr6+UdkqcSIxq7L58+dTGGtUEgsWLDhGCRtONmzYwIEDB4DsOaD169dXuUaV50RiVmUtLS2MHZs90lVfX09LS8sxSthwMm/ePOrr64Hs+5s/f36Va1R5uT2QWOu6urqoe+sNxm27v9pVGdHq3tpDV1dvtatRVQ0NDSxevJi1a9eyePFiJk48YgBrG8ZaWlpob88G26irqxuVPwTcIjEbBlpaWjj//PNH5R+hWtfQ0MCiRYuQxKJFi0blDwG3SI6iqamJXfvHsm/mx6tdlRFt3Lb7aWryXUoNDQ3ccMMN1a6GvUMtLS3s2LFj1P4QcCIxMyvTaP8h4EtbZsPAaH8y2mqbE4nZMDDan4y22uZEYlZlfjLaal2eMyTeLmm3pOeKYtdK+nG/ia4K266R1CnpBUkLiuKzJT2btrWmWRJJMynek+KPS5qW17mY5clPRluty7Oz/Q7ga8Cd/eLXR8T/Kg5ImgksBc4F3gU8KOk9aYbEm4DlwGPAOmAh2QyJy4DXImK6pKXAdcCn8zsdM2htbaWzs3NIj7llyxb6+vqA7MnotWvXsmPHjiH9jOnTp7Nq1aohPaZZQW4tkoh4BHh1kLsvAe6OiP0R8SLZlLpzJE0GJkTEpjQX+53AJUVlCj/d7gUuKrRWzGrJaaedNuC62XBXjdt/PyvpcqAD+MOIeA2YQtbiKOhKsQNpuX+c9P4yQET0SnoDmAj09P9AScvJWjWcddZZQ3oyNrrk8au+p6eHT33qU0QEJ5xwArfeeuuofKjNalelO9tvAs4BZgE7ga+meKmWRAwQH6jMkcGIWyKiOSKaGxsbj6vCZnlraGjg9NNPBxi1T0ZbbatoIomIXRFxMCL6gG8Ac9KmLmBq0a5NwCsp3lQiflgZSWOBUxj8pTSzYeXMM8/kpJNOGrVPRlttq2giSX0eBZ8ECnd0rQWWpjuxzgZmAE9ExE5gr6S5qf/jcuC+ojKFf3WXAg9F4dYXsxpTX1/PjBkz3BqxmpRbH4mkvwc+CjRI6gK+BHxU0iyyS1A7gCsAImKrpDXANqAXWJHu2AK4kuwOsPFkd2u1p/htwF2SOslaIkvzOhczMzu63BJJRPxWifBtA+y/GlhdIt4BnFcivg+4rJw6mplZ+fxku5mZlcWj/w6g7q1Xa2piK+37KQAxbkKVazJ4dW+9CngYebNa5kRyFNOnT692FY7b9u17AZhxTi39YT6zJv9bm9khTiRHUYvDSRTq3NraWuWamNlo4j4SMzMrixOJmZmVxYnEzMzK4kRiZmZlcSIxM7OyOJGYmVlZfPuvmY0aecxwCdDVlU2b1NTUdIw9j18tzG7pRGJmw0pef+wh+4P/85//fMiPWzhmHsfu6urK7b/HUCUpJxIzG1Y6Ozt5autTcGoOBxdwYg7H7cve3jzxzSE/9Ju8SfePu4f8uLw+dIdyIjGz4edU6PtoX7VrMaLVPTx0XeTubDczs7I4kZiZWVnynCHxduDjwO6IOC/FTgfuAaaRzZD4mxHxWtp2DbAMOAisiogHUnw2h2ZIXAdcFREh6QTgTmA2sAf4dETsyOt8rLbk2WGbh+3btwO1N1hoLdxRZPnLs4/kDuBrZH/sC74IbIyIr0j6Ylr/I0kzyabKPRd4F/CgpPek6XZvApYDj5ElkoVk0+0uA16LiOmSlgLXAZ/O8XyshnR2dvL/nvs+Z5188Ng7DwO/cCC7OLBvx5NVrsngvfTmmGpXwYaJPKfafUTStH7hJWTzuAO0AQ8Df5Tid0fEfuDFNA/7HEk7gAkRsQlA0p3AJWSJZAlwbTrWvcDXJCkiIp8zslpz1skH+ZPmob+LxjJ/1nFytatgw0Sl+0gmRcROgPR+RopPAV4u2q8rxaak5f7xw8pERC/wBjCx1IdKWi6pQ1JHd3cOt9GZmY1iw6WzXSViMUB8oDJHBiNuiYjmiGhubGx8h1U0M7NSKp1IdkmaDJDed6d4FzC1aL8m4JUUbyoRP6yMpLHAKcCrudXczMxKqnQiWQu0pOUW4L6i+FJJJ0g6G5gBPJEuf+2VNFeSgMv7lSkc61LgIfePmJlVXp63//49Wcd6g6Qu4EvAV4A1kpYBLwGXAUTEVklrgG1AL7Ai3bEFcCWHbv9tTy+A24C7Usf8q2R3fZlZjevq6oI3hvbJayvhdeiKrmPuNhh53rX1W0fZdNFR9l8NrC4R7wDOKxHfR0pEZmZWPR5ry8yGlaamJrrV7bG2clb3cB1NU4Zm2Hu3Hc3MrCxukdiI1NXVxc/2jvFDczn60d4xnNQ1NNfYrbY5kZjZ8PN6jXW2FwZQqKXfLa9z6PHuMjmR2IjU1NTEvt6dHiIlR3/WcTLjcppattYUBt2cMWVGlWtyHKYM3X9rJxIzG1byHE241kaFhtoYYdmJxMysTOPHj692FarKicTMRo3h/su+VjmR2Ij10pu1c9fWrreyjuVJJ9bOsxMvvTmG91S7EjYsOJFUQV7XafOcZa8WrtMWq7UO27fTdzduWu101r6H2vvvbPlwIhlBRvt12mK1lPTgUH1bW1urXBOz4+dEUgW19kfOzGwgNfTEj5mZDUdOJGZmVhYnEjMzK0tVEomkHZKelfS0pI4UO13SBknb0/tpRftfI6lT0guSFhTFZ6fjdEpqTbMomplZBVWzRfKrETErIprT+heBjRExA9iY1pE0k2z2w3OBhcCNksakMjcBy8mm5p2RtpuZWQUNp7u2lpBNzQvQBjwM/FGK3x0R+4EX09S6cyTtACZExCYASXcCl3BoKl6zIVeLzwBB7T0HZLWlWi2SANZL2ixpeYpNioidAOn9jBSfArxcVLYrxaak5f7xI0haLqlDUkd3d/cQnobZ0Bg/fryfA7KaVa0WyYUR8YqkM4ANkn4wwL6l+j1igPiRwYhbgFsAmpubS+5jNhj+VW92pKq0SCLilfS+G/hHYA6wS9JkgPS+O+3eBUwtKt4EvJLiTSXiZmZWQRVPJJJOkvSLhWVgPvAcsBZoSbu1APel5bXAUkknSDqbrFP9iXT5a6+kuelurcuLypiZWYVU49LWJOAf0526Y4G/i4h/kfQksEbSMuAl4DKAiNgqaQ2wDegFVkTEwXSsK4E7gPFknezuaDczqzBFjK4ug+bm5ujo6Kh2NczMaoqkzUWPaxzGT7abmVlZnEjMzKwsTiRmZlYWJxIzMyvLqOtsl9QN/Kja9chRA9BT7UrYO+LvrraN9O/v3RHRWGrDqEskI52kjqPdWWHDm7+72jaavz9f2jIzs7I4kZiZWVmcSEaeW6pdAXvH/N3VtlH7/bmPxMzMyuIWiZmZlcWJxMzMyuJEMkpI+qik+6tdj9FO0ipJz0v62+Mst0NSQ171smOTNEbSU+/035GkN4e6TsPFcJqz3Y5DmoNFEdFX7brYcfkDYFFEvFjtithxuwp4HphQ7YoMN26R1BBJ09Kv2RuBfwNuS/GrJP1bWj5H0nfT8kJJP0jrv1G1ihsAkr4O/BKwVlIoc6qkPkkfTvs8Kmm6pImS1qdfwDdTemppqxBJTcCvAbem9TMkbU7L70/f51lp/YeSTpR0tqRNkp6U9KfVq33+nEhqz3uBO4EPAuel2IeAPZKmAP8ZeFTSOOAbwCfS9jOrUFcrEhG/TzYd9K8CDwAzyb6vzcCHJJ0ANEVEJ/Al4LsRcQHZLKFnVafWlvw18AWgD/59mvBxkiaQ/fvqIPsO3w3sjoi3gL8BboqIDwA/qUqtK8SJpPb8KCIei4ifACenaYunAn8HfJjsf+pHgV8GXoyI7ZHd4/3NqtXYSnmU7Pv6MPAXZAnlA8CTafuHSd9ZRPwz8FoV6miApI+TJYfN/Tb9X+BCsu/qzzn83x9p29+n5bsqUNWqcSKpPT8rWt4E/A7wAtn/vB8ia6l8L233Q0LDV+H7mgOsA04FPgo8UrSPv7/h4ULg1yXtAO4GPibpmxz6Dt8N3Ae8n+wHwaj7Dp1IatsjwOfT+1Nkl0z2R8QbwA+AsyWdk/b9repU0Y7iceBXgL6I2Ac8DVzBoV+zjwD/BUDSIuC0KtTRgIi4JiKaImIasBR4KCI+Q/YdfQbYnm56eRVYzKEfct9L+0P6LkcqJ5La9ijZZa1HIuIg8DLwXYD0x2k58M+ps30kD51fcyJiP9n39VgKPQr8IvBsWv8y8GFJ3wfmAy9VvJI2oIjYkRYLLZDvAq9HROEy5FXACklPAqdUuHoV5SFSzMysLG6RmJlZWZxIzMysLE4kZmZWFicSMzMrixOJmZmVxYnEbACSrpX0+RLx35d0eYXqMCSjxnoEaMuLR/81O06SxkbE16tdD7Phwi0Ss34k/bGkFyQ9SDZIJpIelvTnkr4DXFVoqUh6n6QnispOk7QlLc+W9B1JmyU9IGlyic/6gqRVafl6SQ+l5YvSMByF/VZLekbSY5ImpVijpG+l0WWflHRhip8k6fYUe0rSkhKf+xFJT6fXU2nMNrN3xInErIik2WTDWlxANvT+B4o2nxoRH4mIrxYCEfE88AuSfimFPg2skVQP3ABcGhGzgduB1SU+8hGy8ZoAmskG4qwnjeKc4icBj0XE+9P+v5fifwNcn0aX/RRpiHPgj8mG8fgA2bA5/1PSSf0+9/PAioiYlT7/58f8j2N2FL60ZXa4DwH/mIYBR9Laom33HKXMGuA3ga+QJZJPk7VkzgM2ZHOQMQbYWaLsZmB2ahHsB75PllA+BKxK+7wN3F+0/7y0fDEwMx0fYEI6znyyQQYLfTvjOHIY+u8Bf5Vmavx2RHQd5dzMjsmJxOxIRxs36GdHid8D/IOkbwMREdsl/Qdga0R8sHhHSVOBf0qrX4+Ir6dRZX+HbFjyLWStiHPIZuMDOBCHxjI6yKF/t3XAByPisNZEmj3zUxHxQr/4pH8/wYivSPpnskEGH5N0cUT84CjnZzYgX9oyO9wjwCcljU+/7j9xrAIR8UOyP/D/g0OtlheARkkfBJBUL+nciHg5ImalV6HDvngU50eB3weejmMPhLce+GxhRdKstPgAsDIlFCRd0L+gpHMi4tmIuI5sUqZfPtZ5mh2NE4lZkYj4PlkyeBr4Fof6KY7lHrIhxdek47wNXApcJ+mZdLxfOUrZR4HJwKaI2AXsG+TnrgKaJW2RtI0sAQH8KVAPbJH0XFrv73OSnkt1+znQPojPMyvJo/+amVlZ3CIxM7OyOJGYmVlZnEjMzKwsTiRmZlYWJxIzMyuLE4mZmZXFicTMzMry/wHZ7Sb7DZCl1AAAAABJRU5ErkJggg==\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": 20,
   "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": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The default setting of \"describe\" skips variables of type object. We can apply the method \"describe\" on the variables of type 'object' as follows:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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": 21,
     "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 <code>df['drive-wheels']</code>, not two brackets <code>df[['drive-wheels']]</code>.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fwd    118\n",
       "rwd     75\n",
       "4wd      8\n",
       "Name: drive-wheels, dtype: int64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can convert the series to a dataframe as follows:\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>drive-wheels</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     drive-wheels\n",
       "fwd           118\n",
       "rwd            75\n",
       "4wd             8"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].value_counts().to_frame()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's repeat the above steps but save the results to the dataframe \"drive_wheels_counts\" and rename the column  'drive-wheels' to 'value_counts'.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "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": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "drive_wheels_counts = df['drive-wheels'].value_counts().to_frame()\n",
    "drive_wheels_counts.rename(columns={'drive-wheels': 'value_counts'}, inplace=True)\n",
    "drive_wheels_counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's rename the index to 'drive-wheels':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "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": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "drive_wheels_counts.index.name = 'drive-wheels'\n",
    "drive_wheels_counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can repeat the above process for the variable 'engine-location'.\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>value_counts</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-location</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>front</th>\n",
       "      <td>198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rear</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 value_counts\n",
       "engine-location              \n",
       "front                     198\n",
       "rear                        3"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# engine-location as variable\n",
    "engine_loc_counts = df['engine-location'].value_counts().to_frame()\n",
    "engine_loc_counts.rename(columns={'engine-location': 'value_counts'}, inplace=True)\n",
