3 - Exploratory Data Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"text-align:center\">\n",
    "    <a href=\"https://skills.network/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2022-01-01\" target=\"_blank\">\n",
    "    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/assets/logos/SN_web_lightmode.png\" width=\"200\" alt=\"Skills Network Logo\"  />\n",
    "    </a>\n",
    "</p>\n",
    "\n",
    "In this notebook we will explore features or charecteristics to predict price of cars\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>What are the main characteristics that have the most impact on the car price?</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import libraries:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#install specific version of libraries used in lab\n",
    "#! mamba install pandas==1.3.3\n",
    "#! mamba install numpy=1.21.2\n",
    "#! mamba install scipy=1.7.1-y\n",
    "#!  mamba install seaborn=0.9.0-y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the data and store it in dataframe `df`:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dataset was hosted on IBM Cloud object. Click <a href=\"https://cocl.us/DA101EN_object_storage?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2022-01-01\">HERE</a> for free storage.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\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": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path='https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Data%20files/automobileEDA.csv'\n",
    "df = pd.read_csv(path)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4> Analyzing Individual Feature Patterns Using Visualization</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To install Seaborn we use pip, the Python package manager.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We import visualization packages \"Matplotlib\" and \"Seaborn\". We also import \"%matplotlib inline\" to plot in a Jupyter notebook.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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": 6,
   "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": [
    "<b>What is the data type of the column \"peak-rpm\"? </b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Data type of the column \"peak-rpm\"\n",
    "df['peak-rpm'].dtypes"
   ]
  },
  {
   "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": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>symboling</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.466264</td>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.365404</td>\n",
       "      <td>-0.242423</td>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.233118</td>\n",
       "      <td>-0.110581</td>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.008245</td>\n",
       "      <td>-0.182196</td>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.279740</td>\n",
       "      <td>-0.035527</td>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.066171</td>\n",
       "      <td>-0.196735</td>\n",
       "      <td>0.196735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>normalized-losses</th>\n",
       "      <td>0.466264</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.101546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wheel-base</th>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>-0.307237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>length</th>\n",
       "      <td>-0.365404</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>-0.211187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>width</th>\n",
       "      <td>-0.242423</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>-0.244356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>height</th>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>-0.281578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>curb-weight</th>\n",
       "      <td>-0.233118</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>-0.221046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>-0.110581</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>-0.070779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>-0.054458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.008245</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>-0.241303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>-0.182196</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.985231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>0.169053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>0.279740</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.475812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-mpg</th>\n",
       "      <td>-0.035527</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>-0.265676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>-0.198690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.110326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-L/100km</th>\n",
       "      <td>0.066171</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>0.241282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diesel</th>\n",
       "      <td>-0.196735</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gas</th>\n",
       "      <td>0.196735</td>\n",
       "      <td>0.101546</td>\n",
       "      <td>-0.307237</td>\n",
       "      <td>-0.211187</td>\n",
       "      <td>-0.244356</td>\n",
       "      <td>-0.281578</td>\n",
       "      <td>-0.221046</td>\n",
       "      <td>-0.070779</td>\n",
       "      <td>-0.054458</td>\n",
       "      <td>-0.241303</td>\n",
       "      <td>-0.985231</td>\n",
       "      <td>0.169053</td>\n",
       "      <td>0.475812</td>\n",
       "      <td>-0.265676</td>\n",
       "      <td>-0.198690</td>\n",
       "      <td>-0.110326</td>\n",
       "      <td>0.241282</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   symboling  normalized-losses  wheel-base    length  \\\n",
       "symboling           1.000000           0.466264   -0.535987 -0.365404   \n",
       "normalized-losses   0.466264           1.000000   -0.056661  0.019424   \n",
       "wheel-base         -0.535987          -0.056661    1.000000  0.876024   \n",
       "length             -0.365404           0.019424    0.876024  1.000000   \n",
       "width              -0.242423           0.086802    0.814507  0.857170   \n",
       "height             -0.550160          -0.373737    0.590742  0.492063   \n",
       "curb-weight        -0.233118           0.099404    0.782097  0.880665   \n",
       "engine-size        -0.110581           0.112360    0.572027  0.685025   \n",
       "bore               -0.140019          -0.029862    0.493244  0.608971   \n",
       "stroke             -0.008245           0.055563    0.158502  0.124139   \n",
       "compression-ratio  -0.182196          -0.114713    0.250313  0.159733   \n",
       "horsepower          0.075819           0.217299    0.371147  0.579821   \n",
       "peak-rpm            0.279740           0.239543   -0.360305 -0.285970   \n",
       "city-mpg           -0.035527          -0.225016   -0.470606 -0.665192   \n",
       "highway-mpg         0.036233          -0.181877   -0.543304 -0.698142   \n",
       "price              -0.082391           0.133999    0.584642  0.690628   \n",
       "city-L/100km        0.066171           0.238567    0.476153  0.657373   \n",
       "diesel             -0.196735          -0.101546    0.307237  0.211187   \n",
       "gas                 0.196735           0.101546   -0.307237 -0.211187   \n",
       "\n",
       "                      width    height  curb-weight  engine-size      bore  \\\n",
       "symboling         -0.242423 -0.550160    -0.233118    -0.110581 -0.140019   \n",
       "normalized-losses  0.086802 -0.373737     0.099404     0.112360 -0.029862   \n",
       "wheel-base         0.814507  0.590742     0.782097     0.572027  0.493244   \n",
       "length             0.857170  0.492063     0.880665     0.685025  0.608971   \n",
       "width              1.000000  0.306002     0.866201     0.729436  0.544885   \n",
