KNN Project.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predicting Car Prices\n",
    "\n",
    "In this project we will learn how to predict the car price using a machine learning workflow.\n",
    " For each car we have information about the technical aspects of the vehicle such as the motor's displacement, the weight of the car, the miles per gallon, how fast the car accelerates, and more. You can read more about the data set [here](https://archive.ics.uci.edu/ml/datasets/automobile) and can download it directly from [here](https://archive.ics.uci.edu/ml/machine-learning-databases/autos/imports-85.data)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>make</th>\n",
       "      <th>fuel-type</th>\n",
       "      <th>aspiration</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>...</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>fuel-system</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-rate</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>?</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>...</td>\n",
       "      <td>130</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.47</td>\n",
       "      <td>2.68</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111</td>\n",
       "      <td>5000</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>13495</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>?</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>...</td>\n",
       "      <td>130</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.47</td>\n",
       "      <td>2.68</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111</td>\n",
       "      <td>5000</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>16500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>?</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>94.5</td>\n",
       "      <td>...</td>\n",
       "      <td>152</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>2.68</td>\n",
       "      <td>3.47</td>\n",
       "      <td>9.0</td>\n",
       "      <td>154</td>\n",
       "      <td>5000</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>gas</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>...</td>\n",
       "      <td>109</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.19</td>\n",
       "      <td>3.40</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102</td>\n",
       "      <td>5500</td>\n",
       "      <td>24</td>\n",
       "      <td>30</td>\n",
       "      <td>13950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>4wd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.4</td>\n",
       "      <td>...</td>\n",
       "      <td>136</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.19</td>\n",
       "      <td>3.40</td>\n",
       "      <td>8.0</td>\n",
       "      <td>115</td>\n",
       "      <td>5500</td>\n",
       "      <td>18</td>\n",
       "      <td>22</td>\n",
       "      <td>17450</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 26 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   symboling normalized-losses         make fuel-type aspiration num-of-doors  \\\n",
       "0          3                 ?  alfa-romero       gas        std          two   \n",
       "1          3                 ?  alfa-romero       gas        std          two   \n",
       "2          1                 ?  alfa-romero       gas        std          two   \n",
       "3          2               164         audi       gas        std         four   \n",
       "4          2               164         audi       gas        std         four   \n",
       "\n",
       "    body-style drive-wheels engine-location  wheel-base  ...  engine-size  \\\n",
       "0  convertible          rwd           front        88.6  ...          130   \n",
       "1  convertible          rwd           front        88.6  ...          130   \n",
       "2    hatchback          rwd           front        94.5  ...          152   \n",
       "3        sedan          fwd           front        99.8  ...          109   \n",
       "4        sedan          4wd           front        99.4  ...          136   \n",
       "\n",
       "   fuel-system  bore  stroke compression-rate horsepower  peak-rpm city-mpg  \\\n",
       "0         mpfi  3.47    2.68              9.0        111      5000       21   \n",
       "1         mpfi  3.47    2.68              9.0        111      5000       21   \n",
       "2         mpfi  2.68    3.47              9.0        154      5000       19   \n",
       "3         mpfi  3.19    3.40             10.0        102      5500       24   \n",
       "4         mpfi  3.19    3.40              8.0        115      5500       18   \n",
       "\n",
       "  highway-mpg  price  \n",
       "0          27  13495  \n",
       "1          27  16500  \n",
       "2          26  16500  \n",
       "3          30  13950  \n",
       "4          22  17450  \n",
       "\n",
       "[5 rows x 26 columns]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "cols = ['symboling', 'normalized-losses', 'make', 'fuel-type', 'aspiration', 'num-of-doors', 'body-style', \n",
