Exploratory-Data-Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 Exploratory Data Analysis</h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "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>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": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "path='https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/automobileEDA.csv'\n",
    "df = pd.read_csv(path)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"pattern_visualization\">Analyzing Individual Feature Patterns using Visualization</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To install seaborn use the pip which is the python package manager.<p>\n",
    "Import visualization packages \"Matplotlib\" and \"Seaborn\", don't forget about \"%matplotlib inline\" to plot in a Jupyter notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "! pip install seaborn\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>When visualizing individual variables, it is important to first understand what type of variable you are dealing with.This helps to find the right visualization method for that variable.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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": [
    "print(df.dtypes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the correlation between variables  of type \"int64\" or \"float64\" using the method \"corr\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>symboling</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.466264</td>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.365404</td>\n",
       "      <td>-0.242423</td>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.233118</td>\n",
       "      <td>-0.110581</td>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.008245</td>\n",
       "      <td>-0.182196</td>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.279740</td>\n",
       "      <td>-0.035527</td>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.066171</td>\n",
       "      <td>-0.196735</td>\n",
       "      <td>0.196735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>normalized-losses</th>\n",
       "      <td>0.466264</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.101546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wheel-base</th>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>-0.307237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>length</th>\n",
       "      <td>-0.365404</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>-0.211187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>width</th>\n",
       "      <td>-0.242423</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>-0.244356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>height</th>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>-0.281578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>curb-weight</th>\n",
       "      <td>-0.233118</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>-0.221046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>-0.110581</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>-0.070779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>-0.054458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.008245</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>-0.241303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>-0.182196</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.985231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>0.169053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>0.279740</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.475812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-mpg</th>\n",
       "      <td>-0.035527</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>-0.265676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>-0.198690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.110326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-L/100km</th>\n",
       "      <td>0.066171</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>0.241282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diesel</th>\n",
       "      <td>-0.196735</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gas</th>\n",
       "      <td>0.196735</td>\n",
       "      <td>0.101546</td>\n",
       "      <td>-0.307237</td>\n",
       "      <td>-0.211187</td>\n",
       "      <td>-0.244356</td>\n",
       "      <td>-0.281578</td>\n",
       "      <td>-0.221046</td>\n",
       "      <td>-0.070779</td>\n",
       "      <td>-0.054458</td>\n",
       "      <td>-0.241303</td>\n",
       "      <td>-0.985231</td>\n",
       "      <td>0.169053</td>\n",
       "      <td>0.475812</td>\n",
       "      <td>-0.265676</td>\n",
       "      <td>-0.198690</td>\n",
       "      <td>-0.110326</td>\n",
       "      <td>0.241282</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   symboling  normalized-losses  wheel-base    length  \\\n",
       "symboling           1.000000           0.466264   -0.535987 -0.365404   \n",
       "normalized-losses   0.466264           1.000000   -0.056661  0.019424   \n",
       "wheel-base         -0.535987          -0.056661    1.000000  0.876024   \n",
       "length             -0.365404           0.019424    0.876024  1.000000   \n",
       "width              -0.242423           0.086802    0.814507  0.857170   \n",
       "height             -0.550160          -0.373737    0.590742  0.492063   \n",
       "curb-weight        -0.233118           0.099404    0.782097  0.880665   \n",
       "engine-size        -0.110581           0.112360    0.572027  0.685025   \n",
       "bore               -0.140019          -0.029862    0.493244  0.608971   \n",
       "stroke             -0.008245           0.055563    0.158502  0.124139   \n",
       "compression-ratio  -0.182196          -0.114713    0.250313  0.159733   \n",
       "horsepower          0.075819           0.217299    0.371147  0.579821   \n",
       "peak-rpm            0.279740           0.239543   -0.360305 -0.285970   \n",
       "city-mpg           -0.035527          -0.225016   -0.470606 -0.665192   \n",
       "highway-mpg         0.036233          -0.181877   -0.543304 -0.698142   \n",
       "price              -0.082391           0.133999    0.584642  0.690628   \n",
