Module_3  Statistics and Selection.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Module 3\n",
    "\n",
    "Hi...\n",
    "Welcome\n",
    "\n",
    "In this module  I introduce some methods for you to find best fetures among all of them to predict prices in best way."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "path = \"cars.csv\"\n",
    "df = pd.read_csv(path)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is more than one way to analyze features \n",
    " - We can use some methods like correlatioins. \n",
    " - We can also use visualization methods."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Using Correlation function\n",
    "\n",
    "By using this method you can see the correlation between features \n",
    "for example, we can calculate the correlation between variables  of type \"int64\" or \"float64\" using the method \"corr\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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       "      <th>normalized-losses</th>\n",
       "      <td>-0.242882</td>\n",
       "      <td>0.469772</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.057068</td>\n",
       "      <td>0.019433</td>\n",
       "      <td>0.086961</td>\n",
       "      <td>-0.377664</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.112362</td>\n",
       "      <td>-0.029867</td>\n",
       "      <td>...</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.238712</td>\n",
       "      <td>-0.101574</td>\n",
       "      <td>0.101574</td>\n",
       "      <td>-0.101574</td>\n",
       "      <td>0.101574</td>\n",
       "      <td>-0.101574</td>\n",
       "      <td>0.101574</td>\n",
       "      <td>-0.101574</td>\n",
       "      <td>0.101574</td>\n",
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       "      <th>wheel-base</th>\n",
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       "      <td>-0.529145</td>\n",
       "      <td>-0.057068</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.879005</td>\n",
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       "      <td>0.484047</td>\n",
       "      <td>0.306706</td>\n",
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       "      <td>-0.306706</td>\n",
       "      <td>0.306706</td>\n",
       "      <td>-0.306706</td>\n",
       "      <td>0.306706</td>\n",
       "      <td>-0.306706</td>\n",
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       "    <tr>\n",
       "      <th>length</th>\n",
       "      <td>0.159841</td>\n",
       "      <td>-0.364511</td>\n",
       "      <td>0.019433</td>\n",
       "      <td>0.879005</td>\n",
       "      <td>1.000000</td>\n",
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       "      <th>width</th>\n",
       "      <td>0.037535</td>\n",
       "      <td>-0.237262</td>\n",
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       "      <td>0.583789</td>\n",
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       "      <td>0.310660</td>\n",
       "      <td>0.076255</td>\n",
       "      <td>0.187794</td>\n",
       "      <td>...</td>\n",
       "      <td>0.137284</td>\n",
       "      <td>0.008923</td>\n",
       "      <td>0.281198</td>\n",
       "      <td>-0.281198</td>\n",
       "      <td>0.281198</td>\n",
       "      <td>-0.281198</td>\n",
       "      <td>0.281198</td>\n",
       "      <td>-0.281198</td>\n",
       "      <td>0.281198</td>\n",
       "      <td>-0.281198</td>\n",
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       "    <tr>\n",
       "      <th>curb-weight</th>\n",
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       "      <td>-0.221082</td>\n",
       "      <td>0.221082</td>\n",
       "      <td>-0.221082</td>\n",
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       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>-0.046450</td>\n",
       "      <td>-0.112069</td>\n",
       "      <td>0.112362</td>\n",
       "      <td>0.576779</td>\n",
       "      <td>0.685531</td>\n",
       "      <td>0.731100</td>\n",
       "      <td>0.076255</td>\n",
       "      <td>0.849090</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.572786</td>\n",
       "      <td>...</td>\n",
       "      <td>0.872337</td>\n",
       "      <td>0.745337</td>\n",
       "      <td>0.070925</td>\n",
       "      <td>-0.070925</td>\n",
       "      <td>0.070925</td>\n",
       "      <td>-0.070925</td>\n",
       "      <td>0.070925</td>\n",
       "      <td>-0.070925</td>\n",
       "      <td>0.070925</td>\n",
       "      <td>-0.070925</td>\n",
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       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>0.253091</td>\n",
       "      <td>-0.145667</td>\n",
       "      <td>-0.029867</td>\n",
       "      <td>0.501534</td>\n",
       "      <td>0.610817</td>\n",
       "      <td>0.548478</td>\n",
       "      <td>0.187794</td>\n",
       "      <td>0.644532</td>\n",
       "      <td>0.572786</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.543431</td>\n",
       "      <td>0.554069</td>\n",
       "      <td>0.055371</td>\n",
       "      <td>-0.055371</td>\n",
       "      <td>0.055371</td>\n",
       "      <td>-0.055371</td>\n",
       "      <td>0.055371</td>\n",
       "      <td>-0.055371</td>\n",
       "      <td>0.055371</td>\n",
       "      <td>-0.055371</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.181985</td>\n",
       "      <td>0.008244</td>\n",
       "      <td>0.055759</td>\n",
       "      <td>0.144675</td>\n",
       "      <td>0.120888</td>\n",
       "      <td>0.182855</td>\n",
       "      <td>-0.081273</td>\n",
       "      <td>0.168642</td>\n",
       "      <td>0.208004</td>\n",
       "      <td>-0.051087</td>\n",
       "      <td>...</td>\n",
       "      <td>0.083296</td>\n",
       "      <td>0.041470</td>\n",
       "      <td>0.240013</td>\n",
       "      <td>-0.240013</td>\n",
       "      <td>0.240013</td>\n",
       "      <td>-0.240013</td>\n",
       "      <td>0.240013</td>\n",
       "      <td>-0.240013</td>\n",
       "      <td>0.240013</td>\n",
       "      <td>-0.240013</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>0.143353</td>\n",
       "      <td>-0.181073</td>\n",
       "      <td>-0.114738</td>\n",
       "      <td>0.249689</td>\n",
       "      <td>0.159203</td>\n",
       "      <td>0.189008</td>\n",
       "      <td>0.259526</td>\n",
       "      <td>0.156444</td>\n",
       "      <td>0.029005</td>\n",
       "      <td>0.002021</td>\n",
       "      <td>...</td>\n",
       "      <td>0.071176</td>\n",
       "      <td>-0.298898</td>\n",
       "      <td>0.985228</td>\n",
       "      <td>-0.985228</td>\n",
       "      <td>0.985228</td>\n",
       "      <td>-0.985228</td>\n",
       "      <td>0.985228</td>\n",
       "      <td>-0.985228</td>\n",
       "      <td>0.985228</td>\n",
       "      <td>-0.985228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>-0.020931</td>\n",
       "      <td>0.074594</td>\n",
       "      <td>0.217323</td>\n",
       "      <td>0.375689</td>\n",
       "      <td>0.580515</td>\n",
       "      <td>0.617062</td>\n",
       "      <td>-0.085763</td>\n",
       "      <td>0.758089</td>\n",
       "      <td>0.822669</td>\n",
       "      <td>0.566736</td>\n",
       "      <td>...</td>\n",
       "      <td>0.809736</td>\n",
       "      <td>0.889595</td>\n",
       "      <td>-0.168698</td>\n",
       "      <td>0.168698</td>\n",
       "      <td>-0.168698</td>\n",
       "      <td>0.168698</td>\n",
       "      <td>-0.168698</td>\n",
       "      <td>0.168698</td>\n",
       "      <td>-0.168698</td>\n",
       "      <td>0.168698</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>-0.202217</td>\n",
       "      <td>0.284011</td>\n",
       "      <td>0.239580</td>\n",
       "      <td>-0.364971</td>\n",
       "      <td>-0.286754</td>\n",
       "      <td>-0.247388</td>\n",
       "      <td>-0.315756</td>\n",
       "      <td>-0.279411</td>\n",
       "      <td>-0.256702</td>\n",
       "      <td>-0.267010</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.101519</td>\n",
       "      <td>0.116510</td>\n",
       "      <td>-0.476377</td>\n",
       "      <td>0.476377</td>\n",
       "      <td>-0.476377</td>\n",
       "      <td>0.476377</td>\n",
       "      <td>-0.476377</td>\n",
       "      <td>0.476377</td>\n",