       "height             0.306002  1.000000     0.307581     0.074694  0.180449   \n",
       "curb-weight        0.866201  0.307581     1.000000     0.849072  0.644060   \n",
       "engine-size        0.729436  0.074694     0.849072     1.000000  0.572609   \n",
       "bore               0.544885  0.180449     0.644060     0.572609  1.000000   \n",
       "stroke             0.188829 -0.062704     0.167562     0.209523 -0.055390   \n",
       "compression-ratio  0.189867  0.259737     0.156433     0.028889  0.001263   \n",
       "horsepower         0.615077 -0.087027     0.757976     0.822676  0.566936   \n",
       "peak-rpm          -0.245800 -0.309974    -0.279361    -0.256733 -0.267392   \n",
       "city-mpg          -0.633531 -0.049800    -0.749543    -0.650546 -0.582027   \n",
       "highway-mpg       -0.680635 -0.104812    -0.794889    -0.679571 -0.591309   \n",
       "price              0.751265  0.135486     0.834415     0.872335  0.543155   \n",
       "city-L/100km       0.673363  0.003811     0.785353     0.745059  0.554610   \n",
       "diesel             0.244356  0.281578     0.221046     0.070779  0.054458   \n",
       "gas               -0.244356 -0.281578    -0.221046    -0.070779 -0.054458   \n",
       "\n",
       "                     stroke  compression-ratio  horsepower  peak-rpm  \\\n",
       "symboling         -0.008245          -0.182196    0.075819  0.279740   \n",
       "normalized-losses  0.055563          -0.114713    0.217299  0.239543   \n",
       "wheel-base         0.158502           0.250313    0.371147 -0.360305   \n",
       "length             0.124139           0.159733    0.579821 -0.285970   \n",
       "width              0.188829           0.189867    0.615077 -0.245800   \n",
       "height            -0.062704           0.259737   -0.087027 -0.309974   \n",
       "curb-weight        0.167562           0.156433    0.757976 -0.279361   \n",
       "engine-size        0.209523           0.028889    0.822676 -0.256733   \n",
       "bore              -0.055390           0.001263    0.566936 -0.267392   \n",
       "stroke             1.000000           0.187923    0.098462 -0.065713   \n",
       "compression-ratio  0.187923           1.000000   -0.214514 -0.435780   \n",
       "horsepower         0.098462          -0.214514    1.000000  0.107885   \n",
       "peak-rpm          -0.065713          -0.435780    0.107885  1.000000   \n",
       "city-mpg          -0.034696           0.331425   -0.822214 -0.115413   \n",
       "highway-mpg       -0.035201           0.268465   -0.804575 -0.058598   \n",
       "price              0.082310           0.071107    0.809575 -0.101616   \n",
       "city-L/100km       0.037300          -0.299372    0.889488  0.115830   \n",
       "diesel             0.241303           0.985231   -0.169053 -0.475812   \n",
       "gas               -0.241303          -0.985231    0.169053  0.475812   \n",
       "\n",
       "                   city-mpg  highway-mpg     price  city-L/100km    diesel  \\\n",
       "symboling         -0.035527     0.036233 -0.082391      0.066171 -0.196735   \n",
       "normalized-losses -0.225016    -0.181877  0.133999      0.238567 -0.101546   \n",
       "wheel-base        -0.470606    -0.543304  0.584642      0.476153  0.307237   \n",
       "length            -0.665192    -0.698142  0.690628      0.657373  0.211187   \n",
       "width             -0.633531    -0.680635  0.751265      0.673363  0.244356   \n",
       "height            -0.049800    -0.104812  0.135486      0.003811  0.281578   \n",
       "curb-weight       -0.749543    -0.794889  0.834415      0.785353  0.221046   \n",
       "engine-size       -0.650546    -0.679571  0.872335      0.745059  0.070779   \n",
       "bore              -0.582027    -0.591309  0.543155      0.554610  0.054458   \n",
       "stroke            -0.034696    -0.035201  0.082310      0.037300  0.241303   \n",
       "compression-ratio  0.331425     0.268465  0.071107     -0.299372  0.985231   \n",
       "horsepower        -0.822214    -0.804575  0.809575      0.889488 -0.169053   \n",
       "peak-rpm          -0.115413    -0.058598 -0.101616      0.115830 -0.475812   \n",
       "city-mpg           1.000000     0.972044 -0.686571     -0.949713  0.265676   \n",
       "highway-mpg        0.972044     1.000000 -0.704692     -0.930028  0.198690   \n",
       "price             -0.686571    -0.704692  1.000000      0.789898  0.110326   \n",
       "city-L/100km      -0.949713    -0.930028  0.789898      1.000000 -0.241282   \n",
       "diesel             0.265676     0.198690  0.110326     -0.241282  1.000000   \n",
       "gas               -0.265676    -0.198690 -0.110326      0.241282 -1.000000   \n",
       "\n",
       "                        gas  \n",
       "symboling          0.196735  \n",
       "normalized-losses  0.101546  \n",
       "wheel-base        -0.307237  \n",
       "length            -0.211187  \n",
       "width             -0.244356  \n",
       "height            -0.281578  \n",
       "curb-weight       -0.221046  \n",
       "engine-size       -0.070779  \n",
       "bore              -0.054458  \n",
       "stroke            -0.241303  \n",
       "compression-ratio -0.985231  \n",
       "horsepower         0.169053  \n",
       "peak-rpm           0.475812  \n",
       "city-mpg          -0.265676  \n",
       "highway-mpg       -0.198690  \n",
       "price             -0.110326  \n",
       "city-L/100km       0.241282  \n",
       "diesel            -1.000000  \n",
       "gas                1.000000  "
      ]
     },
     "execution_count": 8,
     "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": [
    "<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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Correlation between the columns: bore, stroke, compression-ratio, and horsepower.\n",
    "df[['bore','stroke','compression-ratio','horsepower']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Continuous Numerical Variables:</h3> \n",
    "\n",
    "<p>Continuous numerical variables are variables that may contain any value within some range. They can be of type \"int64\" or \"float64\". A great way to visualize these variables is by using scatterplots with fitted lines.</p>\n",
    "\n",
    "<p>In order to start understanding the (linear) relationship between an individual variable and the price, we can use \"regplot\" which plots the scatterplot plus the fitted regression line for the data. This will be useful later on for visualizing the fit of the simple linear regression model as well. </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": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 53114.287743971036)"
      ]
     },
     "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": [
    "# Engine size as potential predictor variable of price\n",
    "sns.regplot(x=\"engine-size\", y=\"price\", data=df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>As the engine-size goes up, the price goes up: this indicates a positive direct correlation between these two variables. Engine size seems like a pretty good predictor of price since the regression line is almost a perfect diagonal line.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'engine-size' and 'price' and see that it's approximately 0.87.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 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>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": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[[\"engine-size\", \"price\"]].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Highway mpg is a potential predictor variable of price. Let's find the scatterplot of \"highway-mpg\" and \"price\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='highway-mpg', 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=\"highway-mpg\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>As highway-mpg goes up, the price goes down: this indicates an inverse/negative relationship between these two variables. Highway mpg could potentially be a predictor of price.