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": 35,
   "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": 36,
   "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": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 37,
     "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": 38,
   "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": 39,
   "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": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df['peak-rpm'].dtypes"
   ]
  },
  {
   "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": 41,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>symboling</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.466264</td>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.365404</td>\n",
       "      <td>-0.242423</td>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.233118</td>\n",
       "      <td>-0.110581</td>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.008245</td>\n",
       "      <td>-0.182196</td>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.279740</td>\n",
       "      <td>-0.035527</td>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.066171</td>\n",
       "      <td>-0.196735</td>\n",
       "      <td>0.196735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>normalized-losses</th>\n",
       "      <td>0.466264</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.101546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wheel-base</th>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>-0.307237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>length</th>\n",
       "      <td>-0.365404</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>-0.211187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>width</th>\n",
       "      <td>-0.242423</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>-0.244356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>height</th>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>-0.281578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>curb-weight</th>\n",
       "      <td>-0.233118</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>-0.221046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>-0.110581</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>-0.070779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>-0.054458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.008245</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>-0.241303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>-0.182196</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.985231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>0.169053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>0.279740</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.475812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-mpg</th>\n",
       "      <td>-0.035527</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>-0.265676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>-0.198690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.110326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-L/100km</th>\n",
       "      <td>0.066171</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>0.241282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diesel</th>\n",
       "      <td>-0.196735</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gas</th>\n",
       "      <td>0.196735</td>\n",
       "      <td>0.101546</td>\n",
       "      <td>-0.307237</td>\n",
       "      <td>-0.211187</td>\n",
       "      <td>-0.244356</td>\n",
       "      <td>-0.281578</td>\n",
       "      <td>-0.221046</td>\n",
       "      <td>-0.070779</td>\n",
       "      <td>-0.054458</td>\n",
       "      <td>-0.241303</td>\n",
       "      <td>-0.985231</td>\n",
       "      <td>0.169053</td>\n",
       "      <td>0.475812</td>\n",
       "      <td>-0.265676</td>\n",
       "      <td>-0.198690</td>\n",
       "      <td>-0.110326</td>\n",
       "      <td>0.241282</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   symboling  normalized-losses  wheel-base    length  \\\n",
       "symboling           1.000000           0.466264   -0.535987 -0.365404   \n",
       "normalized-losses   0.466264           1.000000   -0.056661  0.019424   \n",
       "wheel-base         -0.535987          -0.056661    1.000000  0.876024   \n",
       "length             -0.365404           0.019424    0.876024  1.000000   \n",
       "width              -0.242423           0.086802    0.814507  0.857170   \n",
       "height             -0.550160          -0.373737    0.590742  0.492063   \n",
       "curb-weight        -0.233118           0.099404    0.782097  0.880665   \n",
       "engine-size        -0.110581           0.112360    0.572027  0.685025   \n",
       "bore               -0.140019          -0.029862    0.493244  0.608971   \n",
       "stroke             -0.008245           0.055563    0.158502  0.124139   \n",
       "compression-ratio  -0.182196          -0.114713    0.250313  0.159733   \n",
       "horsepower          0.075819           0.217299    0.371147  0.579821   \n",
       "peak-rpm            0.279740           0.239543   -0.360305 -0.285970   \n",
       "city-mpg           -0.035527          -0.225016   -0.470606 -0.665192   \n",
       "highway-mpg         0.036233          -0.181877   -0.543304 -0.698142   \n",
       "price              -0.082391           0.133999    0.584642  0.690628   \n",
       "city-L/100km        0.066171           0.238567    0.476153  0.657373   \n",
       "diesel             -0.196735          -0.101546    0.307237  0.211187   \n",
       "gas                 0.196735           0.101546   -0.307237 -0.211187   \n",
       "\n",
       "                      width    height  curb-weight  engine-size      bore  \\\n",
       "symboling         -0.242423 -0.550160    -0.233118    -0.110581 -0.140019   \n",
       "normalized-losses  0.086802 -0.373737     0.099404     0.112360 -0.029862   \n",
       "wheel-base         0.814507  0.590742     0.782097     0.572027  0.493244   \n",
       "length             0.857170  0.492063     0.880665     0.685025  0.608971   \n",
       "width              1.000000  0.306002     0.866201     0.729436  0.544885   \n",
       "height             0.306002  1.000000     0.307581     0.074694  0.180449   \n",
       "curb-weight        0.866201  0.307581     1.000000     0.849072  0.644060   \n",
       "engine-size        0.729436  0.074694     0.849072     1.000000  0.572609   \n",
       "bore               0.544885  0.180449     0.644060     0.572609  1.000000   \n",
       "stroke             0.188829 -0.062704     0.167562     0.209523 -0.055390   \n",
       "compression-ratio  0.189867  0.259737     0.156433     0.028889  0.001263   \n",
       "horsepower         0.615077 -0.087027     0.757976     0.822676  0.566936   \n",