       "      <td>-0.476377</td>\n",
       "      <td>0.476377</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-mpg</th>\n",
       "      <td>0.022156</td>\n",
       "      <td>-0.030158</td>\n",
       "      <td>-0.225255</td>\n",
       "      <td>-0.480029</td>\n",
       "      <td>-0.667658</td>\n",
       "      <td>-0.638155</td>\n",
       "      <td>-0.057087</td>\n",
       "      <td>-0.750390</td>\n",
       "      <td>-0.651002</td>\n",
       "      <td>-0.581365</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.687186</td>\n",
       "      <td>-0.949692</td>\n",
       "      <td>0.264947</td>\n",
       "      <td>-0.264947</td>\n",
       "      <td>0.264947</td>\n",
       "      <td>-0.264947</td>\n",
       "      <td>0.264947</td>\n",
       "      <td>-0.264947</td>\n",
       "      <td>0.264947</td>\n",
       "      <td>-0.264947</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>0.015456</td>\n",
       "      <td>0.041248</td>\n",
       "      <td>-0.182011</td>\n",
       "      <td>-0.552211</td>\n",
       "      <td>-0.700186</td>\n",
       "      <td>-0.684700</td>\n",
       "      <td>-0.111568</td>\n",
       "      <td>-0.795515</td>\n",
       "      <td>-0.679877</td>\n",
       "      <td>-0.590753</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.705115</td>\n",
       "      <td>-0.929940</td>\n",
       "      <td>0.197989</td>\n",
       "      <td>-0.197989</td>\n",
       "      <td>0.197989</td>\n",
       "      <td>-0.197989</td>\n",
       "      <td>0.197989</td>\n",
       "      <td>-0.197989</td>\n",
       "      <td>0.197989</td>\n",
       "      <td>-0.197989</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.118475</td>\n",
       "      <td>-0.083327</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.589147</td>\n",
       "      <td>0.691044</td>\n",
       "      <td>0.752795</td>\n",
       "      <td>0.137284</td>\n",
       "      <td>0.834420</td>\n",
       "      <td>0.872337</td>\n",
       "      <td>0.543431</td>\n",
       "      <td>...</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.790291</td>\n",
       "      <td>0.110417</td>\n",
       "      <td>-0.110417</td>\n",
       "      <td>0.110417</td>\n",
       "      <td>-0.110417</td>\n",
       "      <td>0.110417</td>\n",
       "      <td>-0.110417</td>\n",
       "      <td>0.110417</td>\n",
       "      <td>-0.110417</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-L/100km</th>\n",
       "      <td>-0.095105</td>\n",
       "      <td>0.062423</td>\n",
       "      <td>0.238712</td>\n",
       "      <td>0.484047</td>\n",
       "      <td>0.659174</td>\n",
       "      <td>0.677111</td>\n",
       "      <td>0.008923</td>\n",
       "      <td>0.785868</td>\n",
       "      <td>0.745337</td>\n",
       "      <td>0.554069</td>\n",
       "      <td>...</td>\n",
       "      <td>0.790291</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.240676</td>\n",
       "      <td>0.240676</td>\n",
       "      <td>-0.240676</td>\n",
       "      <td>0.240676</td>\n",
       "      <td>-0.240676</td>\n",
       "      <td>0.240676</td>\n",
       "      <td>-0.240676</td>\n",
       "      <td>0.240676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diesel</th>\n",
       "      <td>0.120129</td>\n",
       "      <td>-0.195381</td>\n",
       "      <td>-0.101574</td>\n",
       "      <td>0.306706</td>\n",
       "      <td>0.210616</td>\n",
       "      <td>0.243448</td>\n",
       "      <td>0.281198</td>\n",
       "      <td>0.221082</td>\n",
       "      <td>0.070925</td>\n",
       "      <td>0.055371</td>\n",
       "      <td>...</td>\n",
       "      <td>0.110417</td>\n",
       "      <td>-0.240676</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gas</th>\n",
       "      <td>-0.120129</td>\n",
       "      <td>0.195381</td>\n",
       "      <td>0.101574</td>\n",
       "      <td>-0.306706</td>\n",
       "      <td>-0.210616</td>\n",
       "      <td>-0.243448</td>\n",
       "      <td>-0.281198</td>\n",
       "      <td>-0.221082</td>\n",
       "      <td>-0.070925</td>\n",
       "      <td>-0.055371</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.110417</td>\n",
       "      <td>0.240676</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diesel.1</th>\n",
       "      <td>0.120129</td>\n",
       "      <td>-0.195381</td>\n",
       "      <td>-0.101574</td>\n",
       "      <td>0.306706</td>\n",
       "      <td>0.210616</td>\n",
       "      <td>0.243448</td>\n",
       "      <td>0.281198</td>\n",
       "      <td>0.221082</td>\n",
       "      <td>0.070925</td>\n",
       "      <td>0.055371</td>\n",
       "      <td>...</td>\n",
       "      <td>0.110417</td>\n",
       "      <td>-0.240676</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gas.1</th>\n",
       "      <td>-0.120129</td>\n",
       "      <td>0.195381</td>\n",
       "      <td>0.101574</td>\n",
       "      <td>-0.306706</td>\n",
       "      <td>-0.210616</td>\n",
       "      <td>-0.243448</td>\n",
       "      <td>-0.281198</td>\n",
       "      <td>-0.221082</td>\n",
       "      <td>-0.070925</td>\n",
       "      <td>-0.055371</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.110417</td>\n",
       "      <td>0.240676</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diesel.2</th>\n",
       "      <td>0.120129</td>\n",
       "      <td>-0.195381</td>\n",
       "      <td>-0.101574</td>\n",
       "      <td>0.306706</td>\n",
       "      <td>0.210616</td>\n",
       "      <td>0.243448</td>\n",
       "      <td>0.281198</td>\n",
       "      <td>0.221082</td>\n",
       "      <td>0.070925</td>\n",
       "      <td>0.055371</td>\n",
       "      <td>...</td>\n",
       "      <td>0.110417</td>\n",
       "      <td>-0.240676</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gas.2</th>\n",
       "      <td>-0.120129</td>\n",
       "      <td>0.195381</td>\n",
       "      <td>0.101574</td>\n",
       "      <td>-0.306706</td>\n",
       "      <td>-0.210616</td>\n",
       "      <td>-0.243448</td>\n",
       "      <td>-0.281198</td>\n",
       "      <td>-0.221082</td>\n",
       "      <td>-0.070925</td>\n",
       "      <td>-0.055371</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.110417</td>\n",
       "      <td>0.240676</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diesel.3</th>\n",
       "      <td>0.120129</td>\n",
       "      <td>-0.195381</td>\n",
       "      <td>-0.101574</td>\n",
       "      <td>0.306706</td>\n",
       "      <td>0.210616</td>\n",
       "      <td>0.243448</td>\n",
       "      <td>0.281198</td>\n",
       "      <td>0.221082</td>\n",
       "      <td>0.070925</td>\n",
       "      <td>0.055371</td>\n",
       "      <td>...</td>\n",
       "      <td>0.110417</td>\n",
       "      <td>-0.240676</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gas.3</th>\n",
       "      <td>-0.120129</td>\n",
       "      <td>0.195381</td>\n",
       "      <td>0.101574</td>\n",
       "      <td>-0.306706</td>\n",
       "      <td>-0.210616</td>\n",
       "      <td>-0.243448</td>\n",
       "      <td>-0.281198</td>\n",
       "      <td>-0.221082</td>\n",
       "      <td>-0.070925</td>\n",
       "      <td>-0.055371</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.110417</td>\n",
       "      <td>0.240676</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>26 rows × 26 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                   Unnamed: 0  symboling  normalized-losses  wheel-base  \\\n",
       "Unnamed: 0           1.000000  -0.149081          -0.242882    0.112710   \n",
       "symboling           -0.149081   1.000000           0.469772   -0.529145   \n",
       "normalized-losses   -0.242882   0.469772           1.000000   -0.057068   \n",
       "wheel-base           0.112710  -0.529145          -0.057068    1.000000   \n",
       "length               0.159841  -0.364511           0.019433    0.879005   \n",
       "width                0.037535  -0.237262           0.086961    0.814593   \n",
       "height               0.237930  -0.542261          -0.377664    0.583789   \n",
       "curb-weight          0.065873  -0.234743           0.099404    0.787584   \n",
       "engine-size         -0.046450  -0.112069           0.112362    0.576779   \n",