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'highway-mpg' and 'price' and see it's approximately -0.704.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 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>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": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['highway-mpg', 'price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Weak Linear Relationship</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see if \"peak-rpm\" is a predictor variable of \"price\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='peak-rpm', ylabel='price'>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x=\"peak-rpm\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Peak rpm does not seem like a good predictor of the price at all since the regression line is close to horizontal. Also, the data points are very scattered and far from the fitted line, showing lots of variability. Therefore, it's not a reliable variable.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'peak-rpm' and 'price' and see it's approximately -0.101616.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['peak-rpm','price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Let's find the correlation  between x=\"stroke\" and y=\"price\".</p>\n",
    "<p>Hint: if you would like to select those columns, use the following syntax: df[[\"stroke\",\"price\"]].  </p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Correlation  between x=\"stroke\" and y=\"price\"\n",
    "df[['stroke','price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Given the correlation results between \"price\" and \"stroke\", do we expect a linear relationship?</p> \n",
    "<p>We verify your results using the function \"regplot()\".</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='stroke', ylabel='price'>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualizaton of linear relationship \n",
    "sns.regplot(x='stroke', y='price', data = df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Categorical Variables</h3>\n",
    "\n",
    "<p>These are variables that describe a 'characteristic' of a data unit, and are selected from a small group of categories. The categorical variables can have the type \"object\" or \"int64\". A good way to visualize categorical variables is by using boxplots.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the relationship between \"body-style\" and \"price\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='body-style', ylabel='price'>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"body-style\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We see that the distributions of price between the different body-style categories have a significant overlap, so body-style would not be a good predictor of price. Let's examine engine \"engine-location\" and \"price\":</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='engine-location', ylabel='price'>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"engine-location\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Here we see that the distribution of price between these two engine-location categories, front and rear, are distinct enough to take engine-location as a potential good predictor of price.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's examine \"drive-wheels\" and \"price\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='drive-wheels', ylabel='price'>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# drive-wheels\n",
    "sns.boxplot(x=\"drive-wheels\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Here we see that the distribution of price between the different drive-wheels categories differs. As such, drive-wheels could potentially be a predictor of price.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Descriptive Statistical Analysis</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Let's first take a look at the variables by utilizing a description method.</p>\n",
    "\n",
    "<p>The <b>describe</b> function automatically computes basic statistics for all continuous variables. Any NaN values are automatically skipped in these statistics.</p>\n",
    "\n",
    "This will show:\n",
    "\n",
    "<ul>\n",
    "    <li>the count of that variable</li>\n",
    "    <li>the mean</li>\n",
    "    <li>the standard deviation (std)</li> \n",
    "    <li>the minimum value</li>\n",
    "    <li>the IQR (Interquartile Range: 25%, 50% and 75%)</li>\n",
    "    <li>the maximum value</li>\n",
    "<ul>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can apply the method \"describe\" as follows:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.00000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>197.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.840796</td>\n",
       "      <td>122.00000</td>\n",
       "      <td>98.797015</td>\n",
       "      <td>0.837102</td>\n",
       "      <td>0.915126</td>\n",
       "      <td>53.766667</td>\n",
       "      <td>2555.666667</td>\n",
       "      <td>126.875622</td>\n",
       "      <td>3.330692</td>\n",
       "      <td>3.256904</td>\n",
       "      <td>10.164279</td>\n",
       "      <td>103.405534</td>\n",
       "      <td>5117.665368</td>\n",
       "      <td>25.179104</td>\n",
       "      <td>30.686567</td>\n",
       "      <td>13207.129353</td>\n",
       "      <td>9.944145</td>\n",
       "      <td>0.099502</td>\n",
       "      <td>0.900498</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.254802</td>\n",
       "      <td>31.99625</td>\n",
       "      <td>6.066366</td>\n",
       "      <td>0.059213</td>\n",
       "      <td>0.029187</td>\n",
       "      <td>2.447822</td>\n",
       "      <td>517.296727</td>\n",
       "      <td>41.546834</td>\n",
       "      <td>0.268072</td>\n",
       "      <td>0.319256</td>\n",
       "      <td>4.004965</td>\n",
       "      <td>37.365700</td>\n",
       "      <td>478.113805</td>\n",
       "      <td>6.423220</td>\n",
       "      <td>6.815150</td>\n",
       "      <td>7947.066342</td>\n",
       "      <td>2.534599</td>\n",
       "      <td>0.300083</td>\n",
       "      <td>0.300083</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-2.000000</td>\n",
       "      <td>65.00000</td>\n",
       "      <td>86.600000</td>\n",
       "      <td>0.678039</td>\n",
       "      <td>0.837500</td>\n",
       "      <td>47.800000</td>\n",
       "      <td>1488.000000</td>\n",
       "      <td>61.000000</td>\n",
       "      <td>2.540000</td>\n",
       "      <td>2.070000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>48.000000</td>\n",
       "      <td>4150.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>5118.000000</td>\n",
       "      <td>4.795918</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>101.00000</td>\n",
       "      <td>94.500000</td>\n",
       "      <td>0.801538</td>\n",
       "      <td>0.890278</td>\n",
       "      <td>52.000000</td>\n",
       "      <td>2169.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>3.150000</td>\n",
       "      <td>3.110000</td>\n",
       "      <td>8.600000</td>\n",
       "      <td>70.000000</td>\n",
       "      <td>4800.000000</td>\n",
       "      <td>19.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>7775.000000</td>\n",
       "      <td>7.833333</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>122.00000</td>\n",
       "      <td>97.000000</td>\n",
       "      <td>0.832292</td>\n",
       "      <td>0.909722</td>\n",
       "      <td>54.100000</td>\n",
       "      <td>2414.000000</td>\n",
       "      <td>120.000000</td>\n",
       "      <td>3.310000</td>\n",
       "      <td>3.290000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>95.000000</td>\n",
       "      <td>5125.369458</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>10295.000000</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2.000000</td>\n",
       "      <td>137.00000</td>\n",
       "      <td>102.400000</td>\n",
       "      <td>0.881788</td>\n",
       "      <td>0.925000</td>\n",
