exploratory-data-analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>\n",
    "    <img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/Logos/organization_logo/organization_logo.png\" width=\"300\" alt=\"cognitiveclass.ai logo\"  />\n",
    "</center>\n",
    "\n",
    "# Data Analysis with Python\n",
    "\n",
    "Estaimted time needed: **30** minutes\n",
    "\n",
    "## Objectives\n",
    "\n",
    "After completing this lab you will be able to:\n",
    "\n",
    "-   Explore features or charecteristics to predict price of car\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Table of content</h2>\n",
    "\n",
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "<ol>\n",
    "    <li><a href=\"#import_data\">Import Data from Module</a></li>\n",
    "    <li><a href=\"#pattern_visualization\">Analyzing Individual Feature Patterns using Visualization</a></li>\n",
    "    <li><a href=\"#discriptive_statistics\">Descriptive Statistical Analysis</a></li>\n",
    "    <li><a href=\"#basic_grouping\">Basics of Grouping</a></li>\n",
    "    <li><a href=\"#correlation_causation\">Correlation and Causation</a></li>\n",
    "    <li><a href=\"#anova\">ANOVA</a></li>\n",
    "</ol>\n",
    "    \n",
    "Estimated Time Needed: <strong>30 min</strong>\n",
    "</div>\n",
    " \n",
    "<hr>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>What are the main characteristics which have the most impact on the car price?</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"import_data\">1. Import Data from Module 2</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Setup</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import libraries \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " load data and store in dataframe df:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dataset was hosted on IBM Cloud object click <a href=\"https://cocl.us/DA101EN_object_storage\">HERE</a> for free storage\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>make</th>\n",
       "      <th>aspiration</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>...</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>horsepower-binned</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>13495.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>94.5</td>\n",
       "      <td>0.822681</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>154.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.8</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>24</td>\n",
       "      <td>30</td>\n",
       "      <td>13950.0</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>4wd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.4</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>8.0</td>\n",
       "      <td>115.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>18</td>\n",
       "      <td>22</td>\n",
       "      <td>17450.0</td>\n",
       "      <td>13.055556</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 29 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   symboling  normalized-losses         make aspiration num-of-doors  \\\n",
       "0          3                122  alfa-romero        std          two   \n",
       "1          3                122  alfa-romero        std          two   \n",
       "2          1                122  alfa-romero        std          two   \n",
       "3          2                164         audi        std         four   \n",
       "4          2                164         audi        std         four   \n",
       "\n",
       "    body-style drive-wheels engine-location  wheel-base    length  ...  \\\n",
       "0  convertible          rwd           front        88.6  0.811148  ...   \n",
       "1  convertible          rwd           front        88.6  0.811148  ...   \n",
       "2    hatchback          rwd           front        94.5  0.822681  ...   \n",
       "3        sedan          fwd           front        99.8  0.848630  ...   \n",
       "4        sedan          4wd           front        99.4  0.848630  ...   \n",
       "\n",
       "   compression-ratio  horsepower  peak-rpm city-mpg highway-mpg    price  \\\n",
       "0                9.0       111.0    5000.0       21          27  13495.0   \n",
       "1                9.0       111.0    5000.0       21          27  16500.0   \n",
       "2                9.0       154.0    5000.0       19          26  16500.0   \n",
       "3               10.0       102.0    5500.0       24          30  13950.0   \n",
       "4                8.0       115.0    5500.0       18          22  17450.0   \n",
       "\n",
       "  city-L/100km  horsepower-binned  diesel  gas  \n",
       "0    11.190476             Medium       0    1  \n",
       "1    11.190476             Medium       0    1  \n",
       "2    12.368421             Medium       0    1  \n",
       "3     9.791667             Medium       0    1  \n",
       "4    13.055556             Medium       0    1  \n",
       "\n",
       "[5 rows x 29 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path='https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/automobileEDA.csv'\n",
    "df = pd.read_csv(path)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"pattern_visualization\">2. Analyzing Individual Feature Patterns using Visualization</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To install seaborn we use the pip which is the python package manager.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "! pip install seaborn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import visualization packages \"Matplotlib\" and \"Seaborn\", don't forget about \"%matplotlib inline\" to plot in a Jupyter notebook.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>How to choose the right visualization method?</h4>\n",
    "<p>When visualizing individual variables, it is important to first understand what type of variable you are dealing with. This will help us find the right visualization method for that variable.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "symboling              int64\n",
      "normalized-losses      int64\n",
      "make                  object\n",
      "aspiration            object\n",
      "num-of-doors          object\n",
      "body-style            object\n",
      "drive-wheels          object\n",
      "engine-location       object\n",
      "wheel-base           float64\n",
      "length               float64\n",
      "width                float64\n",
      "height               float64\n",
      "curb-weight            int64\n",
      "engine-type           object\n",
      "num-of-cylinders      object\n",
      "engine-size            int64\n",
      "fuel-system           object\n",
      "bore                 float64\n",
      "stroke               float64\n",
      "compression-ratio    float64\n",
      "horsepower           float64\n",
      "peak-rpm             float64\n",
      "city-mpg               int64\n",
      "highway-mpg            int64\n",
      "price                float64\n",
      "city-L/100km         float64\n",
      "horsepower-binned     object\n",
      "diesel                 int64\n",
      "gas                    int64\n",
      "dtype: object\n"
     ]
    }
   ],
   "source": [
    "# list the data types for each column\n",
    "print(df.dtypes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h3>Question  #1:</h3>\n",
    "\n",
    "<b>What is the data type of the column \"peak-rpm\"? </b>\n",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['peak-rpm'].dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "float64\n",
    "\n",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "for example, we can calculate the correlation between variables  of type \"int64\" or \"float64\" using the method \"corr\":\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>symboling</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.466264</td>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.365404</td>\n",
       "      <td>-0.242423</td>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.233118</td>\n",