    "engine_loc_counts.index.name = 'engine-location'\n",
    "engine_loc_counts.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>After examining the value counts of the engine location, we see that 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, so 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": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['rwd', 'fwd', '4wd'], dtype=object)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>If we want to know, on average, which type of drive wheel is most valuable, we can group \"drive-wheels\" and then average them.</p>\n",
    "\n",
    "<p>We can select the columns 'drive-wheels', 'body-style' and 'price', then assign it to the variable \"df_group_one\".</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "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": 29,
   "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": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# grouping results\n",
    "df_group_one = df_group_one.groupby(['drive-wheels'],as_index=False).mean()\n",
    "df_group_one"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>From our data, it seems rear-wheel drive vehicles are, on average, the most expensive, while 4-wheel and front-wheel are approximately the same in price.</p>\n",
    "\n",
    "<p>You can also group by multiple variables. For example, let's group by both 'drive-wheels' and 'body-style'. This groups the dataframe by the unique combination of 'drive-wheels' and 'body-style'. We can store the results in the variable 'grouped_test1'.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# grouping results\n",
    "df_gptest = df[['drive-wheels','body-style','price']]\n",
    "grouped_test1 = df_gptest.groupby(['drive-wheels','body-style'],as_index=False).mean()\n",
    "grouped_test1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>This grouped data is much easier to visualize when it is made into a pivot table. A pivot table is like an Excel spreadsheet, with one variable along the column and another along the row. We can convert the dataframe to a pivot table using the method \"pivot\" to create a pivot table from the groups.</p>\n",
    "\n",
    "<p>In this case, we will leave the drive-wheels 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": 31,
   "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",
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       "\n",
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       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>body-style</th>\n",
       "      <th>convertible</th>\n",
       "      <th>hardtop</th>\n",
       "      <th>hatchback</th>\n",
       "      <th>sedan</th>\n",
       "      <th>wagon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7603.000000</td>\n",
       "      <td>12647.333333</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>11595.0</td>\n",
       "      <td>8249.000000</td>\n",
       "      <td>8396.387755</td>\n",
       "      <td>9811.800000</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>23949.6</td>\n",
       "      <td>24202.714286</td>\n",
       "      <td>14337.777778</td>\n",
       "      <td>21711.833333</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   price                                            \\\n",
       "body-style   convertible       hardtop     hatchback         sedan   \n",
       "drive-wheels                                                         \n",
       "4wd                  NaN           NaN   7603.000000  12647.333333   \n",
       "fwd              11595.0   8249.000000   8396.387755   9811.800000   \n",
       "rwd              23949.6  24202.714286  14337.777778  21711.833333   \n",
       "\n",
       "                            \n",
       "body-style           wagon  \n",
       "drive-wheels                \n",
       "4wd            9095.750000  \n",
       "fwd            9997.333333  \n",