       "      <td>55.500000</td>\n",
       "      <td>2926.000000</td>\n",
       "      <td>141.000000</td>\n",
       "      <td>3.580000</td>\n",
       "      <td>3.410000</td>\n",
       "      <td>9.400000</td>\n",
       "      <td>116.000000</td>\n",
       "      <td>5500.000000</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>34.000000</td>\n",
       "      <td>16500.000000</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>256.00000</td>\n",
       "      <td>120.900000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>59.800000</td>\n",
       "      <td>4066.000000</td>\n",
       "      <td>326.000000</td>\n",
       "      <td>3.940000</td>\n",
       "      <td>4.170000</td>\n",
       "      <td>23.000000</td>\n",
       "      <td>262.000000</td>\n",
       "      <td>6600.000000</td>\n",
       "      <td>49.000000</td>\n",
       "      <td>54.000000</td>\n",
       "      <td>45400.000000</td>\n",
       "      <td>18.076923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        symboling  normalized-losses  wheel-base      length       width  \\\n",
       "count  201.000000          201.00000  201.000000  201.000000  201.000000   \n",
       "mean     0.840796          122.00000   98.797015    0.837102    0.915126   \n",
       "std      1.254802           31.99625    6.066366    0.059213    0.029187   \n",
       "min     -2.000000           65.00000   86.600000    0.678039    0.837500   \n",
       "25%      0.000000          101.00000   94.500000    0.801538    0.890278   \n",
       "50%      1.000000          122.00000   97.000000    0.832292    0.909722   \n",
       "75%      2.000000          137.00000  102.400000    0.881788    0.925000   \n",
       "max      3.000000          256.00000  120.900000    1.000000    1.000000   \n",
       "\n",
       "           height  curb-weight  engine-size        bore      stroke  \\\n",
       "count  201.000000   201.000000   201.000000  201.000000  197.000000   \n",
       "mean    53.766667  2555.666667   126.875622    3.330692    3.256904   \n",
       "std      2.447822   517.296727    41.546834    0.268072    0.319256   \n",
       "min     47.800000  1488.000000    61.000000    2.540000    2.070000   \n",
       "25%     52.000000  2169.000000    98.000000    3.150000    3.110000   \n",
       "50%     54.100000  2414.000000   120.000000    3.310000    3.290000   \n",
       "75%     55.500000  2926.000000   141.000000    3.580000    3.410000   \n",
       "max     59.800000  4066.000000   326.000000    3.940000    4.170000   \n",
       "\n",
       "       compression-ratio  horsepower     peak-rpm    city-mpg  highway-mpg  \\\n",
       "count         201.000000  201.000000   201.000000  201.000000   201.000000   \n",
       "mean           10.164279  103.405534  5117.665368   25.179104    30.686567   \n",
       "std             4.004965   37.365700   478.113805    6.423220     6.815150   \n",
       "min             7.000000   48.000000  4150.000000   13.000000    16.000000   \n",
       "25%             8.600000   70.000000  4800.000000   19.000000    25.000000   \n",
       "50%             9.000000   95.000000  5125.369458   24.000000    30.000000   \n",
       "75%             9.400000  116.000000  5500.000000   30.000000    34.000000   \n",
       "max            23.000000  262.000000  6600.000000   49.000000    54.000000   \n",
       "\n",
       "              price  city-L/100km      diesel         gas  \n",
       "count    201.000000    201.000000  201.000000  201.000000  \n",
       "mean   13207.129353      9.944145    0.099502    0.900498  \n",
       "std     7947.066342      2.534599    0.300083    0.300083  \n",
       "min     5118.000000      4.795918    0.000000    0.000000  \n",
       "25%     7775.000000      7.833333    0.000000    1.000000  \n",
       "50%    10295.000000      9.791667    0.000000    1.000000  \n",
       "75%    16500.000000     12.368421    0.000000    1.000000  \n",
       "max    45400.000000     18.076923    1.000000    1.000000  "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The default setting of \"describe\" skips variables of type object. We can apply the method \"describe\" on the variables of type 'object' as follows:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>make</th>\n",
       "      <th>aspiration</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>engine-type</th>\n",
       "      <th>num-of-cylinders</th>\n",
       "      <th>fuel-system</th>\n",
       "      <th>horsepower-binned</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>unique</th>\n",
       "      <td>22</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>top</th>\n",
       "      <td>toyota</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>ohc</td>\n",
       "      <td>four</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>Low</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>freq</th>\n",
       "      <td>32</td>\n",
       "      <td>165</td>\n",
       "      <td>115</td>\n",
       "      <td>94</td>\n",
       "      <td>118</td>\n",
       "      <td>198</td>\n",
       "      <td>145</td>\n",
       "      <td>157</td>\n",
       "      <td>92</td>\n",
       "      <td>115</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          make aspiration num-of-doors body-style drive-wheels  \\\n",
       "count      201        201          201        201          201   \n",
       "unique      22          2            2          5            3   \n",
       "top     toyota        std         four      sedan          fwd   \n",
       "freq        32        165          115         94          118   \n",
       "\n",
       "       engine-location engine-type num-of-cylinders fuel-system  \\\n",
       "count              201         201              201         201   \n",
       "unique               2           6                7           8   \n",
       "top              front         ohc             four        mpfi   \n",
       "freq               198         145              157          92   \n",
       "\n",
       "       horsepower-binned  \n",
       "count                200  \n",
       "unique                 3  \n",
       "top                  Low  \n",
       "freq                 115  "
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe(include=['object'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Value Counts</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Value counts is a good way of understanding how many units of each characteristic/variable we have. We can apply the \"value_counts\" method on the column \"drive-wheels\". Don’t forget the method \"value_counts\" only works on pandas series, not pandas dataframes. As a result, we only include one bracket <code>df['drive-wheels']</code>, not two brackets <code>df[['drive-wheels']]</code>.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fwd    118\n",
       "rwd     75\n",
       "4wd      8\n",
       "Name: drive-wheels, dtype: int64"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can convert the series to a dataframe as follows:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     drive-wheels\n",
       "fwd           118\n",
       "rwd            75\n",
       "4wd             8"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].value_counts().to_frame()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's repeat the above steps but save the results to the dataframe \"drive_wheels_counts\" and rename the column  'drive-wheels' to 'value_counts'.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value_counts</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     value_counts\n",
       "fwd           118\n",
       "rwd            75\n",
       "4wd             8"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "drive_wheels_counts = df['drive-wheels'].value_counts().to_frame()\n",
    "drive_wheels_counts.rename(columns={'drive-wheels': 'value_counts'}, inplace=True)\n",