       "bore                 0.253091  -0.145667          -0.029867    0.501534   \n",
       "stroke              -0.181985   0.008244           0.055759    0.144675   \n",
       "compression-ratio    0.143353  -0.181073          -0.114738    0.249689   \n",
       "horsepower          -0.020931   0.074594           0.217323    0.375689   \n",
       "peak-rpm            -0.202217   0.284011           0.239580   -0.364971   \n",
       "city-mpg             0.022156  -0.030158          -0.225255   -0.480029   \n",
       "highway-mpg          0.015456   0.041248          -0.182011   -0.552211   \n",
       "price               -0.118475  -0.083327           0.133999    0.589147   \n",
       "city-L/100km        -0.095105   0.062423           0.238712    0.484047   \n",
       "diesel               0.120129  -0.195381          -0.101574    0.306706   \n",
       "gas                 -0.120129   0.195381           0.101574   -0.306706   \n",
       "diesel.1             0.120129  -0.195381          -0.101574    0.306706   \n",
       "gas.1               -0.120129   0.195381           0.101574   -0.306706   \n",
       "diesel.2             0.120129  -0.195381          -0.101574    0.306706   \n",
       "gas.2               -0.120129   0.195381           0.101574   -0.306706   \n",
       "diesel.3             0.120129  -0.195381          -0.101574    0.306706   \n",
       "gas.3               -0.120129   0.195381           0.101574   -0.306706   \n",
       "\n",
       "                     length     width    height  curb-weight  engine-size  \\\n",
       "Unnamed: 0         0.159841  0.037535  0.237930     0.065873    -0.046450   \n",
       "symboling         -0.364511 -0.237262 -0.542261    -0.234743    -0.112069   \n",
       "normalized-losses  0.019433  0.086961 -0.377664     0.099404     0.112362   \n",
       "wheel-base         0.879005  0.814593  0.583789     0.787584     0.576779   \n",
       "length             1.000000  0.857271  0.492955     0.881058     0.685531   \n",
       "width              0.857271  1.000000  0.300995     0.867720     0.731100   \n",
       "height             0.492955  0.300995  1.000000     0.310660     0.076255   \n",
       "curb-weight        0.881058  0.867720  0.310660     1.000000     0.849090   \n",
       "engine-size        0.685531  0.731100  0.076255     0.849090     1.000000   \n",
       "bore               0.610817  0.548478  0.187794     0.644532     0.572786   \n",
       "stroke             0.120888  0.182855 -0.081273     0.168642     0.208004   \n",
       "compression-ratio  0.159203  0.189008  0.259526     0.156444     0.029005   \n",
       "horsepower         0.580515  0.617062 -0.085763     0.758089     0.822669   \n",
       "peak-rpm          -0.286754 -0.247388 -0.315756    -0.279411    -0.256702   \n",
       "city-mpg          -0.667658 -0.638155 -0.057087    -0.750390    -0.651002   \n",
       "highway-mpg       -0.700186 -0.684700 -0.111568    -0.795515    -0.679877   \n",
       "price              0.691044  0.752795  0.137284     0.834420     0.872337   \n",
       "city-L/100km       0.659174  0.677111  0.008923     0.785868     0.745337   \n",
       "diesel             0.210616  0.243448  0.281198     0.221082     0.070925   \n",
       "gas               -0.210616 -0.243448 -0.281198    -0.221082    -0.070925   \n",
       "diesel.1           0.210616  0.243448  0.281198     0.221082     0.070925   \n",
       "gas.1             -0.210616 -0.243448 -0.281198    -0.221082    -0.070925   \n",
       "diesel.2           0.210616  0.243448  0.281198     0.221082     0.070925   \n",
       "gas.2             -0.210616 -0.243448 -0.281198    -0.221082    -0.070925   \n",
       "diesel.3           0.210616  0.243448  0.281198     0.221082     0.070925   \n",
       "gas.3             -0.210616 -0.243448 -0.281198    -0.221082    -0.070925   \n",
       "\n",
       "                       bore    ...        price  city-L/100km    diesel  \\\n",
       "Unnamed: 0         0.253091    ...    -0.118475     -0.095105  0.120129   \n",
       "symboling         -0.145667    ...    -0.083327      0.062423 -0.195381   \n",
       "normalized-losses -0.029867    ...     0.133999      0.238712 -0.101574   \n",
       "wheel-base         0.501534    ...     0.589147      0.484047  0.306706   \n",
       "length             0.610817    ...     0.691044      0.659174  0.210616   \n",
       "width              0.548478    ...     0.752795      0.677111  0.243448   \n",
       "height             0.187794    ...     0.137284      0.008923  0.281198   \n",
       "curb-weight        0.644532    ...     0.834420      0.785868  0.221082   \n",
       "engine-size        0.572786    ...     0.872337      0.745337  0.070925   \n",
       "bore               1.000000    ...     0.543431      0.554069  0.055371   \n",
       "stroke            -0.051087    ...     0.083296      0.041470  0.240013   \n",
       "compression-ratio  0.002021    ...     0.071176     -0.298898  0.985228   \n",
       "horsepower         0.566736    ...     0.809736      0.889595 -0.168698   \n",
       "peak-rpm          -0.267010    ...    -0.101519      0.116510 -0.476377   \n",
       "city-mpg          -0.581365    ...    -0.687186     -0.949692  0.264947   \n",
       "highway-mpg       -0.590753    ...    -0.705115     -0.929940  0.197989   \n",
       "price              0.543431    ...     1.000000      0.790291  0.110417   \n",
       "city-L/100km       0.554069    ...     0.790291      1.000000 -0.240676   \n",
       "diesel             0.055371    ...     0.110417     -0.240676  1.000000   \n",
       "gas               -0.055371    ...    -0.110417      0.240676 -1.000000   \n",
       "diesel.1           0.055371    ...     0.110417     -0.240676  1.000000   \n",
       "gas.1             -0.055371    ...    -0.110417      0.240676 -1.000000   \n",
       "diesel.2           0.055371    ...     0.110417     -0.240676  1.000000   \n",
       "gas.2             -0.055371    ...    -0.110417      0.240676 -1.000000   \n",
       "diesel.3           0.055371    ...     0.110417     -0.240676  1.000000   \n",
       "gas.3             -0.055371    ...    -0.110417      0.240676 -1.000000   \n",
       "\n",
       "                        gas  diesel.1     gas.1  diesel.2     gas.2  diesel.3  \\\n",
       "Unnamed: 0        -0.120129  0.120129 -0.120129  0.120129 -0.120129  0.120129   \n",
       "symboling          0.195381 -0.195381  0.195381 -0.195381  0.195381 -0.195381   \n",
       "normalized-losses  0.101574 -0.101574  0.101574 -0.101574  0.101574 -0.101574   \n",
       "wheel-base        -0.306706  0.306706 -0.306706  0.306706 -0.306706  0.306706   \n",
       "length            -0.210616  0.210616 -0.210616  0.210616 -0.210616  0.210616   \n",
       "width             -0.243448  0.243448 -0.243448  0.243448 -0.243448  0.243448   \n",
       "height            -0.281198  0.281198 -0.281198  0.281198 -0.281198  0.281198   \n",
       "curb-weight       -0.221082  0.221082 -0.221082  0.221082 -0.221082  0.221082   \n",
       "engine-size       -0.070925  0.070925 -0.070925  0.070925 -0.070925  0.070925   \n",
       "bore              -0.055371  0.055371 -0.055371  0.055371 -0.055371  0.055371   \n",
       "stroke            -0.240013  0.240013 -0.240013  0.240013 -0.240013  0.240013   \n",
       "compression-ratio -0.985228  0.985228 -0.985228  0.985228 -0.985228  0.985228   \n",
       "horsepower         0.168698 -0.168698  0.168698 -0.168698  0.168698 -0.168698   \n",
       "peak-rpm           0.476377 -0.476377  0.476377 -0.476377  0.476377 -0.476377   \n",
       "city-mpg          -0.264947  0.264947 -0.264947  0.264947 -0.264947  0.264947   \n",
       "highway-mpg       -0.197989  0.197989 -0.197989  0.197989 -0.197989  0.197989   \n",
       "price             -0.110417  0.110417 -0.110417  0.110417 -0.110417  0.110417   \n",
       "city-L/100km       0.240676 -0.240676  0.240676 -0.240676  0.240676 -0.240676   \n",
       "diesel            -1.000000  1.000000 -1.000000  1.000000 -1.000000  1.000000   \n",
       "gas                1.000000 -1.000000  1.000000 -1.000000  1.000000 -1.000000   \n",
       "diesel.1          -1.000000  1.000000 -1.000000  1.000000 -1.000000  1.000000   \n",
       "gas.1              1.000000 -1.000000  1.000000 -1.000000  1.000000 -1.000000   \n",
       "diesel.2          -1.000000  1.000000 -1.000000  1.000000 -1.000000  1.000000   \n",