       "rwd           16994.222222  "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_pivot = grouped_test1.pivot(index='drive-wheels',columns='body-style')\n",
    "grouped_pivot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Often, we won't have data for some of the pivot cells. We can fill these missing cells with the value 0, but any other value could potentially be used as well. It should be mentioned that missing data is quite a complex subject and is an entire course on its own.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "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",
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>body-style</th>\n",
       "      <th>convertible</th>\n",
       "      <th>hardtop</th>\n",
       "      <th>hatchback</th>\n",
       "      <th>sedan</th>\n",
       "      <th>wagon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7603.000000</td>\n",
       "      <td>12647.333333</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>11595.0</td>\n",
       "      <td>8249.000000</td>\n",
       "      <td>8396.387755</td>\n",
       "      <td>9811.800000</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>23949.6</td>\n",
       "      <td>24202.714286</td>\n",
       "      <td>14337.777778</td>\n",
       "      <td>21711.833333</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   price                                            \\\n",
       "body-style   convertible       hardtop     hatchback         sedan   \n",
       "drive-wheels                                                         \n",
       "4wd                  0.0      0.000000   7603.000000  12647.333333   \n",
       "fwd              11595.0   8249.000000   8396.387755   9811.800000   \n",
       "rwd              23949.6  24202.714286  14337.777778  21711.833333   \n",
       "\n",
       "                            \n",
       "body-style           wagon  \n",
       "drive-wheels                \n",
       "4wd            9095.750000  \n",
       "fwd            9997.333333  \n",
       "rwd           16994.222222  "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_pivot = grouped_pivot.fillna(0) #fill missing values with 0\n",
    "grouped_pivot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question 4:</h1>\n",
    "\n",
    "<p>Use the \"groupby\" function to find the average \"price\" of each car based on \"body-style\".</p>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "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": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df_gptest1 = df[['drive-wheels','body-style','price']]\n",
    "grouped_test2 = df_gptest1.groupby(['body-style'],as_index=False).mean()\n",
    "grouped_test2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\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",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you did not import \"pyplot\", let's do it again.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "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": 37,
   "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' on 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": 38,
   "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. 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": [
    "<p><b>Pearson Correlation</b></p>\n",
    "<p>The Pearson Correlation measures the linear dependence between two variables X and Y.</p>\n",
    "<p>The resulting coefficient is a value between -1 and 1 inclusive, where:</p>\n",
    "<ul>\n",
    "    <li><b>1</b>: Perfect 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>: Perfect 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": 39,
   "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": 39,
     "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": 40,
   "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": 41,
   "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": [