    "        'drive-wheels', 'engine-location', 'wheel-base', 'length', 'width', 'height', 'curb-weight', 'engine-type', \n",
    "        'num-of-cylinders', 'engine-size', 'fuel-system', 'bore', 'stroke', 'compression-rate', 'horsepower', 'peak-rpm', 'city-mpg', 'highway-mpg', 'price']\n",
    "cars = pd.read_csv('imports-85.data', names=cols)\n",
    "\n",
    "cars.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we had to manually enter the columns because the intial read did not to that for us ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 205 entries, 0 to 204\n",
      "Data columns (total 26 columns):\n",
      " #   Column             Non-Null Count  Dtype  \n",
      "---  ------             --------------  -----  \n",
      " 0   symboling          205 non-null    int64  \n",
      " 1   normalized-losses  205 non-null    object \n",
      " 2   make               205 non-null    object \n",
      " 3   fuel-type          205 non-null    object \n",
      " 4   aspiration         205 non-null    object \n",
      " 5   num-of-doors       205 non-null    object \n",
      " 6   body-style         205 non-null    object \n",
      " 7   drive-wheels       205 non-null    object \n",
      " 8   engine-location    205 non-null    object \n",
      " 9   wheel-base         205 non-null    float64\n",
      " 10  length             205 non-null    float64\n",
      " 11  width              205 non-null    float64\n",
      " 12  height             205 non-null    float64\n",
      " 13  curb-weight        205 non-null    int64  \n",
      " 14  engine-type        205 non-null    object \n",
      " 15  num-of-cylinders   205 non-null    object \n",
      " 16  engine-size        205 non-null    int64  \n",
      " 17  fuel-system        205 non-null    object \n",
      " 18  bore               205 non-null    object \n",
      " 19  stroke             205 non-null    object \n",
      " 20  compression-rate   205 non-null    float64\n",
      " 21  horsepower         205 non-null    object \n",
      " 22  peak-rpm           205 non-null    object \n",
      " 23  city-mpg           205 non-null    int64  \n",
      " 24  highway-mpg        205 non-null    int64  \n",
      " 25  price              205 non-null    object \n",
      "dtypes: float64(5), int64(5), object(16)\n",
      "memory usage: 41.8+ KB\n"
     ]
    }
   ],
   "source": [
    "cars.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>make</th>\n",
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       "      <th>engine-size</th>\n",
       "      <th>fuel-system</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-rate</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>?</td>\n",
       "      <td>alfa-romero</td>\n",
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       "      <td>88.6</td>\n",
       "      <td>...</td>\n",
       "      <td>130</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.47</td>\n",
       "      <td>2.68</td>\n",
       "      <td>9.0</td>\n",
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       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>13495</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>?</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>...</td>\n",
       "      <td>130</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.47</td>\n",
       "      <td>2.68</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111</td>\n",
       "      <td>5000</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>16500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>?</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>94.5</td>\n",
       "      <td>...</td>\n",
       "      <td>152</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>2.68</td>\n",
       "      <td>3.47</td>\n",
       "      <td>9.0</td>\n",
       "      <td>154</td>\n",
       "      <td>5000</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>gas</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>...</td>\n",
       "      <td>109</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.19</td>\n",
       "      <td>3.40</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102</td>\n",
       "      <td>5500</td>\n",
       "      <td>24</td>\n",
       "      <td>30</td>\n",
       "      <td>13950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>4wd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.4</td>\n",
       "      <td>...</td>\n",
       "      <td>136</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.19</td>\n",
       "      <td>3.40</td>\n",
       "      <td>8.0</td>\n",
       "      <td>115</td>\n",
       "      <td>5500</td>\n",
       "      <td>18</td>\n",
       "      <td>22</td>\n",
       "      <td>17450</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 26 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   symboling normalized-losses         make fuel-type aspiration num-of-doors  \\\n",
       "0          3                 ?  alfa-romero       gas        std          two   \n",
       "1          3                 ?  alfa-romero       gas        std          two   \n",
       "2          1                 ?  alfa-romero       gas        std          two   \n",