       "city-L/100km        0.066171           0.238567    0.476153  0.657373   \n",
       "diesel             -0.196735          -0.101546    0.307237  0.211187   \n",
       "gas                 0.196735           0.101546   -0.307237 -0.211187   \n",
       "\n",
       "                      width    height  curb-weight  engine-size      bore  \\\n",
       "symboling         -0.242423 -0.550160    -0.233118    -0.110581 -0.140019   \n",
       "normalized-losses  0.086802 -0.373737     0.099404     0.112360 -0.029862   \n",
       "wheel-base         0.814507  0.590742     0.782097     0.572027  0.493244   \n",
       "length             0.857170  0.492063     0.880665     0.685025  0.608971   \n",
       "width              1.000000  0.306002     0.866201     0.729436  0.544885   \n",
       "height             0.306002  1.000000     0.307581     0.074694  0.180449   \n",
       "curb-weight        0.866201  0.307581     1.000000     0.849072  0.644060   \n",
       "engine-size        0.729436  0.074694     0.849072     1.000000  0.572609   \n",
       "bore               0.544885  0.180449     0.644060     0.572609  1.000000   \n",
       "stroke             0.188829 -0.062704     0.167562     0.209523 -0.055390   \n",
       "compression-ratio  0.189867  0.259737     0.156433     0.028889  0.001263   \n",
       "horsepower         0.615077 -0.087027     0.757976     0.822676  0.566936   \n",
       "peak-rpm          -0.245800 -0.309974    -0.279361    -0.256733 -0.267392   \n",
       "city-mpg          -0.633531 -0.049800    -0.749543    -0.650546 -0.582027   \n",
       "highway-mpg       -0.680635 -0.104812    -0.794889    -0.679571 -0.591309   \n",
       "price              0.751265  0.135486     0.834415     0.872335  0.543155   \n",
       "city-L/100km       0.673363  0.003811     0.785353     0.745059  0.554610   \n",
       "diesel             0.244356  0.281578     0.221046     0.070779  0.054458   \n",
       "gas               -0.244356 -0.281578    -0.221046    -0.070779 -0.054458   \n",
       "\n",
       "                     stroke  compression-ratio  horsepower  peak-rpm  \\\n",
       "symboling         -0.008245          -0.182196    0.075819  0.279740   \n",
       "normalized-losses  0.055563          -0.114713    0.217299  0.239543   \n",
       "wheel-base         0.158502           0.250313    0.371147 -0.360305   \n",
       "length             0.124139           0.159733    0.579821 -0.285970   \n",
       "width              0.188829           0.189867    0.615077 -0.245800   \n",
       "height            -0.062704           0.259737   -0.087027 -0.309974   \n",
       "curb-weight        0.167562           0.156433    0.757976 -0.279361   \n",
       "engine-size        0.209523           0.028889    0.822676 -0.256733   \n",
       "bore              -0.055390           0.001263    0.566936 -0.267392   \n",
       "stroke             1.000000           0.187923    0.098462 -0.065713   \n",
       "compression-ratio  0.187923           1.000000   -0.214514 -0.435780   \n",
       "horsepower         0.098462          -0.214514    1.000000  0.107885   \n",
       "peak-rpm          -0.065713          -0.435780    0.107885  1.000000   \n",
       "city-mpg          -0.034696           0.331425   -0.822214 -0.115413   \n",
       "highway-mpg       -0.035201           0.268465   -0.804575 -0.058598   \n",
       "price              0.082310           0.071107    0.809575 -0.101616   \n",
       "city-L/100km       0.037300          -0.299372    0.889488  0.115830   \n",
       "diesel             0.241303           0.985231   -0.169053 -0.475812   \n",
       "gas               -0.241303          -0.985231    0.169053  0.475812   \n",
       "\n",
       "                   city-mpg  highway-mpg     price  city-L/100km    diesel  \\\n",
       "symboling         -0.035527     0.036233 -0.082391      0.066171 -0.196735   \n",
       "normalized-losses -0.225016    -0.181877  0.133999      0.238567 -0.101546   \n",
       "wheel-base        -0.470606    -0.543304  0.584642      0.476153  0.307237   \n",
       "length            -0.665192    -0.698142  0.690628      0.657373  0.211187   \n",
       "width             -0.633531    -0.680635  0.751265      0.673363  0.244356   \n",
       "height            -0.049800    -0.104812  0.135486      0.003811  0.281578   \n",
       "curb-weight       -0.749543    -0.794889  0.834415      0.785353  0.221046   \n",
       "engine-size       -0.650546    -0.679571  0.872335      0.745059  0.070779   \n",
       "bore              -0.582027    -0.591309  0.543155      0.554610  0.054458   \n",
       "stroke            -0.034696    -0.035201  0.082310      0.037300  0.241303   \n",
       "compression-ratio  0.331425     0.268465  0.071107     -0.299372  0.985231   \n",
       "horsepower        -0.822214    -0.804575  0.809575      0.889488 -0.169053   \n",
       "peak-rpm          -0.115413    -0.058598 -0.101616      0.115830 -0.475812   \n",
       "city-mpg           1.000000     0.972044 -0.686571     -0.949713  0.265676   \n",
       "highway-mpg        0.972044     1.000000 -0.704692     -0.930028  0.198690   \n",
       "price             -0.686571    -0.704692  1.000000      0.789898  0.110326   \n",
       "city-L/100km      -0.949713    -0.930028  0.789898      1.000000 -0.241282   \n",
       "diesel             0.265676     0.198690  0.110326     -0.241282  1.000000   \n",
       "gas               -0.265676    -0.198690 -0.110326      0.241282 -1.000000   \n",
       "\n",
       "                        gas  \n",
       "symboling          0.196735  \n",
       "normalized-losses  0.101546  \n",
       "wheel-base        -0.307237  \n",
       "length            -0.211187  \n",
       "width             -0.244356  \n",
       "height            -0.281578  \n",
       "curb-weight       -0.221046  \n",
       "engine-size       -0.070779  \n",
       "bore              -0.054458  \n",
       "stroke            -0.241303  \n",
       "compression-ratio -0.985231  \n",
       "horsepower         0.169053  \n",
       "peak-rpm           0.475812  \n",
       "city-mpg          -0.265676  \n",
       "highway-mpg       -0.198690  \n",
       "price             -0.110326  \n",