       "gas.2              1.000000 -1.000000  1.000000 -1.000000  1.000000 -1.000000   \n",
       "diesel.3          -1.000000  1.000000 -1.000000  1.000000 -1.000000  1.000000   \n",
       "gas.3              1.000000 -1.000000  1.000000 -1.000000  1.000000 -1.000000   \n",
       "\n",
       "                      gas.3  \n",
       "Unnamed: 0        -0.120129  \n",
       "symboling          0.195381  \n",
       "normalized-losses  0.101574  \n",
       "wheel-base        -0.306706  \n",
       "length            -0.210616  \n",
       "width             -0.243448  \n",
       "height            -0.281198  \n",
       "curb-weight       -0.221082  \n",
       "engine-size       -0.070925  \n",
       "bore              -0.055371  \n",
       "stroke            -0.240013  \n",
       "compression-ratio -0.985228  \n",
       "horsepower         0.168698  \n",
       "peak-rpm           0.476377  \n",
       "city-mpg          -0.264947  \n",
       "highway-mpg       -0.197989  \n",
       "price             -0.110417  \n",
       "city-L/100km       0.240676  \n",
       "diesel            -1.000000  \n",
       "gas                1.000000  \n",
       "diesel.1          -1.000000  \n",
       "gas.1              1.000000  \n",
       "diesel.2          -1.000000  \n",
       "gas.2              1.000000  \n",
       "diesel.3          -1.000000  \n",
       "gas.3              1.000000  \n",
       "\n",
       "[26 rows x 26 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Continuous numerical variables: \n",
    "\n",
    "Continuous numerical variables are variables that may contain any value within some range. Continuous numerical variables can have the type \"int64\" or \"float64\". A great way to visualize these variables is by using scatterplots with fitted lines. \n",
    "\n",
    "In order to start understanding the (linear) relationship between an individual variable and the price. We can do this by using \"regplot\", which plots the scatterplot plus the fitted regression line for the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's find the scatterplot of \"engine-size\" and \"price\" "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Positive linear relationship"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 55863.06854397509)"
      ]
     },
     "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 = 'engine-size', y = 'price', data = df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While engine-size grows price grows too: 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. E"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### also we can use df.corr "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>engine-size</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.872337</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>0.872337</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             engine-size     price\n",
       "engine-size     1.000000  0.872337\n",
       "price           0.872337  1.000000"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['engine-size','price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- As correlaction is a number between -1 and 1.\n",
    "- If it is near 1 so it is positive correlation.\n",
    "- If corr is about -1 it is negative correlation.\n",
    "- If corr is about 0 it calls weak correlation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Negative linear relationship"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fb70e61d0f0>"
      ]
     },
     "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=\"highway-mpg\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the highway-mpg rise, the price decline\n",
    "so it shows there is negetive relation between them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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>-0.705115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.705115</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             highway-mpg     price\n",
       "highway-mpg     1.000000 -0.705115\n",
       "price          -0.705115  1.000000"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['highway-mpg', 'price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here the correlation is about -0.70 it is near -1 as results it is negative relation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Weak Linear Relationship\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fb70e5f9550>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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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": "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>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>-0.101519</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.101519</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          peak-rpm     price\n",
       "peak-rpm  1.000000 -0.101519\n",
       "price    -0.101519  1.000000"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['peak-rpm','price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is about 0 so there is weak linear relationship.\n",
    "so peak-rpm is not really good feature."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Categorical variables\n",
    "\n",
    "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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the relationship between \"body-style\" and \"price\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fb70e55aba8>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"body-style\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fb70e4ac240>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"engine-location\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fb70e410d68>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# drive-wheels\n",
    "sns.boxplot(x=\"drive-wheels\", y=\"price\", data=df)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Statistical Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "you can use statistical analysis to achieve more information about data\n",
    "we can do it by df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can actually get the mean, the std, the count of variables, the minimum value, the IQR (Interquartile Range:25%, 50% and 75%)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</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>...</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "      <th>diesel.1</th>\n",
       "      <th>gas.1</th>\n",
       "      <th>diesel.2</th>\n",
       "      <th>gas.2</th>\n",
       "      <th>diesel.3</th>\n",
       "      <th>gas.3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>102.415000</td>\n",
       "      <td>0.830000</td>\n",
       "      <td>122.000000</td>\n",
       "      <td>98.848000</td>\n",
       "      <td>0.837232</td>\n",
       "      <td>0.915250</td>\n",
       "      <td>0.899523</td>\n",
       "      <td>2555.705000</td>\n",
       "      <td>126.860000</td>\n",
       "      <td>3.330000</td>\n",
       "      <td>...</td>\n",
       "      <td>13205.690000</td>\n",
       "      <td>9.937914</td>\n",
       "      <td>0.100000</td>\n",
       "      <td>0.900000</td>\n",
       "      <td>0.100000</td>\n",
       "      <td>0.900000</td>\n",
       "      <td>0.100000</td>\n",
       "      <td>0.900000</td>\n",
       "      <td>0.100000</td>\n",
       "      <td>0.900000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>58.931634</td>\n",
       "      <td>1.248557</td>\n",
       "      <td>32.076542</td>\n",
       "      <td>6.038261</td>\n",
       "      <td>0.059333</td>\n",
       "      <td>0.029207</td>\n",
       "      <td>0.040610</td>\n",
       "      <td>518.594552</td>\n",
       "      <td>41.650501</td>\n",
       "      <td>0.268562</td>\n",
       "      <td>...</td>\n",
       "      <td>7966.982558</td>\n",
       "      <td>2.539415</td>\n",
       "      <td>0.300753</td>\n",
       "      <td>0.300753</td>\n",
       "      <td>0.300753</td>\n",
       "      <td>0.300753</td>\n",
       "      <td>0.300753</td>\n",
       "      <td>0.300753</td>\n",
       "      <td>0.300753</td>\n",
       "      <td>0.300753</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>-2.000000</td>\n",
       "      <td>65.000000</td>\n",
       "      <td>86.600000</td>\n",
       "      <td>0.678039</td>\n",
       "      <td>0.837500</td>\n",