    "drive_wheels_counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's rename the index to 'drive-wheels':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value_counts</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              value_counts\n",
       "drive-wheels              \n",
       "fwd                    118\n",
       "rwd                     75\n",
       "4wd                      8"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "drive_wheels_counts.index.name = 'drive-wheels'\n",
    "drive_wheels_counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can repeat the above process for the variable 'engine-location'.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 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>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": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# engine-location as variable\n",
    "engine_loc_counts = df['engine-location'].value_counts().to_frame()\n",
    "engine_loc_counts.rename(columns={'engine-location': 'value_counts'}, inplace=True)\n",
    "engine_loc_counts.index.name = 'engine-location'\n",
    "engine_loc_counts.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>After examining the value counts of the engine location, we see that engine location would not be a good predictor variable for the price. This is because we only have three cars with a rear engine and 198 with an engine in the front, so this result is skewed. Thus, we are not able to draw any conclusions about the engine location.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Basics of Grouping</h3>\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": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['rwd', 'fwd', '4wd'], dtype=object)"
      ]
     },
     "execution_count": 38,
     "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": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_group_one = df[['drive-wheels','body-style','price']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then calculate the average price for each of the different categories of data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# grouping results\n",
    "df_group_one = df_group_one.groupby(['drive-wheels'],as_index=False).mean()\n",
    "df_group_one"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>From our data, it seems rear-wheel drive vehicles are, on average, the most expensive, while 4-wheel and front-wheel are approximately the same in price.</p>\n",
    "\n",
    "<p>You can also group by multiple variables. For example, let's group by both 'drive-wheels' and 'body-style'. This groups the dataframe by the unique combination of 'drive-wheels' and 'body-style'. We can store the results in the variable 'grouped_test1'.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "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": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# grouping results\n",
    "df_gptest = df[['drive-wheels','body-style','price']]\n",
    "grouped_test1 = df_gptest.groupby(['drive-wheels','body-style'],as_index=False).mean()\n",
    "grouped_test1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>This grouped data is much easier to visualize when it is made into a pivot table. A pivot table is like an Excel spreadsheet, with one variable along the column and another along the row. We can convert the dataframe to a pivot table using the method \"pivot\" to create a pivot table from the groups.</p>\n",
    "\n",
    "<p>In this case, we will leave the drive-wheels variable as the rows of the table, and pivot body-style to become the columns of the table:</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
       "    .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": 33,
     "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": 34,
   "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",
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       "\n",
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       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>body-style</th>\n",
       "      <th>convertible</th>\n",
       "      <th>hardtop</th>\n",
       "      <th>hatchback</th>\n",
       "      <th>sedan</th>\n",
       "      <th>wagon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7603.000000</td>\n",
       "      <td>12647.333333</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>11595.0</td>\n",
       "      <td>8249.000000</td>\n",
       "      <td>8396.387755</td>\n",
       "      <td>9811.800000</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>23949.6</td>\n",
       "      <td>24202.714286</td>\n",
       "      <td>14337.777778</td>\n",
       "      <td>21711.833333</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   price                                            \\\n",
       "body-style   convertible       hardtop     hatchback         sedan   \n",
       "drive-wheels                                                         \n",
       "4wd                  0.0      0.000000   7603.000000  12647.333333   \n",
       "fwd              11595.0   8249.000000   8396.387755   9811.800000   \n",
       "rwd              23949.6  24202.714286  14337.777778  21711.833333   \n",
       "\n",
       "                            \n",
       "body-style           wagon  \n",
       "drive-wheels                \n",
       "4wd            9095.750000  \n",
       "fwd            9997.333333  \n",
       "rwd           16994.222222  "
      ]
     },
     "execution_count": 34,
     "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": [
    "<p>We use the \"groupby\" function to find the average \"price\" of each car based on \"body-style\".</p>\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>body-style</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>convertible</td>\n",
       "      <td>21890.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>hardtop</td>\n",
       "      <td>22208.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>hatchback</td>\n",
       "      <td>9957.441176</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>sedan</td>\n",
       "      <td>14459.755319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>wagon</td>\n",
       "      <td>12371.960000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    body-style         price\n",
       "0  convertible  21890.500000\n",
       "1      hardtop  22208.500000\n",
       "2    hatchback   9957.441176\n",
       "3        sedan  14459.755319\n",
       "4        wagon  12371.960000"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df_group_two = df[['body-style','price']]\n",
    "df_group_two = df_group_two.groupby(['body-style'], as_index=False).mean()\n",
    "df_group_two"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you did not import \"pyplot\", let's do it again.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Variables: Drive Wheels and Body Style vs. Price</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use a heat map to visualize the relationship between Body Style vs Price.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#use the grouped results\n",
    "plt.pcolor(grouped_pivot, cmap='RdBu')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The heatmap plots the target variable (price) proportional to colour with respect to the variables 'drive-wheel' and 'body-style' on the vertical and horizontal axis, respectively. This allows us to visualize how the price is related to 'drive-wheel' and 'body-style'.</p>\n",
    "\n",
    "<p>The default labels convey no useful information to us. Let's change that:</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "im = ax.pcolor(grouped_pivot, cmap='RdBu')\n",
    "\n",
    "#label names\n",
    "row_labels = grouped_pivot.columns.levels[1]\n",
    "col_labels = grouped_pivot.index\n",
    "\n",
    "#move ticks and labels to the center\n",
    "ax.set_xticks(np.arange(grouped_pivot.shape[1]) + 0.5, minor=False)\n",
    "ax.set_yticks(np.arange(grouped_pivot.shape[0]) + 0.5, minor=False)\n",
    "\n",
    "#insert labels\n",
    "ax.set_xticklabels(row_labels, minor=False)\n",
    "ax.set_yticklabels(col_labels, minor=False)\n",
    "\n",