       "city-L/100km       0.241282  \n",
       "diesel            -1.000000  \n",
       "gas                1.000000  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       bore    stroke  compression-ratio  horsepower\n",
       "bore               1.000000 -0.055390           0.001263    0.566936\n",
       "stroke            -0.055390  1.000000           0.187923    0.098462\n",
       "compression-ratio  0.001263  0.187923           1.000000   -0.214514\n",
       "horsepower         0.566936  0.098462          -0.214514    1.000000"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['bore','stroke','compression-ratio','horsepower']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Continuous numerical variables:</h2> \n",
    "\n",
    "<p>Continuous numerical variables are variables that may contain any value within some range. Continuous numerical variables can have the type \"int64\" or \"float64\". \n",
    "\n",
    "<p>In order to start understanding the (linear) relationship between an individual variable and the price. This can be done by using \"regplot\" which plots the scatterplot plus the fitted regression line for the data.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Positive linear relationship</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scatterplot of \"engine-size\" and \"price\" "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 56078.57437459202)"
      ]
     },
     "execution_count": 8,
     "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can examine the correlation between 'engine-size' and 'price' and see it's approximately  0.87"
   ]
  },
  {
   "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>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": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[[\"engine-size\", \"price\"]].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, Highway mpg is a potential predictor variable of price "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1d711d65d68>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x=\"highway-mpg\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>As the highway-mpg goes up, the price goes down: this indicates an inverse/negative relationship between these two variables. Highway mpg could potentially be a predictor of price.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'highway-mpg' and 'price' and see it's approximately  -0.704"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['highway-mpg', 'price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Weak Linear Relationship</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see if \"Peak-rpm\" as a predictor variable of \"price\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1d711c0f3c8>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x=\"peak-rpm\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Peak rpm does not seem like a good predictor of the price at all since the regression line is close to horizontal. Also, the data points are very scattered and far from the fitted line, showing lots of variability. Therefore it's it is not a reliable variable.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'peak-rpm' and 'price' and see it's approximately -0.101616 "
   ]
  },
  {
   "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>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": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['peak-rpm','price']].corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[[\"stroke\",\"price\"]].corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1d711c79128>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x=\"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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Relationship between \"body-style\" and \"price\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1d711e35c50>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AnxRfHTMzG8sGm1T2iYine57k6X37W0DSoZJukfSgpFWSPprjl0h6VNKK/DipZJmLJHVI+rWkE0vis3OsQ9InS+KHSbpT0mpJ383DCpuZWY0MNqn8UdKre55IOhrYPMAy24B/iIiXA8cC50o6Ms+7PCKm58fivM4jSUMIvwKYDXxF0vh8qu3LQBNwJPDekvV8Pq9rGvAEcPYg98fMzCpgsNdU/g64XtLa/Pxg4PT+FoiIdcC6PP2UpAeByf0scgqwMCKeAX6Tx6rvGXa4Iw9DjKSFwCl5fccDf53LtAKXAFcMcp/MzKxgg2qpRMTdwBHAOcBHgJdHxD2D3YikKaTx6u/MofMkrZQ0X9L+OTYZeKRksc4c6ys+CdgYEdt6xcttf46kdkntXV1dg622mZkNUb9JRdLx+e9fAW8HXgZMA96eYwOStB/wPeDvIuIPpJbE4cB0UkvmP3qKllk8hhF/fjDiyoiYEREzGhoaBlNtMzMbhoFOf70Z+CkpofQWwPf7W1hSHSmhfDsivg8QEY+VzL8KuCk/7QQOLVm8Eeg53VYu3g1MlLRXbq2UljczsxroN6lExFxJ44AlEXHdUFasNNLO1cCDEfGFkvjB+XoLwDuB+/P0IuA7kr4AHEJqEd1FapFMk3QY8CjpYv5fR0RIugU4DVgINAM3DqWOZmZWrAEv1EfEDknnAUNKKqQOKD8A3CdpRY59inT31nRSS2cN6Rf6RMQqSdcBD5DuHDs3IrYD5O0vBcaTfoS5Kq/vE8BCSZcCy0lJzMzMamSwd3+1SfpH4LvAH3uCEbGhrwUi4ueUv+6xuJ9lLgMuKxNfXG65fEfYMb3jZmZWG4NNKn9Dall8pFf8z4qtjpmZjWWDTSpHkhLKG0jJ5Xbgq5WqlJmZjU2DTSqtpAG6WvLz9+bYeypRKTMzG5sGm1T+PCJeVfL8Fkm/qkSFzMxs7Bps31/LJR3b80TSa4H/rkyVzMxsrBpsUnkt8AtJayStAe4A3izpPkkrK1Y72611d3dz/vnn8/jjj9e6KmZWkMGe/ppd0VrYHqm1tZWVK1fS2trKhRdeWOvqmFkBBtuh5G/7e1S6krb76e7uZsmSJUQES5YscWvFbDcx2NNfZoVqbW0lIvX/uWPHDlpbW2tcIzMrgpOK1URbWxtbt24FYOvWrSxbtqzGNTKzIjipWE3MnDmTuro6AOrq6pg1a1aNa2RmRXBSsZpobm4mdWQN48aNo7m5ucY1MrMiOKlYTdTX19PU1IQkmpqamDRpUq2rZGYFGOwtxWaFa25uZs2aNW6lmO1GnFSsZurr65k3b16tq2FmBarY6S9Jh0q6RdKDklZJ+miOHyCpTdLq/Hf/HJekFkkdklZKenXJuppz+dWSmkviR+df9XfkZcuN32JmZlVSyWsq24B/iIiXA8cC50o6EvgkcHNETANuzs8BmkhDCE8D5gBXQEpCwFxSVzHHAHN7ElEuM6dkOf/y38yshiqWVCJiXUTcm6efAh4EJgOnkLrNJ/89NU+fAlwTyS+BiZIOBk4E2iJiQ0Q8AbQBs/O8F0bEHZF+RXdNybrMzKwGqnL3l6QpwF8CdwIHRcQ6SIkHODAXmww8UrJYZ471F+8sEzczsxqp+IV6SfsB3wP+LiL+0M9lj3IzYhjxcnWYQzpNxkte8pKBqmzD0NLSQkdHx5CW6exM3wkaGxuHvL2pU6dywQUXDHk5s5Hq7OzkyU1PcctDC2tdlUJt3LSe6Nw84vVUtKUiqY6UUL4dEd/P4cfyqSvy3/U53gkcWrJ4I7B2gHhjmfjzRMSVETEjImY0NDSMbKesMJs3b2bz5pG/iM1s9KhYSyXfiXU18GBEfKFk1iKgGfhc/ntjSfw8SQtJF+WfjIh1kpYC/1JycX4WcFFEbJD0VB487E7gTMD3p9bIcFoNPcu0tLQMUNJs9GhsbETPPM5bjjij1lUp1C0PLWRy48h/hFzJ01+vBz4A3CdpRY59ipRMrpN0NvA74N153mLgJKAD2AR8ECAnj88Cd+dyn4mIDXn6HGABMAFYkh9mZlYjFUsqEfFzyl/3ADihTPkAzu1jXfOB+WXi7cBRI6immVVQNa+1+Trb6OBf1JvZqOLrbGObk4qZVYyvte153EuxmZkVxknFzMwK49NfZn0YzkXm4Vq9ejUwvNNFw+GL2lYpTipmfejo6GD5quUwsQob25H+LH90eeW3tbHym7A9l5OKWX8mwo7jdtS6FoUad6vPelvl+NVlZmaFcUuF9GOrcZueZJ8Hbqp1VQo1btPjdHZuq3U1zGwP4paKmZkVxi0VUncQjz2zF1uOPLnWVSnUPg/cRGPji2tdDTPbg7ilYmZmhXFSMTOzwjipmJlZYZxUzMysML5Qb2YDcpc1NliVHE54PnAysD4ijsqxS4APAV252KciYnGedxFwNrAduCAilub4bOBLwHjg6xHxuRw/DFgIHADcC3wgIp6t1P6Y7ck6Ojp4aMUKqnEvYc/pk40rVvRbrgi/r/gW9jyVbKksAP4TuKZX/PKI+PfSgKQjgTOAVwCHAD+R9LI8+8vATKATuFvSooh4APh8XtdCSV8lJaQrKrUzZnu6FwNn9zmY69h0NVHrKux2KnZNJSJuAzYMWDA5BVgYEc9ExG9I49Qfkx8dEfFwboUsBE6RJOB44Ia8fCtwaqE7YGZmQ1aLC/XnSVopab6k/XNsMvBISZnOHOsrPgnYGBHbesXLkjRHUruk9q6urr6KmZnZCFU7qVwBHA5MB9YB/5Hj5drUMYx4WRFxZUTMiIgZDQ0NQ6uxmZkNWlXv/oqIx3qmJV0F9PTg2AkcWlK0EVibp8vFu4GJkvbKrZXS8mZmViNVTSqSDo6IdfnpO4H78/Qi4DuSvkC6UD8NuIvUIpmW7/R6lHQx/68jIiTdApxGus7SDNw4krqN27ShKr0Ua8sfAIh9XljxbY3btAGqcr+OmVlSyVuKrwWOA+oldQJzgeMkTSedqloDfBggIlZJug54ANgGnBsR2/N6zgOWkm4pnh8Rq/ImPgEslHQpsBy4erh1nTp16nAXHbLVq58CYNrh1fiwf3FV983MrGJJJSLeWybc5wd/RFwGXFYmvhhYXCb+MOnusBGr5g+ferbV0tJStW2amVWLu2kxM7PCOKmYmVlhnFTMzKwwTipmZlYYJxUzMyuMk4qZmRXGScXMzArjpGJmZoXxyI+2C4/wZ2Yj4aRiu+jo6OB/7r+Xl+y3veLbesHW1FDesubuim/rd0+Pr/g2zMxJZUSG861+JN/Oq/VN+yX7befiGU9XfDvVdGn7frWuwpjW2dnJU+x+IyWuA57u7Kx1NXYrTipVNmHChFpXwcysYpxURsDn521P0djYyMbu7t1yjPqJjY21rsZuxUnFrA+dnZ3wJIy7dTe7SXIjdIZP+Vhl7GbvFjMzq6VKDtI1HzgZWB8RR+XYAcB3gSmkQbreExFPSBLwJeAkYBNwVkTcm5dpBi7Oq700Ilpz/GhgATCBNN7KRyNi97qKaDXV2NhIl7rYcdyOWlelUONuHUfjZJ/yscqoZEtlATC7V+yTwM0RMQ24OT8HaCINITwNmANcAc8lobnAa0kDcs2VtH9e5opctme53tsyM7Mqq1hSiYjbgA29wqcArXm6FTi1JH5NJL8EJko6GDgRaIuIDRHxBNAGzM7zXhgRd+TWyTUl6zIzsxqp9jWVgyJiHUD+e2COTwYeKSnXmWP9xTvLxM3MrIZGy4X6cvcpxjDi5VcuzZHULqm9q6trmFU0M7OBVDupPJZPXZH/rs/xTuDQknKNwNoB4o1l4mVFxJURMSMiZjQ0NIx4J8zMrLxq/05lEdAMfC7/vbEkfp6khaSL8k9GxDpJS4F/Kbk4Pwu4KCI2SHpK0rHAncCZwLxq7oiZ7bk2blrPLQ8trPh2nt7yBAD77bP/ACVHbuOm9Uxm0ojXU8lbiq8FjgPqJXWS7uL6HHCdpLOB3wHvzsUXk24n7iDdUvxBgJw8Pgv09Dj4mYjoufh/DjtvKV6SH2ZmFTV16tSqbWv16vRxN/nwkX/YD2QykwrZt4ollYh4bx+zTihTNoBz+1jPfGB+mXg7cNRI6mhmNlTV7J6pZ1stLS1V2+ZIuZsW20VnZyd/fGr8bter72+fGs+fuDdas4obLXd/mZnZbsAtFdtFY2MjW7at2y3HU9nHvdGaVZyTiplZFVRzUL9aDp3tpGLWn41V6vq+p2FYjUtZGxlW/xO/pzojPz6e/1b+fqe0TxOrsJ3hGouD+jmpmPWhureOpm+k0yZPq/zGJg9936p5LLrysZg4rfLHYiLV27c9ZVA/JxWzPvjW0Z18LGywfPeXmZkVxknFzMwK49NfZlYxe8odT7aTk4qZjSpj8Y4n28lJxZ7nd09Xp5uWxzals68H7Vv5MeB/9/R4XlbxrVhvbjnseZxUbBfVvHX02XyaY58plb919GVUd9/M9lROKrYL3zpqZiPhu7/MzKwwTipmZlaYmpz+krQGeArYDmyLiBmSDgC+C0wB1gDviYgnJAn4EmlkyE3AWRFxb15PM3BxXu2lEdFazf0wK8e30dqerJYtlbdExPSImJGffxK4OSKmATfn5wBNwLT8mANcAZCT0FzSmPbHAHNLxrI3G1MmTJjgW2lttzCaLtSfQhrTHqAVuBX4RI5fk4cc/qWkiZIOzmXbesasl9QGzAaurW61Dar77RxG9zf00Vovs2qoVUslgGWS7pE0J8cOioh1APnvgTk+GXikZNnOHOsr/jyS5khql9Te1dVV4G7YSPjbudnup1YtlddHxFpJBwJtkh7qp6zKxKKf+PODEVcCVwLMmDGj8gNC7IH87dzMoEYtlYhYm/+uB35AuibyWD6tRf67PhfvBA4tWbwRWNtP3MzMaqTqSUXSn0j6055pYBZwP7AIaM7FmoEb8/Qi4EwlxwJP5tNjS4FZkvbPF+hn5ZiZmdVILU5/HQT8IN0pzF7AdyLivyTdDVwn6Wzgd8C7c/nFpNuJO0i3FH8QICI2SPoscHcu95mei/ZmZlYbSjdV7TlmzJgR7e3tta6GmdmYIumekp+A9Mm/qDczs8I4qZiZWWGcVMzMrDBOKmZmVpg97kK9pC7gtzWuRj3QXeM6jBY+Fjv5WOzkY7HTaDkWL42IhoEK7XFJZTSQ1D6Yuyj2BD4WO/lY7ORjsdNYOxY+/WVmZoVxUjEzs8I4qdTGlbWuwCjiY7GTj8VOPhY7jalj4WsqZmZWGLdUzMysME4qo0ge1fIjJc8PkXRDnj5L0n/2sdzTFarPFEn3D6H8qZKOHKDMcZJu6mPeGkn1Q61nmfVU5HhU2lCPt41eRf8ve94bvT8jRiMnlVFC0nhgIvDcCyYi1kbEabWr1ZCdCvSbVMysf5L66z1+l8+I0chJpYSkMyWtlPQrSd+U9FJJN+fYzZJeksstkNQi6ReSHpZ0Wo5/V9JJJetbIOldksZL+jdJd+d1fTjPP07SLZK+A9wHfA44XNKKXL73t51DJf2XpF9LmtvHPnysZDufLuCwjJd0laRVkpZJmiDpQ3kbv5L0PUn7Svo/wDuAf8v1P1zSVEk/yeXulXR4Xud+km6Q9JCkbyuPg5B9TNJd+TE179PbJd0paXle30E5vp+kb0i6L+/vu3odi3pJd0h6WwHHYdDymEE/zvt9v6TTJR0t6WdKQ2gv1c4B6Y7O5e4Azi1ZxxRJt+fjdm8+vj2vmVv7OX6jgqSPS7ogT18u6ad5+gRJ35J0hdIQ36tKX6eSTsr79fP8Hrspxw+Q9MP8f/6lpFfm+CWS5udj8nDPNkeJQb134LnPii9IugX4vKRJeZnlkr7GzpFue39GKP+9P78PTs/rO07SbZJ+IOkBSV+VVJ3P+4jwI92s8Arg10B9fn4A8COgOT//G+CHeXoBcD0pKR8JdOT4O4HWPP0C4BFgAjAHuDjH9wbagcOA44A/AofleVOA+0vq9Nxz4CxgHTApr/N+YEae93T+O4t0p4hy3W4C3jSCYzIF2AZMz8+vA94PTCopcylwfslxOa1k3p3AO/P0PsC+eZ+fJI3UOQ64A3hDLrMG+Kc8fSZwU57en503lfxf4D/y9OeBL5Zsb/+e40Eat+dOYGYNXksiWTEUAAAH60lEQVTvAq4qef4i4BdAQ35+OjA/T68E3pyn/63k/70vsE+enga05+k+j99oegDHAtfn6duBu4A6YC7wYeCAPG88cCvwyvwaeaTk/XBtyWtgHjA3Tx8PrMjTl+Rjuzfpl+ePA3WjYP+H8965CRifn7cA/5yn30YaKr2e539GvAtoy8fxINJYVAfn18kW4M/yvDZK3puVfLilstPxwA0R0Q1pEDDgdcB38vxvAm8oKf/DiNgREQ+Q/pkAS4DjJe0NNAG3RcRm0of9mZJWkD7oJpE+KADuiojfDLKObRHxeF7n93vVh7ydWcBy4F7giJLtDNdvImJFnr6H9KI+Kn+Lvg94Hykh70JpdM/JEfEDgIjYEhGb8uy7IqIzInYAK/I6e1xb8vd1eboRWJq397GS7b0V+HLPghHxRJ6sA24GPh4RbcPa65G5D3irpM9LeiNp2OujgLb8GrgYaJT0ImBiRPwsL/fNknXUAVflfb6eXU8r9nf8Rot7gKPz6+AZUvKbAbyRlGTeI+le0mv1FaT9OwJ4uOT9cG3J+t5APj4R8VNgUj5+AD+OiGfye3c9O9+PtTbU9871EbE9T78J+BZARPwYeILy3gBcGxHbI+Ix4GfAa/K8uyLi4bzOa3n+50VF1GLkx9FKpG8D/Smd/0yvZYmILZJuBU4kfRu9tmT++RGxy3DHko4jtVQGq3f9ej8X8K8R8bUhrHMgpfu5ndRKWgCcGhG/knQW6VtRb/2dkum9ztLXYZSZngd8ISIW5WN2Sck2yv3PtpHexCeS3mRVFRH/I+lo0oil/0r6lrgqIl5XWk7SRPp+zf098BjwKlKLZEvJvP6O36gQEVslrSGN1PoLUovsLcDhwGbgH4HXRMQTkhaQWin9vWbKzes5dqP1eAz1vdP7s2Awv/fo75gN9HlREW6p7HQz6dvTJEjncElvhjPy/PcBPx/EehaS3khvBHqSyFLgHEl1ed0vk/QnZZZ9CvjTftY9M59bnkC6KP7fveYvBf5G0n55O5MlHTiIOg/VnwLr8v68ryT+XP0j4g9Ap6RTc1327jl/PIDTS/7ekadfBDyap5tLyi4Dzut5Imn/PBmk05VHSPrkYHeqKJIOATZFxLeAfwdeCzRIel2eXyfpFRGxEXhSUs83yNJj+SJgXW6NfIB0CmOsuY2UPG4jtU7+ltSyeiHpA/RJpetjTbn8Q8CfSZqSn5/ea13vg+e+jHXn19hY09d7p7fS/W0inQKG539G3AacrnTdtoHUwrkrzztG0mH5WsrpDO7za8RGS0avuYhYJeky4GeStpOa5RcA8yV9DOgiJYuBLAOuARZFxLM59nVS0/fefFG1i5QUetfhcUn/rXRxfgklp3ayn5NOAUwFvhMR7b2WXybp5cAd+drt06TzuOsHUe+h+H+k03i/JZ3q6XmRLySdsrkAOI30Yfg1SZ8BtgLvHsS695Z0J+kLz3tz7BLgekmPAr8kXY+CdE76y/l4bQc+TTotSERsl3QG8CNJf4iIr4xgf4fqL0g3LOwg7fc5pNZTSz5lsxfwRWAV6TU1X9Imdn4JAfgK8D1J7wZuYWgt2tHiduCfgDsi4o+StgC352/py0n7/zD5y1FEbFa6Xfa/JHWz88MR0mvgG5JWApvY9cvFWNLXe6e3TwPX5lOEPyNdKyn3GfFx0mniX5G+TH08In4v6QjSl7LPkV6PtwE/qNhelfAv6s1s1JC0X0Q8nb98fRlYHRGX17peY01uzf1jRJxc7W379JeZjSYfyjczrCKdAizy+qBVgVsqZmZWGLdUzMysME4qZmZWGCcVMzMrjJOK2SBoBL3Oqp+emYe4nrPyb2AGKldIb89mw+GkYjZ2nAUMmFTMaslJxWzw9pLUqtRT7g1KvTOfkHuSvU+pt9y9ASTNVu5tF/irHBsnaXX+5XPP847erYr86+gF2tnz7N8r9YQ9A/i2Ug+1b5P0g5JlZkr6fu8KS3q/Uo/PKyR9TWmIBbOKcVIxG7w/B66MiFcCfwAuJPXldHpE/AXpl/LnSNoHuAp4O6m7nhcD5C5XvsXO7jneCvyqpxPTEtNJnXEeldf7jYi4gdS79fsiYjqwGHh5T4Ii/TL/G6Uryb0rnA68Pi+znf67BjEbMScVs8F7JCJ6+lv7FnACqSfa/8mxVlLfS0fk+OpIPwT7Vsk65pO69YfUP9kuiSB7mNQH1jxJs0kJbBd5vd8E3p87pnwdqduOUicARwN35x8UnkDqCt2sYtz3l9ngDeWXwmXLRsQjkh6TdDypo8n35VNS9+QiiyLinyW9itTL8rnAe0gJqLdvkMb82ULqNn1br/kije9z0RDqbTYibqmYDd5LenoaJnV2+RNgivIIlaQONH9G6m33MO0c6fK9u66Gr5NaL9flcTC2R8T0/PjnfI1lXER8j9QB4avzcrv0UBsRa4G1pPFZFpSp783AaT09Vecerl863J03GwwnFbPBexBozj3lHgBcTrqWcb3SoEs7gK9GxBbSaJ8/zhfqf9trPYuA/Sh/6gtgMnBrPmW1AOhpaSwAvpovuk/IsW+TTss90HslOXYxsCzXuY00KqBZxbjvL7MqkzQDuDwi3ljAuv4TWB4RV4+8ZmYj52sqZlWUBw07hwLuwpJ0D2mclX8Y6brMiuKWipmZFcbXVMzMrDBOKmZmVhgnFTMzK4yTipmZFcZJxczMCuOkYmZmhfn/omI6QJGqFD4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"body-style\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We