       "      <td>-0.110581</td>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.008245</td>\n",
       "      <td>-0.182196</td>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.279740</td>\n",
       "      <td>-0.035527</td>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.066171</td>\n",
       "      <td>-0.196735</td>\n",
       "      <td>0.196735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>normalized-losses</th>\n",
       "      <td>0.466264</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.101546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wheel-base</th>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>-0.307237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>length</th>\n",
       "      <td>-0.365404</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>-0.211187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>width</th>\n",
       "      <td>-0.242423</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>-0.244356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>height</th>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>-0.281578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>curb-weight</th>\n",
       "      <td>-0.233118</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>-0.221046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>-0.110581</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>-0.070779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>-0.054458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.008245</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>-0.241303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>-0.182196</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.985231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>0.169053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>0.279740</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.475812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-mpg</th>\n",
       "      <td>-0.035527</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>-0.265676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>-0.198690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.110326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-L/100km</th>\n",
       "      <td>0.066171</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>0.241282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diesel</th>\n",
       "      <td>-0.196735</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gas</th>\n",
       "      <td>0.196735</td>\n",
       "      <td>0.101546</td>\n",
       "      <td>-0.307237</td>\n",
       "      <td>-0.211187</td>\n",
       "      <td>-0.244356</td>\n",
       "      <td>-0.281578</td>\n",
       "      <td>-0.221046</td>\n",
       "      <td>-0.070779</td>\n",
       "      <td>-0.054458</td>\n",
       "      <td>-0.241303</td>\n",
       "      <td>-0.985231</td>\n",
       "      <td>0.169053</td>\n",
       "      <td>0.475812</td>\n",
       "      <td>-0.265676</td>\n",
       "      <td>-0.198690</td>\n",
       "      <td>-0.110326</td>\n",
       "      <td>0.241282</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   symboling  normalized-losses  wheel-base    length  \\\n",
       "symboling           1.000000           0.466264   -0.535987 -0.365404   \n",
       "normalized-losses   0.466264           1.000000   -0.056661  0.019424   \n",
       "wheel-base         -0.535987          -0.056661    1.000000  0.876024   \n",
       "length             -0.365404           0.019424    0.876024  1.000000   \n",
       "width              -0.242423           0.086802    0.814507  0.857170   \n",
       "height             -0.550160          -0.373737    0.590742  0.492063   \n",
       "curb-weight        -0.233118           0.099404    0.782097  0.880665   \n",
       "engine-size        -0.110581           0.112360    0.572027  0.685025   \n",
       "bore               -0.140019          -0.029862    0.493244  0.608971   \n",
       "stroke             -0.008245           0.055563    0.158502  0.124139   \n",
       "compression-ratio  -0.182196          -0.114713    0.250313  0.159733   \n",
       "horsepower          0.075819           0.217299    0.371147  0.579821   \n",
       "peak-rpm            0.279740           0.239543   -0.360305 -0.285970   \n",
       "city-mpg           -0.035527          -0.225016   -0.470606 -0.665192   \n",
       "highway-mpg         0.036233          -0.181877   -0.543304 -0.698142   \n",
       "price              -0.082391           0.133999    0.584642  0.690628   \n",
       "city-L/100km        0.066171           0.238567    0.476153  0.657373   \n",
       "diesel             -0.196735          -0.101546    0.307237  0.211187   \n",
       "gas                 0.196735           0.101546   -0.307237 -0.211187   \n",
       "\n",
       "                      width    height  curb-weight  engine-size      bore  \\\n",
       "symboling         -0.242423 -0.550160    -0.233118    -0.110581 -0.140019   \n",
       "normalized-losses  0.086802 -0.373737     0.099404     0.112360 -0.029862   \n",
       "wheel-base         0.814507  0.590742     0.782097     0.572027  0.493244   \n",
       "length             0.857170  0.492063     0.880665     0.685025  0.608971   \n",
       "width              1.000000  0.306002     0.866201     0.729436  0.544885   \n",
       "height             0.306002  1.000000     0.307581     0.074694  0.180449   \n",
       "curb-weight        0.866201  0.307581     1.000000     0.849072  0.644060   \n",
       "engine-size        0.729436  0.074694     0.849072     1.000000  0.572609   \n",
       "bore               0.544885  0.180449     0.644060     0.572609  1.000000   \n",
       "stroke             0.188829 -0.062704     0.167562     0.209523 -0.055390   \n",
       "compression-ratio  0.189867  0.259737     0.156433     0.028889  0.001263   \n",
       "horsepower         0.615077 -0.087027     0.757976     0.822676  0.566936   \n",
       "peak-rpm          -0.245800 -0.309974    -0.279361    -0.256733 -0.267392   \n",
       "city-mpg          -0.633531 -0.049800    -0.749543    -0.650546 -0.582027   \n",
       "highway-mpg       -0.680635 -0.104812    -0.794889    -0.679571 -0.591309   \n",
       "price              0.751265  0.135486     0.834415     0.872335  0.543155   \n",
       "city-L/100km       0.673363  0.003811     0.785353     0.745059  0.554610   \n",
       "diesel             0.244356  0.281578     0.221046     0.070779  0.054458   \n",
       "gas               -0.244356 -0.281578    -0.221046    -0.070779 -0.054458   \n",
       "\n",
       "                     stroke  compression-ratio  horsepower  peak-rpm  \\\n",
       "symboling         -0.008245          -0.182196    0.075819  0.279740   \n",
       "normalized-losses  0.055563          -0.114713    0.217299  0.239543   \n",
       "wheel-base         0.158502           0.250313    0.371147 -0.360305   \n",
       "length             0.124139           0.159733    0.579821 -0.285970   \n",
       "width              0.188829           0.189867    0.615077 -0.245800   \n",
       "height            -0.062704           0.259737   -0.087027 -0.309974   \n",
       "curb-weight        0.167562           0.156433    0.757976 -0.279361   \n",
       "engine-size        0.209523           0.028889    0.822676 -0.256733   \n",
       "bore              -0.055390           0.001263    0.566936 -0.267392   \n",
       "stroke             1.000000           0.187923    0.098462 -0.065713   \n",
       "compression-ratio  0.187923           1.000000   -0.214514 -0.435780   \n",
       "horsepower         0.098462          -0.214514    1.000000  0.107885   \n",
       "peak-rpm          -0.065713          -0.435780    0.107885  1.000000   \n",
       "city-mpg          -0.034696           0.331425   -0.822214 -0.115413   \n",
       "highway-mpg       -0.035201           0.268465   -0.804575 -0.058598   \n",