       "3          2               164         audi       gas        std         four   \n",
       "4          2               164         audi       gas        std         four   \n",
       "\n",
       "    body-style drive-wheels engine-location  wheel-base  ...  engine-size  \\\n",
       "0  convertible          rwd           front        88.6  ...          130   \n",
       "1  convertible          rwd           front        88.6  ...          130   \n",
       "2    hatchback          rwd           front        94.5  ...          152   \n",
       "3        sedan          fwd           front        99.8  ...          109   \n",
       "4        sedan          4wd           front        99.4  ...          136   \n",
       "\n",
       "   fuel-system  bore  stroke compression-rate horsepower  peak-rpm city-mpg  \\\n",
       "0         mpfi  3.47    2.68              9.0        111      5000       21   \n",
       "1         mpfi  3.47    2.68              9.0        111      5000       21   \n",
       "2         mpfi  2.68    3.47              9.0        154      5000       19   \n",
       "3         mpfi  3.19    3.40             10.0        102      5500       24   \n",
       "4         mpfi  3.19    3.40              8.0        115      5500       18   \n",
       "\n",
       "  highway-mpg  price  \n",
       "0          27  13495  \n",
       "1          27  16500  \n",
       "2          26  16500  \n",
       "3          30  13950  \n",
       "4          22  17450  \n",
       "\n",
       "[5 rows x 26 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cars.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   symboling normalized-losses         make fuel-type aspiration num-of-doors  \\\n",
      "0          3               NaN  alfa-romero       gas        std          two   \n",
      "1          3               NaN  alfa-romero       gas        std          two   \n",
      "2          1               NaN  alfa-romero       gas        std          two   \n",
      "3          2               164         audi       gas        std         four   \n",
      "4          2               164         audi       gas        std         four   \n",
      "\n",
      "    body-style drive-wheels engine-location  wheel-base  ...  engine-size  \\\n",
      "0  convertible          rwd           front        88.6  ...          130   \n",
      "1  convertible          rwd           front        88.6  ...          130   \n",
      "2    hatchback          rwd           front        94.5  ...          152   \n",
      "3        sedan          fwd           front        99.8  ...          109   \n",
      "4        sedan          4wd           front        99.4  ...          136   \n",
      "\n",
      "   fuel-system  bore  stroke compression-rate horsepower  peak-rpm city-mpg  \\\n",
      "0         mpfi  3.47    2.68              9.0        111      5000       21   \n",
      "1         mpfi  3.47    2.68              9.0        111      5000       21   \n",
      "2         mpfi  2.68    3.47              9.0        154      5000       19   \n",
      "3         mpfi  3.19    3.40             10.0        102      5500       24   \n",
      "4         mpfi  3.19    3.40              8.0        115      5500       18   \n",
      "\n",
      "  highway-mpg  price  \n",
      "0          27  13495  \n",
      "1          27  16500  \n",
      "2          26  16500  \n",
      "3          30  13950  \n",
      "4          22  17450  \n",
      "\n",
      "[5 rows x 26 columns]\n"
     ]
    }
   ],
   "source": [
    "# we have unusual ? in normlaise losses which we will replace with nan\n",
    "# to use k-nearest neighbors, all features columns have to be numerical, so we will have to perform data cleaning \n",
    "\n",
    "cars = cars.replace('?',np.nan)\n",
    "print(cars.head())\n",
    "cars['normalized-losses'] = cars['normalized-losses'].astype('float64')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>compression-rate</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "      <td>88.6</td>\n",
       "      <td>168.8</td>\n",
       "      <td>64.1</td>\n",
       "      <td>48.8</td>\n",
       "      <td>2548</td>\n",
       "      <td>130</td>\n",
       "      <td>9.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "      <td>88.6</td>\n",
       "      <td>168.8</td>\n",
       "      <td>64.1</td>\n",
       "      <td>48.8</td>\n",
       "      <td>2548</td>\n",
       "      <td>130</td>\n",
       "      <td>9.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>94.5</td>\n",
       "      <td>171.2</td>\n",
       "      <td>65.5</td>\n",
       "      <td>52.4</td>\n",
       "      <td>2823</td>\n",
       "      <td>152</td>\n",
       "      <td>9.0</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>164.0</td>\n",
       "      <td>99.8</td>\n",
       "      <td>176.6</td>\n",
       "      <td>66.2</td>\n",
       "      <td>54.3</td>\n",
       "      <td>2337</td>\n",
       "      <td>109</td>\n",
       "      <td>10.0</td>\n",
       "      <td>24</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>164.0</td>\n",
       "      <td>99.4</td>\n",