see that the distributions of price between the different body-style categories have a significant overlap, and so body-style would not be a good predictor of price. Let's examine engine \"engine-location\" and \"price\":</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1d713279cc0>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Relationship between \"drive-wheels\" and \"price\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1d71330a048>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"discriptive_statistics\">Descriptive Statistical Analysis</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<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",
    "<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": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 18,
     "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe(include=['object'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Value Counts</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Value-counts is a good way of understanding how many units of each characteristic/variable we have. We can apply the \"value_counts\" method on the column 'drive-wheels'. Don’t forget the method \"value_counts\" only works on Pandas series, not Pandas Dataframes. As a result, we only include one bracket \"df['drive-wheels']\" not two brackets \"df[['drive-wheels']]\".</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fwd    118\n",
       "rwd     75\n",
       "4wd      8\n",
       "Name: drive-wheels, dtype: int64"
      ]
     },
     "execution_count": 20,
     "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 :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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": 21,
     "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'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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": 22,
     "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':"
   ]
  },
  {
   "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>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": 23,
     "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'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value_counts</th>\n",
       "    </tr>\n",
       "    <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": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "engine_loc_counts = df['engine-location'].value_counts().to_frame()\n",
    "engine_loc_counts.rename(columns={'engine-location': 'value_counts'}, inplace=True)\n",
    "engine_loc_counts.index.name = 'engine-location'\n",
    "engine_loc_counts.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Examining the value counts of the engine location would not be a good predictor variable for the price. This is because we only have three cars with a rear engine and 198 with an engine in the front, this result is skewed. Thus, we are not able to draw any conclusions about the engine location.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"basic_grouping\"> Basics of Grouping</h2>"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['rwd', 'fwd', '4wd'], dtype=object)"
      ]
     },
     "execution_count": 31,
     "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
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       "</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": 33,
     "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 that <b>rear-wheel drive vehicles</b> are on average, the <b>most expensive</b>, whereas <b>4-wheel and front-wheel</b> are <b>approximately the same in price</b> </p>\n",
    "\n",
    "<p>Grouping with multiple variables.\n",
    " Let's group by both 'drive-wheels' and 'body-style'. This groups the dataframe by the unique combinations 'drive-wheels' and 'body-style'. We can store the results in the variable 'grouped_test1'.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# grouping results\n",
    "df_gptest = df[['drive-wheels','body-style','price']]\n",
    "grouped_test1 = df_gptest.groupby(['drive-wheels','body-style'],as_index=False).mean()\n",
    "grouped_test1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>This grouped data is much easier to visualize when it is made into a pivot table. A pivot table is like an Excel spreadsheet, with one variable along the column and another along the row. We can convert the dataframe to a pivot table using the method \"pivot \" to create a pivot table from the groups.</p>\n",
    "\n",
    "<p>In this case, we will leave the drive-wheel variable as the rows of the table, and pivot body-style to become the columns of the table:</p>"
   ]
  },
  {
   "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 tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\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": 26,
     "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>"
   ]
  },
  {
   "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",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>body-style</th>\n",
       "      <th>convertible</th>\n",
       "      <th>hardtop</th>\n",
       "      <th>hatchback</th>\n",
       "      <th>sedan</th>\n",
       "      <th>wagon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7603.000000</td>\n",
       "      <td>12647.333333</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>11595.0</td>\n",
       "      <td>8249.000000</td>\n",
       "      <td>8396.387755</td>\n",
       "      <td>9811.800000</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>23949.6</td>\n",
       "      <td>24202.714286</td>\n",
       "      <td>14337.777778</td>\n",
       "      <td>21711.833333</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   price                                            \\\n",
       "body-style   convertible       hardtop     hatchback         sedan   \n",
       "drive-wheels                                                         \n",
       "4wd                  0.0      0.000000   7603.000000  12647.333333   \n",