       "price              0.082310           0.071107    0.809575 -0.101616   \n",
       "city-L/100km       0.037300          -0.299372    0.889488  0.115830   \n",
       "diesel             0.241303           0.985231   -0.169053 -0.475812   \n",
       "gas               -0.241303          -0.985231    0.169053  0.475812   \n",
       "\n",
       "                   city-mpg  highway-mpg     price  city-L/100km    diesel  \\\n",
       "symboling         -0.035527     0.036233 -0.082391      0.066171 -0.196735   \n",
       "normalized-losses -0.225016    -0.181877  0.133999      0.238567 -0.101546   \n",
       "wheel-base        -0.470606    -0.543304  0.584642      0.476153  0.307237   \n",
       "length            -0.665192    -0.698142  0.690628      0.657373  0.211187   \n",
       "width             -0.633531    -0.680635  0.751265      0.673363  0.244356   \n",
       "height            -0.049800    -0.104812  0.135486      0.003811  0.281578   \n",
       "curb-weight       -0.749543    -0.794889  0.834415      0.785353  0.221046   \n",
       "engine-size       -0.650546    -0.679571  0.872335      0.745059  0.070779   \n",
       "bore              -0.582027    -0.591309  0.543155      0.554610  0.054458   \n",
       "stroke            -0.034696    -0.035201  0.082310      0.037300  0.241303   \n",
       "compression-ratio  0.331425     0.268465  0.071107     -0.299372  0.985231   \n",
       "horsepower        -0.822214    -0.804575  0.809575      0.889488 -0.169053   \n",
       "peak-rpm          -0.115413    -0.058598 -0.101616      0.115830 -0.475812   \n",
       "city-mpg           1.000000     0.972044 -0.686571     -0.949713  0.265676   \n",
       "highway-mpg        0.972044     1.000000 -0.704692     -0.930028  0.198690   \n",
       "price             -0.686571    -0.704692  1.000000      0.789898  0.110326   \n",
       "city-L/100km      -0.949713    -0.930028  0.789898      1.000000 -0.241282   \n",
       "diesel             0.265676     0.198690  0.110326     -0.241282  1.000000   \n",
       "gas               -0.265676    -0.198690 -0.110326      0.241282 -1.000000   \n",
       "\n",
       "                        gas  \n",
       "symboling          0.196735  \n",
       "normalized-losses  0.101546  \n",
       "wheel-base        -0.307237  \n",
       "length            -0.211187  \n",
       "width             -0.244356  \n",
       "height            -0.281578  \n",
       "curb-weight       -0.221046  \n",
       "engine-size       -0.070779  \n",
       "bore              -0.054458  \n",
       "stroke            -0.241303  \n",
       "compression-ratio -0.985231  \n",
       "horsepower         0.169053  \n",
       "peak-rpm           0.475812  \n",
       "city-mpg          -0.265676  \n",
       "highway-mpg       -0.198690  \n",
       "price             -0.110326  \n",
       "city-L/100km       0.241282  \n",
       "diesel            -1.000000  \n",
       "gas                1.000000  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The diagonal elements are always one; we will study correlation more precisely Pearson correlation in-depth at the end of the notebook.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #2: </h1>\n",
    "\n",
    "<p>Find the correlation between the following columns: bore, stroke,compression-ratio , and horsepower.</p>\n",
    "<p>Hint: if you would like to select those columns  use the following syntax: df[['bore','stroke' ,'compression-ratio','horsepower']]</p>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       bore    stroke  compression-ratio  horsepower\n",
       "bore               1.000000 -0.055390           0.001263    0.566936\n",
       "stroke            -0.055390  1.000000           0.187923    0.098462\n",
       "compression-ratio  0.001263  0.187923           1.000000   -0.214514\n",
       "horsepower         0.566936  0.098462          -0.214514    1.000000"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df[['bore','stroke' ,'compression-ratio','horsepower']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "df[['bore', 'stroke', 'compression-ratio', 'horsepower']].corr()  \n",
    "\n",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Continuous numerical variables:</h2> \n",
    "\n",
    "<p>Continuous numerical variables are variables that may contain any value within some range. Continuous numerical variables can have the type \"int64\" or \"float64\". A great way to visualize these variables is by using scatterplots with fitted lines.</p>\n",
    "\n",
    "<p>In order to start understanding the (linear) relationship between an individual variable and the price. We can do this by using \"regplot\", which plots the scatterplot plus the fitted regression line for the data.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's see several examples of different linear relationships:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Positive linear relationship</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's find the scatterplot of \"engine-size\" and \"price\" \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 56402.921575364555)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Engine size as potential predictor variable of price\n",
    "sns.regplot(x=\"engine-size\", y=\"price\", data=df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>As the engine-size goes up, the price goes up: this indicates a positive direct correlation between these two variables. Engine size seems like a pretty good predictor of price since the regression line is almost a perfect diagonal line.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can examine the correlation between 'engine-size' and 'price' and see it's approximately  0.87\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>engine-size</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.872335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>0.872335</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             engine-size     price\n",
       "engine-size     1.000000  0.872335\n",
       "price           0.872335  1.000000"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[[\"engine-size\", \"price\"]].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Highway mpg is a potential predictor variable of price \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='highway-mpg', ylabel='price'>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x=\"highway-mpg\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>As the highway-mpg goes up, the price goes down: this indicates an inverse/negative relationship between these two variables. Highway mpg could potentially be a predictor of price.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'highway-mpg' and 'price' and see it's approximately  -0.704\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             highway-mpg     price\n",
       "highway-mpg     1.000000 -0.704692\n",
       "price          -0.704692  1.000000"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['highway-mpg', 'price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Weak Linear Relationship</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see if \"Peak-rpm\" as a predictor variable of \"price\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='peak-rpm', ylabel='price'>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x=\"peak-rpm\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Peak rpm does not seem like a good predictor of the price at all since the regression line is close to horizontal. Also, the data points are very scattered and far from the fitted line, showing lots of variability. Therefore it's it is not a reliable variable.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'peak-rpm' and 'price' and see it's approximately -0.101616 \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.101616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.101616</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          peak-rpm     price\n",
       "peak-rpm  1.000000 -0.101616\n",