       "peak-rpm          -0.245800 -0.309974    -0.279361    -0.256733 -0.267392   \n",
       "city-mpg          -0.633531 -0.049800    -0.749543    -0.650546 -0.582027   \n",
       "highway-mpg       -0.680635 -0.104812    -0.794889    -0.679571 -0.591309   \n",
       "price              0.751265  0.135486     0.834415     0.872335  0.543155   \n",
       "city-L/100km       0.673363  0.003811     0.785353     0.745059  0.554610   \n",
       "diesel             0.244356  0.281578     0.221046     0.070779  0.054458   \n",
       "gas               -0.244356 -0.281578    -0.221046    -0.070779 -0.054458   \n",
       "\n",
       "                     stroke  compression-ratio  horsepower  peak-rpm  \\\n",
       "symboling         -0.008245          -0.182196    0.075819  0.279740   \n",
       "normalized-losses  0.055563          -0.114713    0.217299  0.239543   \n",
       "wheel-base         0.158502           0.250313    0.371147 -0.360305   \n",
       "length             0.124139           0.159733    0.579821 -0.285970   \n",
       "width              0.188829           0.189867    0.615077 -0.245800   \n",
       "height            -0.062704           0.259737   -0.087027 -0.309974   \n",
       "curb-weight        0.167562           0.156433    0.757976 -0.279361   \n",
       "engine-size        0.209523           0.028889    0.822676 -0.256733   \n",
       "bore              -0.055390           0.001263    0.566936 -0.267392   \n",
       "stroke             1.000000           0.187923    0.098462 -0.065713   \n",
       "compression-ratio  0.187923           1.000000   -0.214514 -0.435780   \n",
       "horsepower         0.098462          -0.214514    1.000000  0.107885   \n",
       "peak-rpm          -0.065713          -0.435780    0.107885  1.000000   \n",
       "city-mpg          -0.034696           0.331425   -0.822214 -0.115413   \n",
       "highway-mpg       -0.035201           0.268465   -0.804575 -0.058598   \n",
       "price              0.082310           0.071107    0.809575 -0.101616   \n",
       "city-L/100km       0.037300          -0.299372    0.889488  0.115830   \n",
       "diesel             0.241303           0.985231   -0.169053 -0.475812   \n",
       "gas               -0.241303          -0.985231    0.169053  0.475812   \n",
       "\n",
       "                   city-mpg  highway-mpg     price  city-L/100km    diesel  \\\n",
       "symboling         -0.035527     0.036233 -0.082391      0.066171 -0.196735   \n",
       "normalized-losses -0.225016    -0.181877  0.133999      0.238567 -0.101546   \n",
       "wheel-base        -0.470606    -0.543304  0.584642      0.476153  0.307237   \n",
       "length            -0.665192    -0.698142  0.690628      0.657373  0.211187   \n",
       "width             -0.633531    -0.680635  0.751265      0.673363  0.244356   \n",
       "height            -0.049800    -0.104812  0.135486      0.003811  0.281578   \n",
       "curb-weight       -0.749543    -0.794889  0.834415      0.785353  0.221046   \n",
       "engine-size       -0.650546    -0.679571  0.872335      0.745059  0.070779   \n",
       "bore              -0.582027    -0.591309  0.543155      0.554610  0.054458   \n",
       "stroke            -0.034696    -0.035201  0.082310      0.037300  0.241303   \n",
       "compression-ratio  0.331425     0.268465  0.071107     -0.299372  0.985231   \n",
       "horsepower        -0.822214    -0.804575  0.809575      0.889488 -0.169053   \n",
       "peak-rpm          -0.115413    -0.058598 -0.101616      0.115830 -0.475812   \n",
       "city-mpg           1.000000     0.972044 -0.686571     -0.949713  0.265676   \n",
       "highway-mpg        0.972044     1.000000 -0.704692     -0.930028  0.198690   \n",
       "price             -0.686571    -0.704692  1.000000      0.789898  0.110326   \n",
       "city-L/100km      -0.949713    -0.930028  0.789898      1.000000 -0.241282   \n",
       "diesel             0.265676     0.198690  0.110326     -0.241282  1.000000   \n",
       "gas               -0.265676    -0.198690 -0.110326      0.241282 -1.000000   \n",
       "\n",
       "                        gas  \n",
       "symboling          0.196735  \n",
       "normalized-losses  0.101546  \n",
       "wheel-base        -0.307237  \n",
       "length            -0.211187  \n",
       "width             -0.244356  \n",
       "height            -0.281578  \n",
       "curb-weight       -0.221046  \n",
       "engine-size       -0.070779  \n",
       "bore              -0.054458  \n",
       "stroke            -0.241303  \n",
       "compression-ratio -0.985231  \n",
       "horsepower         0.169053  \n",
       "peak-rpm           0.475812  \n",
       "city-mpg          -0.265676  \n",
       "highway-mpg       -0.198690  \n",
       "price             -0.110326  \n",
       "city-L/100km       0.241282  \n",
       "diesel            -1.000000  \n",
       "gas                1.000000  "
      ]
     },
     "execution_count": 41,
     "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": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<bound method DataFrame.corr of      bore  stroke  compression-ratio  horsepower\n",
       "0    3.47    2.68                9.0       111.0\n",
       "1    3.47    2.68                9.0       111.0\n",
       "2    2.68    3.47                9.0       154.0\n",
       "3    3.19    3.40               10.0       102.0\n",
       "4    3.19    3.40                8.0       115.0\n",
       "..    ...     ...                ...         ...\n",
       "196  3.78    3.15                9.5       114.0\n",
       "197  3.78    3.15                8.7       160.0\n",
       "198  3.58    2.87                8.8       134.0\n",
       "199  3.01    3.40               23.0       106.0\n",
       "200  3.78    3.15                9.5       114.0\n",
       "\n",
       "[201 rows x 4 columns]>"
      ]
     },
     "execution_count": 42,
     "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": 43,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 55804.69760791211)"
      ]
     },
     "execution_count": 43,
     "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": 44,
   "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": 44,
     "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": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='highway-mpg', ylabel='price'>"
      ]
     },
     "execution_count": 45,
     "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": 46,
   "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": 46,
     "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": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='peak-rpm', ylabel='price'>"
      ]
     },
     "execution_count": 47,
     "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": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 48,