       "      <td>176.6</td>\n",
       "      <td>66.4</td>\n",
       "      <td>54.3</td>\n",
       "      <td>2824</td>\n",
       "      <td>136</td>\n",
       "      <td>8.0</td>\n",
       "      <td>18</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   symboling  normalized-losses  wheel-base  length  width  height  \\\n",
       "0          3                NaN        88.6   168.8   64.1    48.8   \n",
       "1          3                NaN        88.6   168.8   64.1    48.8   \n",
       "2          1                NaN        94.5   171.2   65.5    52.4   \n",
       "3          2              164.0        99.8   176.6   66.2    54.3   \n",
       "4          2              164.0        99.4   176.6   66.4    54.3   \n",
       "\n",
       "   curb-weight  engine-size  compression-rate  city-mpg  highway-mpg  \n",
       "0         2548          130               9.0        21           27  \n",
       "1         2548          130               9.0        21           27  \n",
       "2         2823          152               9.0        19           26  \n",
       "3         2337          109              10.0        24           30  \n",
       "4         2824          136               8.0        18           22  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numeric_cars = cars.select_dtypes(include = ['int64','float64'])\n",
    "numeric_cars.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(205, 11)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numeric_cars.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-7-2c3bfb49337a>:3: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  numeric_cars[i] = cars[i]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "normalized-losses    41\n",
       "wheel-base            0\n",
       "length                0\n",
       "width                 0\n",
       "height                0\n",
       "curb-weight           0\n",
       "engine-size           0\n",
       "compression-rate      0\n",
       "city-mpg              0\n",
       "highway-mpg           0\n",
       "bore                  4\n",
       "stroke                4\n",
       "horsepower            2\n",
       "peak-rpm              2\n",
       "price                 4\n",
       "dtype: int64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "additional_columns = ['bore','stroke','compression-rate','horsepower','peak-rpm','price']\n",
    "for i in additional_columns:\n",
    "    numeric_cars[i] = cars[i]\n",
    "numeric_cars = numeric_cars.drop(['symboling'],axis = 1)\n",
    "numeric_cars.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "normalized-losses    0\n",
       "wheel-base           0\n",
       "length               0\n",
       "width                0\n",
       "height               0\n",
       "curb-weight          0\n",
       "engine-size          0\n",
       "compression-rate     0\n",
       "city-mpg             0\n",
       "highway-mpg          0\n",
       "bore                 0\n",
       "stroke               0\n",
       "horsepower           0\n",
       "peak-rpm             0\n",
       "price                0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numeric_cars = numeric_cars.astype('float')\n",
    "numeric_cars = numeric_cars.fillna(numeric_cars.mean())\n",
    "# Confirm that there's no more missing values!\n",
    "numeric_cars.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# converting values such that they range between 0 and 1, as the columns may vary hugely in the their individual\n",
    "# ranges and when calculating mse, we might get improper results or preferences. Even though n-1 features may match,\n",
    "#but if the last feature differ hugely in their value, the two cars may be considered drastically different. \n",
    "#Converting them still correlates each column values with their own column values with the same parameter\n",
    "\n",
    "price_column = numeric_cars['price']\n",
    "numeric_cars = (numeric_cars - numeric_cars.min())/(numeric_cars.max() - numeric_cars.min())\n",
    "numeric_cars['price'] = price_column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['normalized-losses',\n",
       " 'wheel-base',\n",
       " 'length',\n",
       " 'width',\n",
       " 'height',\n",
       " 'curb-weight',\n",
       " 'engine-size',\n",
       " 'compression-rate',\n",
       " 'city-mpg',\n",
       " 'highway-mpg',\n",
       " 'bore',\n",
       " 'stroke',\n",
       " 'horsepower',\n",
       " 'peak-rpm']"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numerical_columns = numeric_cars.columns.tolist()\n",
    "numerical_columns.pop()\n",
    "numerical_columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "compression-rate     0.070990\n",
       "stroke               0.082095\n",
       "peak-rpm             0.100854\n",
       "normalized-losses    0.133999\n",
       "height               0.134388\n",
       "bore                 0.532300\n",
       "wheel-base           0.583168\n",
       "city-mpg             0.667449\n",
       "length               0.682986\n",
       "highway-mpg          0.690526\n",
       "width                0.728699\n",