       "price    -0.101616  1.000000"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['peak-rpm','price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " <div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  3 a): </h1>\n",
    "\n",
    "<p>Find the correlation  between x=\"stroke\", y=\"price\".</p>\n",
    "<p>Hint: if you would like to select those columns  use the following syntax: df[[\"stroke\",\"price\"]]  </p>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>stroke</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>1.00000</td>\n",
       "      <td>0.08231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>0.08231</td>\n",
       "      <td>1.00000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         stroke    price\n",
       "stroke  1.00000  0.08231\n",
       "price   0.08231  1.00000"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute\n",
    "df[[\"stroke\",\"price\"]].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "#The correlation is 0.0823, the non-diagonal elements of the table.\n",
    "#code:\n",
    "df[[\"stroke\",\"price\"]].corr() \n",
    "\n",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question  3 b):</h1>\n",
    "\n",
    "<p>Given the correlation results between \"price\" and \"stroke\" do you expect a linear relationship?</p> \n",
    "<p>Verify your results using the function \"regplot()\".</p>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='stroke', ylabel='price'>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "sns.regplot(x=\"stroke\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "#There is a weak correlation between the variable 'stroke' and 'price.' as such regression will not work well.  We #can see this use \"regplot\" to demonstrate this.\n",
    "\n",
    "#Code: \n",
    "sns.regplot(x=\"stroke\", y=\"price\", data=df)\n",
    "\n",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Categorical variables</h3>\n",
    "\n",
    "<p>These are variables that describe a 'characteristic' of a data unit, and are selected from a small group of categories. The categorical variables can have the type \"object\" or \"int64\". A good way to visualize categorical variables is by using boxplots.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the relationship between \"body-style\" and \"price\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='body-style', ylabel='price'>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"body-style\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We see that the distributions of price between the different body-style categories have a significant overlap, and so body-style would not be a good predictor of price. Let's examine engine \"engine-location\" and \"price\":</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='engine-location', ylabel='price'>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"engine-location\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Here we see that the distribution of price between these two engine-location categories, front and rear, are distinct enough to take engine-location as a potential good predictor of price.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's examine \"drive-wheels\" and \"price\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='drive-wheels', ylabel='price'>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\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": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.00000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>197.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.840796</td>\n",
       "      <td>122.00000</td>\n",
       "      <td>98.797015</td>\n",
       "      <td>0.837102</td>\n",
       "      <td>0.915126</td>\n",
       "      <td>53.766667</td>\n",
       "      <td>2555.666667</td>\n",
       "      <td>126.875622</td>\n",
       "      <td>3.330692</td>\n",
       "      <td>3.256904</td>\n",
       "      <td>10.164279</td>\n",
       "      <td>103.405534</td>\n",
       "      <td>5117.665368</td>\n",
       "      <td>25.179104</td>\n",
       "      <td>30.686567</td>\n",
       "      <td>13207.129353</td>\n",
       "      <td>9.944145</td>\n",
       "      <td>0.099502</td>\n",
       "      <td>0.900498</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.254802</td>\n",
       "      <td>31.99625</td>\n",
       "      <td>6.066366</td>\n",
       "      <td>0.059213</td>\n",
       "      <td>0.029187</td>\n",
       "      <td>2.447822</td>\n",
       "      <td>517.296727</td>\n",
       "      <td>41.546834</td>\n",
       "      <td>0.268072</td>\n",
       "      <td>0.319256</td>\n",
       "      <td>4.004965</td>\n",
       "      <td>37.365700</td>\n",
       "      <td>478.113805</td>\n",
       "      <td>6.423220</td>\n",
       "      <td>6.815150</td>\n",
       "      <td>7947.066342</td>\n",
       "      <td>2.534599</td>\n",
       "      <td>0.300083</td>\n",
       "      <td>0.300083</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-2.000000</td>\n",
       "      <td>65.00000</td>\n",
       "      <td>86.600000</td>\n",
       "      <td>0.678039</td>\n",
       "      <td>0.837500</td>\n",
       "      <td>47.800000</td>\n",
       "      <td>1488.000000</td>\n",
       "      <td>61.000000</td>\n",
       "      <td>2.540000</td>\n",
       "      <td>2.070000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>48.000000</td>\n",
       "      <td>4150.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>5118.000000</td>\n",
       "      <td>4.795918</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>101.00000</td>\n",
       "      <td>94.500000</td>\n",
       "      <td>0.801538</td>\n",
       "      <td>0.890278</td>\n",
       "      <td>52.000000</td>\n",
       "      <td>2169.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>3.150000</td>\n",
       "      <td>3.110000</td>\n",
       "      <td>8.600000</td>\n",
       "      <td>70.000000</td>\n",
       "      <td>4800.000000</td>\n",
       "      <td>19.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>7775.000000</td>\n",
       "      <td>7.833333</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>122.00000</td>\n",
       "      <td>97.000000</td>\n",
       "      <td>0.832292</td>\n",
       "      <td>0.909722</td>\n",
       "      <td>54.100000</td>\n",
       "      <td>2414.000000</td>\n",
       "      <td>120.000000</td>\n",
       "      <td>3.310000</td>\n",
       "      <td>3.290000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>95.000000</td>\n",
       "      <td>5125.369458</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>10295.000000</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2.000000</td>\n",
       "      <td>137.00000</td>\n",
       "      <td>102.400000</td>\n",
       "      <td>0.881788</td>\n",
       "      <td>0.925000</td>\n",
       "      <td>55.500000</td>\n",
       "      <td>2926.000000</td>\n",
       "      <td>141.000000</td>\n",
       "      <td>3.580000</td>\n",
       "      <td>3.410000</td>\n",
       "      <td>9.400000</td>\n",
       "      <td>116.000000</td>\n",
       "      <td>5500.000000</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>34.000000</td>\n",
       "      <td>16500.000000</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>256.00000</td>\n",
       "      <td>120.900000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>59.800000</td>\n",
       "      <td>4066.000000</td>\n",
       "      <td>326.000000</td>\n",
       "      <td>3.940000</td>\n",
       "      <td>4.170000</td>\n",
       "      <td>23.000000</td>\n",
       "      <td>262.000000</td>\n",
       "      <td>6600.000000</td>\n",
       "      <td>49.000000</td>\n",
       "      <td>54.000000</td>\n",
       "      <td>45400.000000</td>\n",
       "      <td>18.076923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        symboling  normalized-losses  wheel-base      length       width  \\\n",
       "count  201.000000          201.00000  201.000000  201.000000  201.000000   \n",