       "      <td>0.799331</td>\n",
       "      <td>1488.000000</td>\n",
       "      <td>61.000000</td>\n",
       "      <td>2.540000</td>\n",
       "      <td>...</td>\n",
       "      <td>5118.000000</td>\n",
       "      <td>4.795918</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>52.750000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>100.250000</td>\n",
       "      <td>94.500000</td>\n",
       "      <td>0.800937</td>\n",
       "      <td>0.891319</td>\n",
       "      <td>0.869565</td>\n",
       "      <td>2163.000000</td>\n",
       "      <td>97.750000</td>\n",
       "      <td>3.150000</td>\n",
       "      <td>...</td>\n",
       "      <td>7775.000000</td>\n",
       "      <td>7.833333</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>102.500000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>122.000000</td>\n",
       "      <td>97.000000</td>\n",
       "      <td>0.832292</td>\n",
       "      <td>0.909722</td>\n",
       "      <td>0.904682</td>\n",
       "      <td>2414.000000</td>\n",
       "      <td>119.500000</td>\n",
       "      <td>3.310000</td>\n",
       "      <td>...</td>\n",
       "      <td>10270.000000</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>153.250000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>138.250000</td>\n",
       "      <td>102.400000</td>\n",
       "      <td>0.881788</td>\n",
       "      <td>0.926042</td>\n",
       "      <td>0.928512</td>\n",
       "      <td>2928.250000</td>\n",
       "      <td>142.000000</td>\n",
       "      <td>3.582500</td>\n",
       "      <td>...</td>\n",
       "      <td>16500.750000</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>203.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>256.000000</td>\n",
       "      <td>120.900000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>4066.000000</td>\n",
       "      <td>326.000000</td>\n",
       "      <td>3.940000</td>\n",
       "      <td>...</td>\n",
       "      <td>45400.000000</td>\n",
       "      <td>18.076923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 26 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       Unnamed: 0   symboling  normalized-losses  wheel-base      length  \\\n",
       "count  200.000000  200.000000         200.000000  200.000000  200.000000   \n",
       "mean   102.415000    0.830000         122.000000   98.848000    0.837232   \n",
       "std     58.931634    1.248557          32.076542    6.038261    0.059333   \n",
       "min      0.000000   -2.000000          65.000000   86.600000    0.678039   \n",
       "25%     52.750000    0.000000         100.250000   94.500000    0.800937   \n",
       "50%    102.500000    1.000000         122.000000   97.000000    0.832292   \n",
       "75%    153.250000    2.000000         138.250000  102.400000    0.881788   \n",
       "max    203.000000    3.000000         256.000000  120.900000    1.000000   \n",
       "\n",
       "            width      height  curb-weight  engine-size        bore  \\\n",
       "count  200.000000  200.000000   200.000000   200.000000  200.000000   \n",
       "mean     0.915250    0.899523  2555.705000   126.860000    3.330000   \n",
       "std      0.029207    0.040610   518.594552    41.650501    0.268562   \n",
       "min      0.837500    0.799331  1488.000000    61.000000    2.540000   \n",
       "25%      0.891319    0.869565  2163.000000    97.750000    3.150000   \n",
       "50%      0.909722    0.904682  2414.000000   119.500000    3.310000   \n",
       "75%      0.926042    0.928512  2928.250000   142.000000    3.582500   \n",
       "max      1.000000    1.000000  4066.000000   326.000000    3.940000   \n",
       "\n",
       "          ...             price  city-L/100km      diesel         gas  \\\n",
       "count     ...        200.000000    200.000000  200.000000  200.000000   \n",
       "mean      ...      13205.690000      9.937914    0.100000    0.900000   \n",
       "std       ...       7966.982558      2.539415    0.300753    0.300753   \n",
       "min       ...       5118.000000      4.795918    0.000000    0.000000   \n",
       "25%       ...       7775.000000      7.833333    0.000000    1.000000   \n",
       "50%       ...      10270.000000      9.791667    0.000000    1.000000   \n",
       "75%       ...      16500.750000     12.368421    0.000000    1.000000   \n",
       "max       ...      45400.000000     18.076923    1.000000    1.000000   \n",
       "\n",
       "         diesel.1       gas.1    diesel.2       gas.2    diesel.3       gas.3  \n",
       "count  200.000000  200.000000  200.000000  200.000000  200.000000  200.000000  \n",
       "mean     0.100000    0.900000    0.100000    0.900000    0.100000    0.900000  \n",
       "std      0.300753    0.300753    0.300753    0.300753    0.300753    0.300753  \n",
       "min      0.000000    0.000000    0.000000    0.000000    0.000000    0.000000  \n",
       "25%      0.000000    1.000000    0.000000    1.000000    0.000000    1.000000  \n",
       "50%      0.000000    1.000000    0.000000    1.000000    0.000000    1.000000  \n",
       "75%      0.000000    1.000000    0.000000    1.000000    0.000000    1.000000  \n",
       "max      1.000000    1.000000    1.000000    1.000000    1.000000    1.000000  \n",
       "\n",
       "[8 rows x 26 columns]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Value counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "value counts can help us to understand how many value does we have in our particular column.\n",
    "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']]\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fwd    118\n",
       "rwd     74\n",
       "4wd      8\n",
       "Name: drive-wheels, dtype: int64"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also we can convert it into a dataframe as "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>74</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            74\n",
       "4wd             8"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].value_counts().to_frame()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's repeat the above steps but save the results to the dataframe \"engine-location\" and rename the column  'engine-location' to 'value_counts'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value_counts</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-location</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>front</th>\n",
       "      <td>197</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                     197\n",
       "rear                        3"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# engine-location as variable\n",
    "engine_loc_counts = df['engine-location'].value_counts().to_frame()\n",
    "engine_loc_counts.rename(columns={'engine-location': 'value_counts'}, inplace=True)\n",
    "engine_loc_counts.index.name = 'engine-location'\n",
    "engine_loc_counts.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Grouping"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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.\n",
    "\n",
    " For example, let's group by the variable \"drive-wheels\". We see that there are 3 different categories of drive wheels."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Split Data into Groups"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pandas object can be split into any of their objects. There are multiple ways to split an object like −"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    obj.groupby('key')\n",
    "    obj.groupby(['key1','key2'])\n",
    "    obj.groupby(key,axis=1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pandas.core.groupby.groupby.DataFrameGroupBy object at 0x7fb70e3c8470>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby('engine-size')\n",