       "fwd              11595.0   8249.000000   8396.387755   9811.800000   \n",
       "rwd              23949.6  24202.714286  14337.777778  21711.833333   \n",
       "\n",
       "                            \n",
       "body-style           wagon  \n",
       "drive-wheels                \n",
       "4wd            9095.750000  \n",
       "fwd            9997.333333  \n",
       "rwd           16994.222222  "
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_pivot = grouped_pivot.fillna(0) #fill missing values with 0\n",
    "grouped_pivot"
   ]
  },
  {
   "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_gptest2 = df[['body-style','price']]\n",
    "grouped_test_bodystyle = df_gptest2.groupby(['body-style'],as_index=False).mean()\n",
    "grouped_test_bodystyle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use a heat map to visualize the relationship between Body Style vs Price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#use the grouped results\n",
    "plt.pcolor(grouped_pivot, cmap='RdBu')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The heatmap plots the target variable (price) proportional to colour with respect to the variables 'drive-wheel' and 'body-style' in the vertical and horizontal axis respectively. This allows us to visualize how the price is related to 'drive-wheel' and 'body-style'.</p>\n",
    "\n",
    "<p>The default labels convey no useful information to us. Let's change that:</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "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>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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"correlation_causation\">Correlation and Causation</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p><b>Correlation</b>: a measure of the extent of interdependence between variables.</p>\n",
    "\n",
    "<p><b>Causation</b>: the relationship between cause and effect between two variables.</p>\n",
    "\n",
    "<p>It is important to know the difference between these two and that correlation does not imply causation. Determining correlation is much simpler  the determining causation as causation may require independent experimentation.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p3>Pearson Correlation</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>: Total positive linear correlation.</li>\n",
    "    <li><b>0</b>: No linear correlation, the two variables most likely do not affect each other.</li>\n",
    "    <li><b>-1</b>: Total negative linear correlation.</li>\n",
    "</ul>"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "        vertical-align: top;\n",
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       "        text-align: right;\n",
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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": 36,
     "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. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>P-value</b>: \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",
    "<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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can obtain this information using  \"stats\" module in the \"scipy\"  library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Wheel-base vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the  Pearson Correlation Coefficient and P-value of 'wheel-base' and 'price'. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.5846418222655081  with a P-value of P = 8.076488270732955e-20\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['wheel-base'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between wheel-base and price is statistically significant, although the linear relationship isn't extremely strong (~0.585)</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Horsepower vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the  Pearson Correlation Coefficient and P-value of 'horsepower' and 'price'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8095745670036559  with a P-value of P =  6.36905742825998e-48\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['horsepower'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between horsepower and price is statistically significant, and the linear relationship is quite strong (~0.809, close to 1)</p>"
   ]
  },
  {
   "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'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.690628380448364  with a P-value of P =  8.016477466159053e-30\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['length'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between length and price is statistically significant, and the linear relationship is moderately strong (~0.691).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Width vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the Pearson Correlation Coefficient and P-value of 'width' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.7512653440522674  with a P-value of P = 9.200335510481426e-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)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Curb-weight vs Price"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the Pearson Correlation Coefficient and P-value of 'curb-weight' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8344145257702846  with a P-value of P =  2.1895772388936997e-53\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['curb-weight'], df['price'])\n",
    "print( \"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between curb-weight and price is statistically significant, and the linear relationship is quite strong (~0.834).</p>"
   ]
  },
  {