     "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": 49,
   "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": 49,
     "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": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='stroke', ylabel='price'>"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "sns.regplot(x=\"stroke\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<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": 51,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='body-style', ylabel='price'>"
      ]
     },
     "execution_count": 51,
     "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": 52,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='engine-location', ylabel='price'>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"engine-location\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Here we see that the distribution of price between these two engine-location categories, front and rear, are distinct enough to take engine-location as a potential good predictor of price.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's examine \"drive-wheels\" and \"price\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='drive-wheels', ylabel='price'>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# drive-wheels\n",
    "sns.boxplot(x=\"drive-wheels\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Here we see that the distribution of price between the different drive-wheels categories differs. As such, drive-wheels could potentially be a predictor of price.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"discriptive_statistics\">3. Descriptive Statistical Analysis</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Let's first take a look at the variables by utilizing a description method.</p>\n",
    "\n",
    "<p>The <b>describe</b> function automatically computes basic statistics for all continuous variables. Any NaN values are automatically skipped in these statistics.</p>\n",
    "\n",
    "This will show:\n",
    "\n",
    "<ul>\n",
    "    <li>the count of that variable</li>\n",
    "    <li>the mean</li>\n",
    "    <li>the standard deviation (std)</li> \n",
    "    <li>the minimum value</li>\n",
    "    <li>the IQR (Interquartile Range: 25%, 50% and 75%)</li>\n",
    "    <li>the maximum value</li>\n",
    "<ul>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can apply the method \"describe\" as follows:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "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": 54,
     "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": 55,
   "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": 55,
     "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": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fwd    118\n",
       "rwd     75\n",
       "4wd      8\n",
       "Name: drive-wheels, dtype: int64"
      ]
     },
     "execution_count": 56,
     "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": 57,
   "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": 57,
     "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": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 58,
     "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": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 59,
     "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": 60,
   "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": 60,
     "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": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['rwd', 'fwd', '4wd'], dtype=object)"
      ]
     },
     "execution_count": 61,
     "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": 62,
   "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": 63,
   "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": 63,
     "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": 64,
   "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": 64,
     "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": 65,
   "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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       "</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": 65,
     "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": 66,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "<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": 66,
     "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": 67,
   "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": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df_grptest2 = df[['body-style','price']]\n",
    "grp_test_bodystyle = df_grptest2.groupby(['body-style'],as_index=False).mean()\n",
    "grp_test_bodystyle"
   ]
  },
  {
   "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": 68,
   "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": 69,
   "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": 70,
   "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": 71,
   "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": 71,
     "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": 72,
   "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": 73,
   "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": 74,
   "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": 75,
   "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": 76,
   "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": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8344145257702846  with a P-value of P =  2.1895772388936914e-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": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8723351674455185  with a P-value of P = 9.265491622198389e-64\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['engine-size'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<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": 79,
   "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": 80,
   "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": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.7046922650589529  with a P-value of P =  1.7495471144477352e-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": 82,
   "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": 82,
     "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": 83,
   "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": 83,
     "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": 84,
   "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": 84,
     "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": 85,
   "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": 86,
   "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": 87,
   "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": 88,
   "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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