    "df.groupby(['engine-size','price'])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " we can select the columns 'drive-wheels','body-style' and 'price' , then assign it to the variable \"df_group_one\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_group_one=df[['drive-wheels','body-style','price']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>body-style</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>13950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4wd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>17450.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>15250.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>17710.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>18920.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>23875.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>16430.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>16925.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>20970.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>21105.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>24565.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>30760.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>41315.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>36880.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>5151.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6295.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>6575.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>5572.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6377.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7957.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6229.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>6692.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7609.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>8558.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>8921.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>12964.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6479.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6855.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>170</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>9988.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>171</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>10898.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>172</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>11248.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>173</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>16558.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>174</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>15998.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>175</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>15690.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>176</th>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>15750.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>177</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7775.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>178</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7975.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>179</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7995.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>180</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>8195.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>181</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>8495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>182</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>183</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9995.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>184</th>\n",
       "      <td>fwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>11595.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>185</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>9980.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>186</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>13295.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>187</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>13845.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>188</th>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>12290.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>189</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>12940.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>190</th>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>13415.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>191</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>15985.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>192</th>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>16515.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>193</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>18420.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>194</th>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>18950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>195</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>16845.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>196</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>19045.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>197</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>21485.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>22470.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>199</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>22625.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>200 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    drive-wheels   body-style    price\n",
       "0            rwd  convertible  16500.0\n",
       "1            rwd    hatchback  16500.0\n",
       "2            fwd        sedan  13950.0\n",
       "3            4wd        sedan  17450.0\n",
       "4            fwd        sedan  15250.0\n",
       "5            fwd        sedan  17710.0\n",
       "6            fwd        wagon  18920.0\n",
       "7            fwd        sedan  23875.0\n",
       "8            rwd        sedan  16430.0\n",
       "9            rwd        sedan  16925.0\n",
       "10           rwd        sedan  20970.0\n",
       "11           rwd        sedan  21105.0\n",
       "12           rwd        sedan  24565.0\n",
       "13           rwd        sedan  30760.0\n",
       "14           rwd        sedan  41315.0\n",
       "15           rwd        sedan  36880.0\n",
       "16           fwd    hatchback   5151.0\n",
       "17           fwd    hatchback   6295.0\n",
       "18           fwd        sedan   6575.0\n",
       "19           fwd    hatchback   5572.0\n",
       "20           fwd    hatchback   6377.0\n",
       "21           fwd    hatchback   7957.0\n",
       "22           fwd    hatchback   6229.0\n",
       "23           fwd        sedan   6692.0\n",
       "24           fwd        sedan   7609.0\n",
       "25           fwd        sedan   8558.0\n",
       "26           fwd        wagon   8921.0\n",
       "27           fwd    hatchback  12964.0\n",
       "28           fwd    hatchback   6479.0\n",
       "29           fwd    hatchback   6855.0\n",
       "..           ...          ...      ...\n",
       "170          fwd    hatchback   9988.0\n",
       "171          fwd        sedan  10898.0\n",
       "172          fwd    hatchback  11248.0\n",
       "173          rwd    hatchback  16558.0\n",
       "174          rwd    hatchback  15998.0\n",
       "175          rwd        sedan  15690.0\n",
       "176          rwd        wagon  15750.0\n",
       "177          fwd        sedan   7775.0\n",
       "178          fwd        sedan   7975.0\n",
       "179          fwd        sedan   7995.0\n",
       "180          fwd        sedan   8195.0\n",
       "181          fwd        sedan   8495.0\n",
       "182          fwd        sedan   9495.0\n",
       "183          fwd        sedan   9995.0\n",
       "184          fwd  convertible  11595.0\n",
       "185          fwd    hatchback   9980.0\n",
       "186          fwd        sedan  13295.0\n",
       "187          fwd        sedan  13845.0\n",
       "188          fwd        wagon  12290.0\n",
       "189          rwd        sedan  12940.0\n",
       "190          rwd        wagon  13415.0\n",
       "191          rwd        sedan  15985.0\n",
       "192          rwd        wagon  16515.0\n",
       "193          rwd        sedan  18420.0\n",
       "194          rwd        wagon  18950.0\n",
       "195          rwd        sedan  16845.0\n",
       "196          rwd        sedan  19045.0\n",
       "197          rwd        sedan  21485.0\n",
       "198          rwd        sedan  22470.0\n",
       "199          rwd        sedan  22625.0\n",
       "\n",