   "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':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8723351674455185  with a P-value of P = 9.265491622197996e-64\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['engine-size'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between engine-size and price is statistically significant, and the linear relationship is very strong (~0.872).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Bore vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the  Pearson Correlation Coefficient and P-value of 'bore' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.5431553832626602  with a P-value of P =   8.049189483935364e-17\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['bore'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =  \", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between bore and price is statistically significant, but the linear relationship is only moderate (~0.521).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can relate the process for each 'City-mpg'  and 'Highway-mpg':"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>City-mpg vs Price</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.6865710067844677  with a P-value of P =  2.3211320655676368e-29\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['city-mpg'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between city-mpg and price is statistically significant, and the coefficient of ~ -0.687 shows that the relationship is negative and moderately strong.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Highway-mpg vs Price</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.7046922650589529  with a P-value of P =  1.7495471144476807e-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",
    "Since the p-value is < 0.001, the correlation between highway-mpg and price is statistically significant, and the coefficient of ~ -0.705 shows that the relationship is negative and moderately strong."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"anova\"> ANOVA</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>ANOVA: Analysis of Variance</h3>\n",
    "<p>The Analysis of Variance  (ANOVA) is a statistical method used to test whether there are significant differences between the means of two or more groups. ANOVA returns two parameters:</p>\n",
    "\n",
    "<p><b>F-test score</b>: ANOVA assumes the means of all groups are the same, calculates how much the actual means deviate from the assumption, and reports it as the F-test score. A larger score means there is a larger difference between the means.</p>\n",
    "\n",
    "<p><b>P-value</b>:  P-value tells how statistically significant is our calculated score value.</p>\n",
    "\n",
    "<p>If our price variable is strongly correlated with the variable we are analyzing, expect ANOVA to return a sizeable F-test score and a small p-value.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Drive Wheels</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Since ANOVA analyzes the difference between different groups of the same variable, the groupby function will come in handy. Because the ANOVA algorithm averages the data automatically, we do not need to take the average before hand.</p>\n",
    "\n",
    "<p>Let's see if different types 'drive-wheels' impact  'price', we group the data.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "</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",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>rwd</td>\n",
       "      <td>16500.0</td>\n",
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       "    <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": 47,
     "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": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
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       "      <th>2</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>16500.0</td>\n",
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       "      <th>3</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
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       "      <th>4</th>\n",
       "      <td>4wd</td>\n",
       "      <td>sedan</td>\n",
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       "      <th>5</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>17710.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>18920.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>23875.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>16430.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>16925.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>20970.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>21105.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>24565.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>30760.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>41315.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>36880.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>5151.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6295.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>6575.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>5572.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6377.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7957.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6229.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>6692.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7609.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>8558.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>8921.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>12964.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6479.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>171</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>9988.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>172</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>10898.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>173</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>11248.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>174</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>16558.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>175</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>15998.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>176</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>15690.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>177</th>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>15750.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>178</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7775.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>179</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7975.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>180</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7995.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>181</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>8195.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>182</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>8495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>183</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>184</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9995.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>185</th>\n",