    "#rotate label if too long\n",
    "plt.xticks(rotation=90)\n",
    "\n",
    "fig.colorbar(im)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Visualization is very important in data science, and Python visualization packages provide great freedom. We will go more in-depth in a separate Python visualizations course.</p>\n",
    "\n",
    "<p>The main question we want to answer in this module is, \"What are the main characteristics which have the most impact on the car price?\".</p>\n",
    "\n",
    "<p>To get a better measure of the important characteristics, we look at the correlation of these variables with the car price. In other words: how is the car price dependent on this variable?</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Correlation and Causation</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p><b>Correlation</b>: a measure of the extent of interdependence between variables.</p>\n",
    "\n",
    "<p><b>Causation</b>: the relationship between cause and effect between two variables.</p>\n",
    "\n",
    "<p>It is important to know the difference between these two. Correlation does not imply causation. Determining correlation is much simpler  the determining causation as causation may require independent experimentation.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p><b>Pearson Correlation</b></p>\n",
    "<p>The Pearson Correlation measures the linear dependence between two variables X and Y.</p>\n",
    "<p>The resulting coefficient is a value between -1 and 1 inclusive, where:</p>\n",
    "<ul>\n",
    "    <li><b>1</b>: Perfect positive linear correlation.</li>\n",
    "    <li><b>0</b>: No linear correlation, the two variables most likely do not affect each other.</li>\n",
    "    <li><b>-1</b>: Perfect negative linear correlation.</li>\n",
    "</ul>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Pearson Correlation is the default method of the function \"corr\". Like before, we can calculate the Pearson Correlation of the of the 'int64' or 'float64'  variables.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>symboling</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.466264</td>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.365404</td>\n",
       "      <td>-0.242423</td>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.233118</td>\n",
       "      <td>-0.110581</td>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.008245</td>\n",
       "      <td>-0.182196</td>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.279740</td>\n",
       "      <td>-0.035527</td>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.066171</td>\n",
       "      <td>-0.196735</td>\n",
       "      <td>0.196735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>normalized-losses</th>\n",
       "      <td>0.466264</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.101546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wheel-base</th>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>-0.307237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>length</th>\n",
       "      <td>-0.365404</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>-0.211187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>width</th>\n",
       "      <td>-0.242423</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>-0.244356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>height</th>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>-0.281578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>curb-weight</th>\n",
       "      <td>-0.233118</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>-0.221046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>-0.110581</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>-0.070779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>-0.054458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.008245</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>-0.241303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>-0.182196</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.985231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>0.169053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>0.279740</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.475812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-mpg</th>\n",
       "      <td>-0.035527</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>-0.265676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>-0.198690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.110326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-L/100km</th>\n",
       "      <td>0.066171</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>0.241282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diesel</th>\n",
       "      <td>-0.196735</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gas</th>\n",
       "      <td>0.196735</td>\n",
       "      <td>0.101546</td>\n",
       "      <td>-0.307237</td>\n",
       "      <td>-0.211187</td>\n",
       "      <td>-0.244356</td>\n",
       "      <td>-0.281578</td>\n",
       "      <td>-0.221046</td>\n",
       "      <td>-0.070779</td>\n",
       "      <td>-0.054458</td>\n",
       "      <td>-0.241303</td>\n",
       "      <td>-0.985231</td>\n",
       "      <td>0.169053</td>\n",
       "      <td>0.475812</td>\n",
       "      <td>-0.265676</td>\n",
       "      <td>-0.198690</td>\n",
       "      <td>-0.110326</td>\n",
       "      <td>0.241282</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   symboling  normalized-losses  wheel-base    length  \\\n",
       "symboling           1.000000           0.466264   -0.535987 -0.365404   \n",
       "normalized-losses   0.466264           1.000000   -0.056661  0.019424   \n",
       "wheel-base         -0.535987          -0.056661    1.000000  0.876024   \n",
       "length             -0.365404           0.019424    0.876024  1.000000   \n",
       "width              -0.242423           0.086802    0.814507  0.857170   \n",
       "height             -0.550160          -0.373737    0.590742  0.492063   \n",
       "curb-weight        -0.233118           0.099404    0.782097  0.880665   \n",
       "engine-size        -0.110581           0.112360    0.572027  0.685025   \n",
       "bore               -0.140019          -0.029862    0.493244  0.608971   \n",
       "stroke             -0.008245           0.055563    0.158502  0.124139   \n",
       "compression-ratio  -0.182196          -0.114713    0.250313  0.159733   \n",
       "horsepower          0.075819           0.217299    0.371147  0.579821   \n",
       "peak-rpm            0.279740           0.239543   -0.360305 -0.285970   \n",
       "city-mpg           -0.035527          -0.225016   -0.470606 -0.665192   \n",
       "highway-mpg         0.036233          -0.181877   -0.543304 -0.698142   \n",
       "price              -0.082391           0.133999    0.584642  0.690628   \n",
       "city-L/100km        0.066171           0.238567    0.476153  0.657373   \n",
       "diesel             -0.196735          -0.101546    0.307237  0.211187   \n",
       "gas                 0.196735           0.101546   -0.307237 -0.211187   \n",
       "\n",
       "                      width    height  curb-weight  engine-size      bore  \\\n",
       "symboling         -0.242423 -0.550160    -0.233118    -0.110581 -0.140019   \n",
       "normalized-losses  0.086802 -0.373737     0.099404     0.112360 -0.029862   \n",
       "wheel-base         0.814507  0.590742     0.782097     0.572027  0.493244   \n",
       "length             0.857170  0.492063     0.880665     0.685025  0.608971   \n",
       "width              1.000000  0.306002     0.866201     0.729436  0.544885   \n",
       "height             0.306002  1.000000     0.307581     0.074694  0.180449   \n",
       "curb-weight        0.866201  0.307581     1.000000     0.849072  0.644060   \n",
       "engine-size        0.729436  0.074694     0.849072     1.000000  0.572609   \n",
       "bore               0.544885  0.180449     0.644060     0.572609  1.000000   \n",