    "<h4>Conclusion:</h4>\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": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.809574567003656  with a P-value of P =  6.369057428259557e-48\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['horsepower'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Conclusion:</h4>\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": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.690628380448364  with a P-value of P =  8.016477466158986e-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": [
    "<h4>Conclusion:</h4>\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": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.7512653440522674  with a P-value of P = 9.200335510481516e-38\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['width'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Conclusion:\n",
    "\n",
    "Since the p-value is < 0.001, the correlation between width and price is statistically significant, and the linear relationship is quite strong (\\~0.751).\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": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8344145257702845  with a P-value of P =  2.189577238893816e-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": [
    "<h4>Conclusion:</h4>\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": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8723351674455186  with a P-value of P = 9.265491622197335e-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": [
    "<h4>Conclusion:</h4>\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": 47,
   "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": [
    "<h4>Conclusion:</h4>\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": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.6865710067844677  with a P-value of P =  2.321132065567674e-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": [
    "<h4>Conclusion:</h4>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between city-mpg and price is statistically significant, and the coefficient of about -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": 49,
   "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 < 0.001, the correlation between highway-mpg and price is statistically significant, and the coefficient of about -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 our calculated score value is.</p>\n",
    "\n",
    "<p>If our price variable is strongly correlated with the variable we are analyzing, we 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>To see if different types of 'drive-wheels' impact  'price', we group the data.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "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": 50,
     "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": 51,
   "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": 51,
     "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": 52,
   "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": 52,
     "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": 53,
   "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",
    "\n",
    "Let's examine them separately.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### fwd and rwd\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "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": 55,
   "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": 56,
   "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",
    "\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/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\" target=\"_blank\">Joseph Santarcangelo</a>\n",
    "\n",
    "### Other Contributors\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\" 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/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\" target=\"_blank\">Fiorella Wenver</a>\n",
    "\n",
    "<a href=\"https:// 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",
    "| 2020-10-30        | 2.1     | Lakshmi    | changed URL of csv                 |\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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