       "mean     0.840796          122.00000   98.797015    0.837102    0.915126   \n",
       "std      1.254802           31.99625    6.066366    0.059213    0.029187   \n",
       "min     -2.000000           65.00000   86.600000    0.678039    0.837500   \n",
       "25%      0.000000          101.00000   94.500000    0.801538    0.890278   \n",
       "50%      1.000000          122.00000   97.000000    0.832292    0.909722   \n",
       "75%      2.000000          137.00000  102.400000    0.881788    0.925000   \n",
       "max      3.000000          256.00000  120.900000    1.000000    1.000000   \n",
       "\n",
       "           height  curb-weight  engine-size        bore      stroke  \\\n",
       "count  201.000000   201.000000   201.000000  201.000000  197.000000   \n",
       "mean    53.766667  2555.666667   126.875622    3.330692    3.256904   \n",
       "std      2.447822   517.296727    41.546834    0.268072    0.319256   \n",
       "min     47.800000  1488.000000    61.000000    2.540000    2.070000   \n",
       "25%     52.000000  2169.000000    98.000000    3.150000    3.110000   \n",
       "50%     54.100000  2414.000000   120.000000    3.310000    3.290000   \n",
       "75%     55.500000  2926.000000   141.000000    3.580000    3.410000   \n",
       "max     59.800000  4066.000000   326.000000    3.940000    4.170000   \n",
       "\n",
       "       compression-ratio  horsepower     peak-rpm    city-mpg  highway-mpg  \\\n",
       "count         201.000000  201.000000   201.000000  201.000000   201.000000   \n",
       "mean           10.164279  103.405534  5117.665368   25.179104    30.686567   \n",
       "std             4.004965   37.365700   478.113805    6.423220     6.815150   \n",
       "min             7.000000   48.000000  4150.000000   13.000000    16.000000   \n",
       "25%             8.600000   70.000000  4800.000000   19.000000    25.000000   \n",
       "50%             9.000000   95.000000  5125.369458   24.000000    30.000000   \n",
       "75%             9.400000  116.000000  5500.000000   30.000000    34.000000   \n",
       "max            23.000000  262.000000  6600.000000   49.000000    54.000000   \n",
       "\n",
       "              price  city-L/100km      diesel         gas  \n",
       "count    201.000000    201.000000  201.000000  201.000000  \n",
       "mean   13207.129353      9.944145    0.099502    0.900498  \n",
       "std     7947.066342      2.534599    0.300083    0.300083  \n",
       "min     5118.000000      4.795918    0.000000    0.000000  \n",
       "25%     7775.000000      7.833333    0.000000    1.000000  \n",
       "50%    10295.000000      9.791667    0.000000    1.000000  \n",
       "75%    16500.000000     12.368421    0.000000    1.000000  \n",
       "max    45400.000000     18.076923    1.000000    1.000000  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The default setting of \"describe\" skips variables of type object. We can apply the method \"describe\" on the variables of type 'object' as follows:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>make</th>\n",
       "      <th>aspiration</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>engine-type</th>\n",
       "      <th>num-of-cylinders</th>\n",
       "      <th>fuel-system</th>\n",
       "      <th>horsepower-binned</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>unique</th>\n",
       "      <td>22</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>top</th>\n",
       "      <td>toyota</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>ohc</td>\n",
       "      <td>four</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>Low</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>freq</th>\n",
       "      <td>32</td>\n",
       "      <td>165</td>\n",
       "      <td>115</td>\n",
       "      <td>94</td>\n",
       "      <td>118</td>\n",
       "      <td>198</td>\n",
       "      <td>145</td>\n",
       "      <td>157</td>\n",
       "      <td>92</td>\n",
       "      <td>115</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          make aspiration num-of-doors body-style drive-wheels  \\\n",
       "count      201        201          201        201          201   \n",
       "unique      22          2            2          5            3   \n",
       "top     toyota        std         four      sedan          fwd   \n",
       "freq        32        165          115         94          118   \n",
       "\n",
       "       engine-location engine-type num-of-cylinders fuel-system  \\\n",
       "count              201         201              201         201   \n",
       "unique               2           6                7           8   \n",
       "top              front         ohc             four        mpfi   \n",
       "freq               198         145              157          92   \n",
       "\n",
       "       horsepower-binned  \n",
       "count                200  \n",
       "unique                 3  \n",
       "top                  Low  \n",
       "freq                 115  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe(include=['object'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Value Counts</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Value-counts is a good way of understanding how many units of each characteristic/variable we have. We can apply the \"value_counts\" method on the column 'drive-wheels'. Don’t forget the method \"value_counts\" only works on Pandas series, not Pandas Dataframes. As a result, we only include one bracket \"df['drive-wheels']\" not two brackets \"df[['drive-wheels']]\".</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fwd    118\n",
       "rwd     75\n",
       "4wd      8\n",
       "Name: drive-wheels, dtype: int64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can convert the series to a Dataframe as follows :\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     drive-wheels\n",
       "fwd           118\n",
       "rwd            75\n",
       "4wd             8"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].value_counts().to_frame()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's repeat the above steps but save the results to the dataframe \"drive_wheels_counts\" and rename the column  'drive-wheels' to 'value_counts'.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value_counts</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     value_counts\n",
       "fwd           118\n",
       "rwd            75\n",
       "4wd             8"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "drive_wheels_counts = df['drive-wheels'].value_counts().to_frame()\n",
    "drive_wheels_counts.rename(columns={'drive-wheels': 'value_counts'}, inplace=True)\n",
    "drive_wheels_counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Now let's rename the index to 'drive-wheels':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value_counts</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              value_counts\n",
       "drive-wheels              \n",
       "fwd                    118\n",
       "rwd                     75\n",
       "4wd                      8"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "drive_wheels_counts.index.name = 'drive-wheels'\n",
    "drive_wheels_counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can repeat the above process for the variable 'engine-location'.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value_counts</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-location</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>front</th>\n",
       "      <td>198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rear</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 value_counts\n",
       "engine-location              \n",
       "front                     198\n",
       "rear                        3"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# engine-location as variable\n",