       "stroke             0.188829 -0.062704     0.167562     0.209523 -0.055390   \n",
       "compression-ratio  0.189867  0.259737     0.156433     0.028889  0.001263   \n",
       "horsepower         0.615077 -0.087027     0.757976     0.822676  0.566936   \n",
       "peak-rpm          -0.245800 -0.309974    -0.279361    -0.256733 -0.267392   \n",
       "city-mpg          -0.633531 -0.049800    -0.749543    -0.650546 -0.582027   \n",
       "highway-mpg       -0.680635 -0.104812    -0.794889    -0.679571 -0.591309   \n",
       "price              0.751265  0.135486     0.834415     0.872335  0.543155   \n",
       "city-L/100km       0.673363  0.003811     0.785353     0.745059  0.554610   \n",
       "diesel             0.244356  0.281578     0.221046     0.070779  0.054458   \n",
       "gas               -0.244356 -0.281578    -0.221046    -0.070779 -0.054458   \n",
       "\n",
       "                     stroke  compression-ratio  horsepower  peak-rpm  \\\n",
       "symboling         -0.008245          -0.182196    0.075819  0.279740   \n",
       "normalized-losses  0.055563          -0.114713    0.217299  0.239543   \n",
       "wheel-base         0.158502           0.250313    0.371147 -0.360305   \n",
       "length             0.124139           0.159733    0.579821 -0.285970   \n",
       "width              0.188829           0.189867    0.615077 -0.245800   \n",
       "height            -0.062704           0.259737   -0.087027 -0.309974   \n",
       "curb-weight        0.167562           0.156433    0.757976 -0.279361   \n",
       "engine-size        0.209523           0.028889    0.822676 -0.256733   \n",
       "bore              -0.055390           0.001263    0.566936 -0.267392   \n",
       "stroke             1.000000           0.187923    0.098462 -0.065713   \n",
       "compression-ratio  0.187923           1.000000   -0.214514 -0.435780   \n",
       "horsepower         0.098462          -0.214514    1.000000  0.107885   \n",
       "peak-rpm          -0.065713          -0.435780    0.107885  1.000000   \n",
       "city-mpg          -0.034696           0.331425   -0.822214 -0.115413   \n",
       "highway-mpg       -0.035201           0.268465   -0.804575 -0.058598   \n",
       "price              0.082310           0.071107    0.809575 -0.101616   \n",
       "city-L/100km       0.037300          -0.299372    0.889488  0.115830   \n",
       "diesel             0.241303           0.985231   -0.169053 -0.475812   \n",
       "gas               -0.241303          -0.985231    0.169053  0.475812   \n",
       "\n",
       "                   city-mpg  highway-mpg     price  city-L/100km    diesel  \\\n",
       "symboling         -0.035527     0.036233 -0.082391      0.066171 -0.196735   \n",
       "normalized-losses -0.225016    -0.181877  0.133999      0.238567 -0.101546   \n",
       "wheel-base        -0.470606    -0.543304  0.584642      0.476153  0.307237   \n",
       "length            -0.665192    -0.698142  0.690628      0.657373  0.211187   \n",
       "width             -0.633531    -0.680635  0.751265      0.673363  0.244356   \n",
       "height            -0.049800    -0.104812  0.135486      0.003811  0.281578   \n",
       "curb-weight       -0.749543    -0.794889  0.834415      0.785353  0.221046   \n",
       "engine-size       -0.650546    -0.679571  0.872335      0.745059  0.070779   \n",
       "bore              -0.582027    -0.591309  0.543155      0.554610  0.054458   \n",
       "stroke            -0.034696    -0.035201  0.082310      0.037300  0.241303   \n",
       "compression-ratio  0.331425     0.268465  0.071107     -0.299372  0.985231   \n",
       "horsepower        -0.822214    -0.804575  0.809575      0.889488 -0.169053   \n",
       "peak-rpm          -0.115413    -0.058598 -0.101616      0.115830 -0.475812   \n",
       "city-mpg           1.000000     0.972044 -0.686571     -0.949713  0.265676   \n",
       "highway-mpg        0.972044     1.000000 -0.704692     -0.930028  0.198690   \n",
       "price             -0.686571    -0.704692  1.000000      0.789898  0.110326   \n",
       "city-L/100km      -0.949713    -0.930028  0.789898      1.000000 -0.241282   \n",
       "diesel             0.265676     0.198690  0.110326     -0.241282  1.000000   \n",
       "gas               -0.265676    -0.198690 -0.110326      0.241282 -1.000000   \n",
       "\n",
       "                        gas  \n",
       "symboling          0.196735  \n",
       "normalized-losses  0.101546  \n",
       "wheel-base        -0.307237  \n",
       "length            -0.211187  \n",
       "width             -0.244356  \n",
       "height            -0.281578  \n",
       "curb-weight       -0.221046  \n",
       "engine-size       -0.070779  \n",
       "bore              -0.054458  \n",
       "stroke            -0.241303  \n",
       "compression-ratio -0.985231  \n",
       "horsepower         0.169053  \n",
       "peak-rpm           0.475812  \n",
       "city-mpg          -0.265676  \n",
       "highway-mpg       -0.198690  \n",
       "price             -0.110326  \n",
       "city-L/100km       0.241282  \n",
       "diesel            -1.000000  \n",
       "gas                1.000000  "
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sometimes we would like to know the significant of the correlation estimate.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>P-value</b>\n",
    "\n",
    "<p>What is this P-value? The P-value is the probability value that the correlation between these two variables is statistically significant. Normally, we choose a significance level of 0.05, which means that we are 95% confident that the correlation between the variables is significant.</p>\n",
    "\n",
    "By convention, when the\n",
    "\n",
    "<ul>\n",
    "    <li>p-value is $<$ 0.001: we say there is strong evidence that the correlation is significant.</li>\n",
    "    <li>the p-value is $<$ 0.05: there is moderate evidence that the correlation is significant.</li>\n",
    "    <li>the p-value is $<$ 0.1: there is weak evidence that the correlation is significant.</li>\n",
    "    <li>the p-value is $>$ 0.1: there is no evidence that the correlation is significant.</li>\n",
    "</ul>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can obtain this information using  \"stats\" module in the \"scipy\"  library.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Wheel-Base vs. Price</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the  Pearson Correlation Coefficient and P-value of 'wheel-base' and 'price'.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.5846418222655081  with a P-value of P = 8.076488270732989e-20\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['wheel-base'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Conclusion:</h4>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between wheel-base and price is statistically significant, although the linear relationship isn't extremely strong (~0.585).</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Horsepower vs. Price</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the  Pearson Correlation Coefficient and P-value of 'horsepower' and 'price'.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.809574567003656  with a P-value of P =  6.369057428259557e-48\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['horsepower'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Conclusion:</h4>\n",
    "\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between horsepower and price is statistically significant, and the linear relationship is quite strong (~0.809, close to 1).</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Length vs. Price</h3>\n",
    "\n",