       "      <td>fwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>11595.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>186</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>9980.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>187</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>13295.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>188</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>13845.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>189</th>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>12290.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>190</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>12940.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>191</th>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>13415.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>192</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>15985.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>193</th>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>16515.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>194</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>18420.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>195</th>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>18950.0</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",
       "5            fwd        sedan  15250.0\n",
       "6            fwd        sedan  17710.0\n",
       "7            fwd        wagon  18920.0\n",
       "8            fwd        sedan  23875.0\n",
       "9            rwd        sedan  16430.0\n",
       "10           rwd        sedan  16925.0\n",
       "11           rwd        sedan  20970.0\n",
       "12           rwd        sedan  21105.0\n",
       "13           rwd        sedan  24565.0\n",
       "14           rwd        sedan  30760.0\n",
       "15           rwd        sedan  41315.0\n",
       "16           rwd        sedan  36880.0\n",
       "17           fwd    hatchback   5151.0\n",
       "18           fwd    hatchback   6295.0\n",
       "19           fwd        sedan   6575.0\n",
       "20           fwd    hatchback   5572.0\n",
       "21           fwd    hatchback   6377.0\n",
       "22           fwd    hatchback   7957.0\n",
       "23           fwd    hatchback   6229.0\n",
       "24           fwd        sedan   6692.0\n",
       "25           fwd        sedan   7609.0\n",
       "26           fwd        sedan   8558.0\n",
       "27           fwd        wagon   8921.0\n",
       "28           fwd    hatchback  12964.0\n",
       "29           fwd    hatchback   6479.0\n",
       "..           ...          ...      ...\n",
       "171          fwd    hatchback   9988.0\n",
       "172          fwd        sedan  10898.0\n",
       "173          fwd    hatchback  11248.0\n",
       "174          rwd    hatchback  16558.0\n",
       "175          rwd    hatchback  15998.0\n",
       "176          rwd        sedan  15690.0\n",
       "177          rwd        wagon  15750.0\n",
       "178          fwd        sedan   7775.0\n",
       "179          fwd        sedan   7975.0\n",
       "180          fwd        sedan   7995.0\n",
       "181          fwd        sedan   8195.0\n",
       "182          fwd        sedan   8495.0\n",
       "183          fwd        sedan   9495.0\n",
       "184          fwd        sedan   9995.0\n",
       "185          fwd  convertible  11595.0\n",
       "186          fwd    hatchback   9980.0\n",
       "187          fwd        sedan  13295.0\n",
       "188          fwd        sedan  13845.0\n",
       "189          fwd        wagon  12290.0\n",
       "190          rwd        sedan  12940.0\n",
       "191          rwd        wagon  13415.0\n",
       "192          rwd        sedan  15985.0\n",
       "193          rwd        wagon  16515.0\n",
       "194          rwd        sedan  18420.0\n",
       "195          rwd        wagon  18950.0\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": 48,
     "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\".  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "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": 49,
     "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>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "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? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Separately: fwd and rwd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "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 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4wd and rwd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 0.665465750252303 , P = 0.41620116697845666\n"
     ]
    }
   ],
   "source": [
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('4wd')['price'], grouped_test2.get_group('fwd')['price'])  \n",
    " \n",
    "print(\"ANOVA results: F=\", f_val, \", P =\", p_val)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Conclusion: Important Variables</h3>"
   ]
  },
  {
   "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",
    "<ul>\n",
    "    <li>Length</li>\n",
    "    <li>Width</li>\n",
    "    <li>Curb-weight</li>\n",
    "    <li>Engine-size</li>\n",
    "    <li>Horsepower</li>\n",
    "    <li>City-mpg</li>\n",
    "    <li>Highway-mpg</li>\n",
    "    <li>Wheel-base</li>\n",
    "    <li>Bore</li>\n",
    "</ul>\n",
    "    \n",
    "Categorical variables:\n",
    "<ul>\n",
    "    <li>Drive-wheels</li>\n",
    "</ul>\n",
    "\n",
    "<p>As we now move into building machine learning models to automate our analysis, feeding the model with variables that meaningfully affect our target variable will improve our model's prediction performance.</p>"
   ]
  }
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