    "engine_loc_counts = df['engine-location'].value_counts().to_frame()\n",
    "engine_loc_counts.rename(columns={'engine-location': 'value_counts'}, inplace=True)\n",
    "engine_loc_counts.index.name = 'engine-location'\n",
    "engine_loc_counts.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Examining the value counts of the engine location would not be a good predictor variable for the price. This is because we only have three cars with a rear engine and 198 with an engine in the front, this result is skewed. Thus, we are not able to draw any conclusions about the engine location.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"basic_grouping\">4. Basics of Grouping</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The \"groupby\" method groups data by different categories. The data is grouped based on one or several variables and analysis is performed on the individual groups.</p>\n",
    "\n",
    "<p>For example, let's group by the variable \"drive-wheels\". We see that there are 3 different categories of drive wheels.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['rwd', 'fwd', '4wd'], dtype=object)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>If we want to know, on average, which type of drive wheel is most valuable, we can group \"drive-wheels\" and then average them.</p>\n",
    "\n",
    "<p>We can select the columns 'drive-wheels', 'body-style' and 'price', then assign it to the variable \"df_group_one\".</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\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": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_group_one = df[['drive-wheels','body-style','price']]\n",
    "\n",
    "df_group_one"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then calculate the average price for each of the different categories of data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4wd</td>\n",
       "      <td>10241.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>fwd</td>\n",
       "      <td>9244.779661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>rwd</td>\n",
       "      <td>19757.613333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  drive-wheels         price\n",
       "0          4wd  10241.000000\n",
       "1          fwd   9244.779661\n",
       "2          rwd  19757.613333"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# grouping results\n",
    "df_group_one = df_group_one.groupby(['drive-wheels'],as_index=False).mean()\n",
    "df_group_one"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>From our data, it seems rear-wheel drive vehicles are, on average, the most expensive, while 4-wheel and front-wheel are approximately the same in price.</p>\n",
    "\n",
    "<p>You can also group with multiple variables. For example, let's group by both 'drive-wheels' and 'body-style'. This groups the dataframe by the unique combinations 'drive-wheels' and 'body-style'. We can store the results in the variable 'grouped_test1'.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>body-style</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4wd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7603.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4wd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>12647.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4wd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>fwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>11595.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>8249.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>8396.387755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9811.800000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>23949.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>24202.714286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>14337.777778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>21711.833333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   drive-wheels   body-style         price\n",
       "0           4wd    hatchback   7603.000000\n",
       "1           4wd        sedan  12647.333333\n",
       "2           4wd        wagon   9095.750000\n",
       "3           fwd  convertible  11595.000000\n",
       "4           fwd      hardtop   8249.000000\n",
       "5           fwd    hatchback   8396.387755\n",
       "6           fwd        sedan   9811.800000\n",
       "7           fwd        wagon   9997.333333\n",
       "8           rwd  convertible  23949.600000\n",
       "9           rwd      hardtop  24202.714286\n",
       "10          rwd    hatchback  14337.777778\n",
       "11          rwd        sedan  21711.833333\n",
       "12          rwd        wagon  16994.222222"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# grouping results\n",
    "df_gptest = df[['drive-wheels','body-style','price']]\n",
    "grouped_test1 = df_gptest.groupby(['drive-wheels','body-style'],as_index=False).mean()\n",
    "grouped_test1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>This grouped data is much easier to visualize when it is made into a pivot table. A pivot table is like an Excel spreadsheet, with one variable along the column and another along the row. We can convert the dataframe to a pivot table using the method \"pivot \" to create a pivot table from the groups.</p>\n",
    "\n",
    "<p>In this case, we will leave the drive-wheel variable as the rows of the table, and pivot body-style to become the columns of the table:</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
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       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>body-style</th>\n",
       "      <th>convertible</th>\n",
       "      <th>hardtop</th>\n",
       "      <th>hatchback</th>\n",
       "      <th>sedan</th>\n",
       "      <th>wagon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7603.000000</td>\n",
       "      <td>12647.333333</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>11595.0</td>\n",
       "      <td>8249.000000</td>\n",
       "      <td>8396.387755</td>\n",
       "      <td>9811.800000</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>23949.6</td>\n",
       "      <td>24202.714286</td>\n",
       "      <td>14337.777778</td>\n",
       "      <td>21711.833333</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   price                                            \\\n",
       "body-style   convertible       hardtop     hatchback         sedan   \n",
       "drive-wheels                                                         \n",
       "4wd                  NaN           NaN   7603.000000  12647.333333   \n",
       "fwd              11595.0   8249.000000   8396.387755   9811.800000   \n",
       "rwd              23949.6  24202.714286  14337.777778  21711.833333   \n",
       "\n",
       "                            \n",
       "body-style           wagon  \n",
       "drive-wheels                \n",
       "4wd            9095.750000  \n",
       "fwd            9997.333333  \n",
       "rwd           16994.222222  "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_pivot = grouped_test1.pivot(index='drive-wheels',columns='body-style')\n",
    "grouped_pivot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Often, we won't have data for some of the pivot cells. We can fill these missing cells with the value 0, but any other value could potentially be used as well. It should be mentioned that missing data is quite a complex subject and is an entire course on its own.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>body-style</th>\n",
       "      <th>convertible</th>\n",
       "      <th>hardtop</th>\n",
       "      <th>hatchback</th>\n",
       "      <th>sedan</th>\n",
       "      <th>wagon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7603.000000</td>\n",
       "      <td>12647.333333</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>11595.0</td>\n",
       "      <td>8249.000000</td>\n",
       "      <td>8396.387755</td>\n",