    "Let's calculate the  Pearson Correlation Coefficient and P-value of 'length' and 'price'.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.690628380448364  with a P-value of P =  8.016477466158986e-30\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['length'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Conclusion:</h4>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between length and price is statistically significant, and the linear relationship is moderately strong (~0.691).</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Width vs. Price</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the Pearson Correlation Coefficient and P-value of 'width' and 'price':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.7512653440522674  with a P-value of P = 9.200335510481516e-38\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['width'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Conclusion:\n",
    "\n",
    "Since the p-value is < 0.001, the correlation between width and price is statistically significant, and the linear relationship is quite strong (\\~0.751).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Curb-Weight vs. Price\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the Pearson Correlation Coefficient and P-value of 'curb-weight' and 'price':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8344145257702846  with a P-value of P =  2.1895772388936914e-53\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['curb-weight'], df['price'])\n",
    "print( \"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Conclusion:</h4>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between curb-weight and price is statistically significant, and the linear relationship is quite strong (~0.834).</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Engine-Size vs. Price</h3>\n",
    "\n",
    "Let's calculate the Pearson Correlation Coefficient and P-value of 'engine-size' and 'price':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8723351674455185  with a P-value of P = 9.265491622198389e-64\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['engine-size'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Conclusion:</h4>\n",
    "\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between engine-size and price is statistically significant, and the linear relationship is very strong (~0.872).</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Bore vs. Price</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the  Pearson Correlation Coefficient and P-value of 'bore' and 'price':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.5431553832626602  with a P-value of P =   8.049189483935489e-17\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['bore'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =  \", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Conclusion:</h4>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between bore and price is statistically significant, but the linear relationship is only moderate (~0.521).</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can relate the process for each 'city-mpg'  and 'highway-mpg':\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>City-mpg vs. Price</h3>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.6865710067844677  with a P-value of P =  2.321132065567674e-29\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['city-mpg'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Conclusion:</h4>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between city-mpg and price is statistically significant, and the coefficient of about -0.687 shows that the relationship is negative and moderately strong.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Highway-mpg vs. Price</h3>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.7046922650589529  with a P-value of P =  1.7495471144477352e-31\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['highway-mpg'], df['price'])\n",
    "print( \"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Conclusion:\n",
    "\n",
    "Since the p-value is < 0.001, the correlation between highway-mpg and price is statistically significant, and the coefficient of about -0.705 shows that the relationship is negative and moderately strong.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>ANOVA: Analysis of Variance</h3>\n",
    "<p>The Analysis of Variance  (ANOVA) is a statistical method used to test whether there are significant differences between the means of two or more groups. ANOVA returns two parameters:</p>\n",
    "\n",
    "<p><b>F-test score</b>: ANOVA assumes the means of all groups are the same, calculates how much the actual means deviate from the assumption, and reports it as the F-test score. A larger score means there is a larger difference between the means.</p>\n",
    "\n",
    "<p><b>P-value</b>:  P-value tells how statistically significant our calculated score value is.</p>\n",
    "\n",
    "<p>If our price variable is strongly correlated with the variable we are analyzing, we expect ANOVA to return a sizeable F-test score and a small p-value.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Drive Wheels</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Since ANOVA analyzes the difference between different groups of the same variable, the groupby function will come in handy. Because the ANOVA algorithm averages the data automatically, we do not need to take the average before hand.</p>\n",
    "\n",
    "<p>To see if different types of 'drive-wheels' impact  'price', we group the data.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "        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": 54,
     "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": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\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": 55,
     "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": 56,
   "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": 56,
     "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": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 67.95406500780399 , P = 3.3945443577151245e-23\n"
     ]
    }
   ],
   "source": [
    "# ANOVA\n",
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('fwd')['price'], grouped_test2.get_group('rwd')['price'], grouped_test2.get_group('4wd')['price'])  \n",
    " \n",
    "print( \"ANOVA results: F=\", f_val, \", P =\", p_val)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a great result with a large F-test score showing a strong correlation and a P-value of almost 0 implying almost certain statistical significance. But does this mean all three tested groups are all this highly correlated?\n",
    "\n",
    "Let's examine them separately.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### fwd and rwd\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "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": 59,
   "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": 60,
   "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": [
    "We notice that ANOVA for the categories `4wd` and `fwd` yields a high p-value > 0.1, so the calculated F-test score is not very statistically significant. This suggests we can't reject the assumption that the means of these two groups are the same, or, in other words, we can't conclude the difference in correlation to be significant.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Conclusion: Important Variables</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We now have a better idea of what our data looks like and which variables are important to take into account when predicting the car price. We have narrowed it down to the following variables:</p>\n",
    "\n",
    "Continuous numerical variables:\n",
    "\n",
    "<ul>\n",
    "    <li>Length</li>\n",
    "    <li>Width</li>\n",
    "    <li>Curb-weight</li>\n",
    "    <li>Engine-size</li>\n",
    "    <li>Horsepower</li>\n",
    "    <li>City-mpg</li>\n",
    "    <li>Highway-mpg</li>\n",
    "    <li>Wheel-base</li>\n",
    "    <li>Bore</li>\n",
    "</ul>\n",
    "\n",
    "Categorical variables:\n",
    "\n",
    "<ul>\n",
    "    <li>Drive-wheels</li>\n",
    "</ul>\n",
    "\n",
    "<p>As we now move into building machine learning models to automate our analysis, feeding the model with variables that meaningfully affect our target variable will improve our model's prediction performance.</p>\n"
   ]
  }
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