       "[200 rows x 3 columns]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_group_one"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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>19842.243243</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  19842.243243"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_group_one=df_group_one.groupby(['drive-wheels'],as_index= False).mean()\n",
    "df_group_one"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "UsageError: Line magic function `%` not found.\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "% matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What are correlation and causation and how are they different?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Two or more variables considered to be related, in a statistical context, if their values change so that as the value of one variable increases or decreases so does the value of the other variable (although it may be in the opposite direction).\n",
    "\n",
    "For example, for the two variables \"hours worked\" and \"income earned\" there is a relationship between the two if the increase in hours worked is associated with an increase in income earned. If we consider the two variables \"price\" and \"purchasing power\", as the price of goods increases a person's ability to buy these goods decreases (assuming a constant income).\n",
    "\n",
    "\n",
    "Correlation is a statistical measure (expressed as a number) that describes the size and direction of a relationship between two or more variables. A correlation between variables, however, does not automatically mean that the change in one variable is the cause of the change in the values of the other variable.\n",
    "\n",
    "\n",
    "Causation indicates that one event is the result of the occurrence of the other event; i.e. there is a causal relationship between the two events. This is also referred to as cause and effect.\n",
    "\n",
    "\n",
    "Theoretically, the difference between the two types of relationships are easy to identify — an action or occurrence can cause another (e.g. smoking causes an increase in the risk of developing lung cancer), or it can correlate with another (e.g. smoking is correlated with alcoholism, but it does not cause alcoholism). In practice, however, it remains difficult to clearly establish cause and effect, compared with establishing correlation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Why are correlation and causation important?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The objective of much research or scientific analysis is to identify the extent to which one variable relates to another variable. For example:\n",
    "\n",
    "   - Is there a relationship between a person's education level and their health?\n",
    "   - Is pet ownership associated with living longer?\n",
    "   - Did a company's marketing campaign increase their product sales? \n",
    "\n",
    "\n",
    "These and other questions are exploring whether a correlation exists between the two variables, and if there is a correlation then this may guide further research into investigating whether one action causes the other. By understanding correlation and causality, it allows for policies and programs that aim to bring about a desired outcome to be better targeted.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pearson Correlation\n",
    "The Pearson Correlation measures the linear dependence between two variables X and Y.\n",
    "The resulting coefficient is a value between -1 and 1 inclusive, where:\n",
    "- **1**: total positive linear correlation,\n",
    "- **0**: no linear correlation, the two variables most likely do not affect each other\n",
    "- **-1**: total negative linear correlation.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**P-value**: \n",
    "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. \n",
    "\n",
    "By convention, when the \n",
    "- p-value is < 0.001 we say there is strong evidence that the correlation is significant,\n",
    "- the p-value is < 0.05; there is moderate evidence that the correlation is significant,\n",
    "- the p-value is < 0.1; there is weak evidence that the correlation is significant, and\n",
    "- the p-value is > 0.1; there is no evidence that the correlation is significant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can obtain this information using  \"stats\" module in the \"scipy\"  library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "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": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.5891470005448702  with a P-value of P = 4.4570195020502404e-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": [
    "### Width vs Price\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the Pearson Correlation Coefficient and P-value of 'width' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.752794863183261  with a P-value of P = 8.256714148308006e-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": [
    "### ANOVA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Analysis of Variance (ANOVA) is probably one of the most popular and commonly used statistical procedures. In this course, Professor Conway will cover the essentials of ANOVA such as one-way between groups ANOVA, post-hoc tests, and repeated measures ANOVA."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**F-test score**: 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.\n",
    "\n",
    "**P-value**:  P-value tells how statistically significant is our calculated score value\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>rwd</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>fwd</td>\n",
       "      <td>13950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4wd</td>\n",
       "      <td>17450.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>fwd</td>\n",
       "      <td>15250.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>135</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  16500.0\n",
       "1            rwd  16500.0\n",
       "2            fwd  13950.0\n",
       "3            4wd  17450.0\n",
       "4            fwd  15250.0\n",
       "135          4wd   7603.0"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_gptest=df[['drive-wheels','body-style','price']]\n",
    "\n",
    "grouped_test2=df_gptest[['drive-wheels','price']].groupby(['drive-wheels'])\n",
    "grouped_test2.head(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can obtain the values of the method group using the method \"get_group\".  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3      17450.0\n",
       "135     7603.0\n",
       "139     9233.0\n",
       "140    11259.0\n",
       "143     8013.0\n",
       "144    11694.0\n",
       "149     7898.0\n",
       "150     8778.0\n",
       "Name: price, dtype: float64"
      ]
     },
     "execution_count": 47,
     "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 **F-test score** and **P-value**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 68.49603532807176 , P = 2.6116313994533863e-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": [
    "### Write queries and selection in pandas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "pd.DataFrame.loc can take one or two indexers. For the rest of the post, I'll represent the first indexer as i and the second indexer as j.\n",
    "\n",
    "If only one indexer is provided, it applies to the index of the dataframe and the missing indexer is assumed to represent all columns. So the following two examples are equivalent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " - df.loc[i]\n",
    " - df.loc[i, :]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Where : is used to represent all columns.\n",
    "If both indexers are present, i references index values and j references column values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "for this purpose it is better to set index in df to select easier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>symboling</th>\n",
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       "      <th>gas.3</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>make</th>\n",
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       "      <td>12.368421</td>\n",
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       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "      <th>audi</th>\n",
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       "      <td>2</td>\n",
       "      <td>164</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",