       "      <td>9811.800000</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>23949.6</td>\n",
       "      <td>24202.714286</td>\n",
       "      <td>14337.777778</td>\n",
       "      <td>21711.833333</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   price                                            \\\n",
       "body-style   convertible       hardtop     hatchback         sedan   \n",
       "drive-wheels                                                         \n",
       "4wd                  0.0      0.000000   7603.000000  12647.333333   \n",
       "fwd              11595.0   8249.000000   8396.387755   9811.800000   \n",
       "rwd              23949.6  24202.714286  14337.777778  21711.833333   \n",
       "\n",
       "                            \n",
       "body-style           wagon  \n",
       "drive-wheels                \n",
       "4wd            9095.750000  \n",
       "fwd            9997.333333  \n",
       "rwd           16994.222222  "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_pivot = grouped_pivot.fillna(0) #fill missing values with 0\n",
    "grouped_pivot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question 4:</h1>\n",
    "\n",
    "<p>Use the \"groupby\" function to find the average \"price\" of each car based on \"body-style\" ? </p>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "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": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df_gptest2 = df[['body-style','price']]\n",
    "grouped_test_bodystyle = df_gptest2.groupby(['body-style'],as_index= False).mean()\n",
    "grouped_test_bodystyle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "# grouping results\n",
    "df_gptest2 = df[['body-style','price']]\n",
    "grouped_test_bodystyle = df_gptest2.groupby(['body-style'],as_index= False).mean()\n",
    "grouped_test_bodystyle\n",
    "\n",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you did not import \"pyplot\" let's do it again. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#use the grouped results\n",
    "plt.pcolor(grouped_pivot, cmap='RdBu')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The heatmap plots the target variable (price) proportional to colour with respect to the variables 'drive-wheel' and 'body-style' in the vertical and horizontal axis respectively. This allows us to visualize how the price is related to 'drive-wheel' and 'body-style'.</p>\n",
    "\n",
    "<p>The default labels convey no useful information to us. Let's change that:</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "im = ax.pcolor(grouped_pivot, cmap='RdBu')\n",
    "\n",
    "#label names\n",
    "row_labels = grouped_pivot.columns.levels[1]\n",
    "col_labels = grouped_pivot.index\n",
    "\n",
    "#move ticks and labels to the center\n",
    "ax.set_xticks(np.arange(grouped_pivot.shape[1]) + 0.5, minor=False)\n",
    "ax.set_yticks(np.arange(grouped_pivot.shape[0]) + 0.5, minor=False)\n",
    "\n",
    "#insert labels\n",
    "ax.set_xticklabels(row_labels, minor=False)\n",
    "ax.set_yticklabels(col_labels, minor=False)\n",
    "\n",
    "#rotate label if too long\n",
    "plt.xticks(rotation=90)\n",
    "\n",
    "fig.colorbar(im)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Visualization is very important in data science, and Python visualization packages provide great freedom. We will go more in-depth in a separate Python Visualizations course.</p>\n",
    "\n",
    "<p>The main question we want to answer in this module, is \"What are the main characteristics which have the most impact on the car price?\".</p>\n",
    "\n",
    "<p>To get a better measure of the important characteristics, we look at the correlation of these variables with the car price, in other words: how is the car price dependent on this variable?</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"correlation_causation\">5. Correlation and Causation</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p><b>Correlation</b>: a measure of the extent of interdependence between variables.</p>\n",
    "\n",
    "<p><b>Causation</b>: the relationship between cause and effect between two variables.</p>\n",
    "\n",
    "<p>It is important to know the difference between these two and that correlation does not imply causation. Determining correlation is much simpler  the determining causation as causation may require independent experimentation.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p3>Pearson Correlation</p>\n",
    "\n",
    "<p>The Pearson Correlation measures the linear dependence between two variables X and Y.</p>\n",
    "<p>The resulting coefficient is a value between -1 and 1 inclusive, where:</p>\n",
    "<ul>\n",
    "    <li><b>1</b>: Total positive linear correlation.</li>\n",
    "    <li><b>0</b>: No linear correlation, the two variables most likely do not affect each other.</li>\n",
    "    <li><b>-1</b>: Total negative linear correlation.</li>\n",
    "</ul>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Pearson Correlation is the default method of the function \"corr\".  Like before we can calculate the Pearson Correlation of the of the 'int64' or 'float64'  variables.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "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": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " sometimes we would like to know the significant of the correlation estimate. \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": 38,
   "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": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.584641822265508  with a P-value of P = 8.076488270733218e-20\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['wheel-base'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between wheel-base and price is statistically significant, although the linear relationship isn't extremely strong (~0.585)</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Horsepower vs Price</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the  Pearson Correlation Coefficient and P-value of 'horsepower' and 'price'.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8095745670036559  with a P-value of P =  6.369057428260101e-48\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['horsepower'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between horsepower and price is statistically significant, and the linear relationship is quite strong (~0.809, close to 1)</p>\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": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.6906283804483638  with a P-value of P =  8.016477466159556e-30\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['length'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between length and price is statistically significant, and the linear relationship is moderately strong (~0.691).</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Width vs Price</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the Pearson Correlation Coefficient and P-value of 'width' and 'price':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.7512653440522673  with a P-value of P = 9.200335510481646e-38\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['width'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Conclusion:\n",
    "\n",
    "Since the p-value is &lt; 0.001, the correlation between width and price is statistically significant, and the linear relationship is quite strong (~0.751).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Curb-weight vs Price\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the Pearson Correlation Coefficient and P-value of 'curb-weight' and 'price':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8344145257702843  with a P-value of P =  2.189577238894065e-53\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['curb-weight'], df['price'])\n",
    "print( \"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between curb-weight and price is statistically significant, and the linear relationship is quite strong (~0.834).</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Engine-size vs Price</h3>\n",
    "\n",
    "Let's calculate the Pearson Correlation Coefficient and P-value of 'engine-size' and 'price':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8723351674455185  with a P-value of P = 9.265491622198389e-64\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['engine-size'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between engine-size and price is statistically significant, and the linear relationship is very strong (~0.872).</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Bore vs Price</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the  Pearson Correlation Coefficient and P-value of 'bore' and 'price':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.5431553832626602  with a P-value of P =   8.049189483935489e-17\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['bore'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =  \", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between bore and price is statistically significant, but the linear relationship is only moderate (~0.521).</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can relate the process for each 'City-mpg'  and 'Highway-mpg':\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>City-mpg vs Price</h3>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.6865710067844678  with a P-value of P =  2.321132065567641e-29\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['city-mpg'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between city-mpg and price is statistically significant, and the coefficient of ~ -0.687 shows that the relationship is negative and moderately strong.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Highway-mpg vs Price</h3>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.704692265058953  with a P-value of P =  1.7495471144476358e-31\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['highway-mpg'], df['price'])\n",
    "print( \"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Conclusion:\n",
    "\n",
    "Since the p-value is &lt; 0.001, the correlation between highway-mpg and price is statistically significant, and the coefficient of ~ -0.705 shows that the relationship is negative and moderately strong.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"anova\">6. ANOVA</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>ANOVA: Analysis of Variance</h3>\n",
    "<p>The Analysis of Variance  (ANOVA) is a statistical method used to test whether there are significant differences between the means of two or more groups. ANOVA returns two parameters:</p>\n",
    "\n",
    "<p><b>F-test score</b>: ANOVA assumes the means of all groups are the same, calculates how much the actual means deviate from the assumption, and reports it as the F-test score. A larger score means there is a larger difference between the means.</p>\n",
    "\n",
    "<p><b>P-value</b>:  P-value tells how statistically significant is our calculated score value.</p>\n",
    "\n",
    "<p>If our price variable is strongly correlated with the variable we are analyzing, expect ANOVA to return a sizeable F-test score and a small p-value.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Drive Wheels</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Since ANOVA analyzes the difference between different groups of the same variable, the groupby function will come in handy. Because the ANOVA algorithm averages the data automatically, we do not need to take the average before hand.</p>\n",
    "\n",
    "<p>Let's see if different types 'drive-wheels' impact  'price', we group the data.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's see if different types 'drive-wheels' impact  'price', we group the data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>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": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_test2=df_gptest[['drive-wheels', 'price']].groupby(['drive-wheels'])\n",
    "grouped_test2.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "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": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_gptest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can obtain the values of the method group using the method \"get_group\".  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "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": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_test2.get_group('4wd')['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can use the function 'f_oneway' in the module 'stats'  to obtain the <b>F-test score</b> and <b>P-value</b>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 67.95406500780399 , P = 3.3945443577151245e-23\n"
     ]
    }
   ],
   "source": [
    "# ANOVA\n",
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('fwd')['price'], grouped_test2.get_group('rwd')['price'], grouped_test2.get_group('4wd')['price'])  \n",
    " \n",
    "print( \"ANOVA results: F=\", f_val, \", P =\", p_val)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a great result, with a large F test score showing a strong correlation and a P value of almost 0 implying almost certain statistical significance. But does this mean all three tested groups are all this highly correlated? \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Separately: fwd and rwd\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "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": 53,
   "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": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 0.665465750252303 , P = 0.41620116697845666\n"
     ]
    }
   ],
   "source": [
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('4wd')['price'], grouped_test2.get_group('fwd')['price'])  \n",
    " \n",
    "print(\"ANOVA results: F=\", f_val, \", P =\", p_val)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Conclusion: Important Variables</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We now have a better idea of what our data looks like and which variables are important to take into account when predicting the car price. We have narrowed it down to the following variables:</p>\n",
    "\n",
    "Continuous numerical variables:\n",
    "\n",
    "<ul>\n",
    "    <li>Length</li>\n",
    "    <li>Width</li>\n",
    "    <li>Curb-weight</li>\n",
    "    <li>Engine-size</li>\n",
    "    <li>Horsepower</li>\n",
    "    <li>City-mpg</li>\n",
    "    <li>Highway-mpg</li>\n",
    "    <li>Wheel-base</li>\n",
    "    <li>Bore</li>\n",
    "</ul>\n",
    "    \n",
    "Categorical variables:\n",
    "<ul>\n",
    "    <li>Drive-wheels</li>\n",
    "</ul>\n",
    "\n",
    "<p>As we now move into building machine learning models to automate our analysis, feeding the model with variables that meaningfully affect our target variable will improve our model's prediction performance.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Thank you for completing this lab!\n",
    "\n",
    "## Author\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>\n",
    "\n",
    "### Other Contributors\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/\" target=\"_blank\">Mahdi Noorian PhD</a>\n",
    "\n",
    "Bahare Talayian\n",
    "\n",
    "Eric Xiao\n",
    "\n",
    "Steven Dong\n",
    "\n",
    "Parizad\n",
    "\n",
    "Hima Vasudevan\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/fiorellawever/\" target=\"_blank\">Fiorella Wenver</a>\n",
    "\n",
    "<a href=\" https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n",
    "\n",
    "## Change Log\n",
    "\n",
    "| Date (YYYY-MM-DD) | Version | Changed By | Change Description                 |\n",
    "| ----------------- | ------- | ---------- | ---------------------------------- |\n",
    "| 2020-08-27        | 2.0     | Lavanya    | Moved lab to course repo in GitLab |\n",
    "\n",
    "<hr>\n",
    "\n",
    "## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n"
   ]
  }
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