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       "      <td>Medium</td>\n",
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       "      <td>sedan</td>\n",
       "      <td>4wd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.4</td>\n",
       "      <td>0.848630</td>\n",
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      ],
      "text/plain": [
       "             Unnamed: 0  symboling  normalized-losses aspiration num-of-doors  \\\n",
       "make                                                                            \n",
       "alfa-romero           0          3                122        std          two   \n",
       "alfa-romero           1          1                122        std          two   \n",
       "audi                  2          2                164        std         four   \n",
       "audi                  3          2                164        std         four   \n",
       "audi                  4          2                122        std          two   \n",
       "\n",
       "              body-style drive-wheels engine-location  wheel-base    length  \\\n",
       "make                                                                          \n",
       "alfa-romero  convertible          rwd           front        88.6  0.811148   \n",
       "alfa-romero    hatchback          rwd           front        94.5  0.822681   \n",
       "audi               sedan          fwd           front        99.8  0.848630   \n",
       "audi               sedan          4wd           front        99.4  0.848630   \n",
       "audi               sedan          fwd           front        99.8  0.851994   \n",
       "\n",
       "             ...    city-L/100km  horsepower-binned  diesel gas diesel.1  \\\n",
       "make         ...                                                           \n",
       "alfa-romero  ...       11.190476             Medium       0   1        0   \n",
       "alfa-romero  ...       12.368421             Medium       0   1        0   \n",
       "audi         ...        9.791667             Medium       0   1        0   \n",
       "audi         ...       13.055556             Medium       0   1        0   \n",
       "audi         ...       12.368421             Medium       0   1        0   \n",
       "\n",
       "             gas.1 diesel.2  gas.2  diesel.3  gas.3  \n",
       "make                                                 \n",
       "alfa-romero      1        0      1         0      1  \n",
       "alfa-romero      1        0      1         0      1  \n",
       "audi             1        0      1         0      1  \n",
       "audi             1        0      1         0      1  \n",
       "audi             1        0      1         0      1  \n",
       "\n",
       "[5 rows x 35 columns]"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.set_index('make', inplace = True)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>front</td>\n",
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       "      <th>audi</th>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>122</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>wagon</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>105.8</td>\n",
       "      <td>0.925997</td>\n",
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       "      <td>0</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>audi</th>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>158</td>\n",
       "      <td>turbo</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>105.8</td>\n",
       "      <td>0.925997</td>\n",
       "      <td>...</td>\n",
       "      <td>13.823529</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 35 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             Unnamed: 0  symboling  normalized-losses aspiration num-of-doors  \\\n",
       "make                                                                            \n",
       "alfa-romero           0          3                122        std          two   \n",
       "alfa-romero           1          1                122        std          two   \n",
       "audi                  2          2                164        std         four   \n",
       "audi                  3          2                164        std         four   \n",
       "audi                  4          2                122        std          two   \n",
       "audi                  5          1                158        std         four   \n",
       "audi                  6          1                122        std         four   \n",
       "audi                  7          1                158      turbo         four   \n",
       "\n",
       "              body-style drive-wheels engine-location  wheel-base    length  \\\n",
       "make                                                                          \n",
       "alfa-romero  convertible          rwd           front        88.6  0.811148   \n",
       "alfa-romero    hatchback          rwd           front        94.5  0.822681   \n",
       "audi               sedan          fwd           front        99.8  0.848630   \n",
       "audi               sedan          4wd           front        99.4  0.848630   \n",
       "audi               sedan          fwd           front        99.8  0.851994   \n",
       "audi               sedan          fwd           front       105.8  0.925997   \n",
       "audi               wagon          fwd           front       105.8  0.925997   \n",
       "audi               sedan          fwd           front       105.8  0.925997   \n",
       "\n",
       "             ...    city-L/100km  horsepower-binned  diesel gas diesel.1  \\\n",
       "make         ...                                                           \n",
       "alfa-romero  ...       11.190476             Medium       0   1        0   \n",
       "alfa-romero  ...       12.368421             Medium       0   1        0   \n",
       "audi         ...        9.791667             Medium       0   1        0   \n",
       "audi         ...       13.055556             Medium       0   1        0   \n",
       "audi         ...       12.368421             Medium       0   1        0   \n",
       "audi         ...       12.368421             Medium       0   1        0   \n",
       "audi         ...       12.368421             Medium       0   1        0   \n",
       "audi         ...       13.823529             Medium       0   1        0   \n",
       "\n",
       "             gas.1 diesel.2  gas.2  diesel.3  gas.3  \n",
       "make                                                 \n",
       "alfa-romero      1        0      1         0      1  \n",
       "alfa-romero      1        0      1         0      1  \n",
       "audi             1        0      1         0      1  \n",
       "audi             1        0      1         0      1  \n",
       "audi             1        0      1         0      1  \n",
       "audi             1        0      1         0      1  \n",
       "audi             1        0      1         0      1  \n",
       "audi             1        0      1         0      1  \n",
       "\n",
       "[8 rows x 35 columns]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.loc[['alfa-romero', 'audi']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we get only the rows which consists of alfa-romero and audi cars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "make\n",
       "alfa-romero    3\n",
       "alfa-romero    1\n",
       "Name: symboling, dtype: int64"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.loc['alfa-romero', 'symboling']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "make\n",
       "alfa-romero    convertible\n",
       "alfa-romero      hatchback\n",
       "Name: body-style, dtype: object"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.loc['alfa-romero', 'body-style']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "make\n",
       "audi    Medium\n",
       "audi    Medium\n",
       "audi    Medium\n",
       "audi    Medium\n",
       "audi    Medium\n",
       "audi    Medium\n",
       "Name: horsepower-binned, dtype: object"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.loc['audi', 'horsepower-binned']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### GOOD LOCK"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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