       "horsepower           0.757917\n",
       "curb-weight          0.820825\n",
       "engine-size          0.861752\n",
       "price                1.000000\n",
       "Name: price, dtype: float64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# before training and mse calculation we can find some relations in the data\n",
    "\n",
    "corr = numeric_cars.corr()\n",
    "sorted_corr = abs(corr['price']).sort_values()\n",
    "sorted_corr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the correlation values, we can get an essence of the features that mighht affect the price the most. But we have to calculate the errors of actual model training and calculation before finalising anything."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Univariate k-nearest neighbors\n",
    "\n",
    "Here, we will be using one feature to train and test against price using Sci-Kit Learn. We will rank them based on their root mean squared error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.neighbors import KNeighborsRegressor\n",
    "from sklearn.metrics import mean_squared_error\n",
    "def knn_train_test(train_feature, target_col, df):\n",
    "    \n",
    "    np.random.seed(1)\n",
    "        \n",
    "    # Randomize order of rows in data frame.\n",
    "    shuffled_index = np.random.permutation(df.index)\n",
    "    rand_df = df.reindex(shuffled_index)\n",
    "    \n",
    "    # defining train and test datasets\n",
    "    mid = int(len(df)/2)\n",
    "    train_df = df.iloc[:mid,:]\n",
    "    test_df = df.iloc[mid:,:]\n",
    "    \n",
    "    knn = KNeighborsRegressor()\n",
    "    knn.fit(train_df[[train_feature]],train_df[target_col])\n",
    "    predictions = knn.predict(test_df[[train_feature]])\n",
    "    mse = mean_squared_error(test_df[target_col],predictions)\n",
    "    rmse = np.sqrt(mse)\n",
    "    return rmse\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['normalized-losses',\n",
       " 'wheel-base',\n",
       " 'length',\n",
       " 'width',\n",
       " 'height',\n",
       " 'curb-weight',\n",
       " 'engine-size',\n",
       " 'compression-rate',\n",
       " 'city-mpg',\n",
       " 'highway-mpg',\n",
       " 'bore',\n",
       " 'stroke',\n",
       " 'horsepower',\n",
       " 'peak-rpm']"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numerical_columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "rmse_uni = {}\n",
    "for i in numerical_columns:\n",
    "    rmse_uni[i] = knn_train_test(i,'price',numeric_cars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'normalized-losses': 8246.797180940934,\n",
       " 'wheel-base': 9649.74827452917,\n",
       " 'length': 8827.576764096792,\n",
       " 'width': 6819.524241906653,\n",
       " 'height': 10888.31474142904,\n",
       " 'curb-weight': 5981.5961011543495,\n",
       " 'engine-size': 4821.1058157726975,\n",
       " 'compression-rate': 7931.911082144877,\n",
       " 'city-mpg': 4826.908842041854,\n",
       " 'highway-mpg': 4702.996454439048,\n",
       " 'bore': 13323.697665030348,\n",
       " 'stroke': 9192.843085497168,\n",
       " 'horsepower': 4996.5931612626255,\n",
       " 'peak-rpm': 9659.574802371517}"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rmse_uni"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'highway-mpg'"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rmse_uni_min = min(rmse_uni,key = rmse_uni.get) \n",
    "rmse_uni_min"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the column <b>highway-mpg</b> is the feature that has the lowest rmse for the default K = 5 value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "import matplotlib.pyplot as plt\n",
    "def knn_train_test_k(train_feature, target_col, df,k):\n",
    "    knn = KNeighborsRegressor(n_neighbors = k)\n",
    "    np.random.seed(1)\n",
    "        \n",
    "    # Randomize order of rows in data frame.\n",
    "    shuffled_index = np.random.permutation(df.index)\n",
    "    rand_df = df.reindex(shuffled_index)\n",
    "    train_df = df.iloc[:int(len(df)/2),:]\n",
    "    test_df = df.iloc[int(len(df)/2):,:]\n",
    "    knn.fit(train_df[[train_feature]],train_df[target_col])\n",
    "    predictions = knn.predict(test_df[[train_feature]])\n",
    "    mse = mean_squared_error(test_df[target_col],predictions)\n",
    "    rmse = np.sqrt(mse)\n",
    "    return rmse, list(test_df[target_col]),list(predictions)\n",
    "k = [1,3,5,7,9]\n",
    "x = numerical_columns \n",
    "rmse_uni_k = {}\n",
    "colors = ['r','b','y','c','m']\n",
    "\n",
    "# these are the changes I am adding to analyse further\n",
    "prices_uni_k = {}\n",
    "predictions_uni_k = {}\n",
    "for i in numerical_columns:\n",
    "    d = {}\n",
    "    prices = {}\n",
    "    predictions = {}\n",
    "    for j in k:\n",
    "        z,price,predict = knn_train_test_k(i,'price',numeric_cars,j)\n",
    "        d[j] = z\n",
    "        prices[j] = price\n",
    "        predictions[j] = predict\n",
    "        plt.scatter(z,i,color = colors[int((j-1)/2)])\n",
    "        plt.legend(k)\n",
    "    rmse_uni_k[i] = d\n",
    "    prices_uni_k[i] = prices\n",
    "    predictions_uni_k[i] = predictions\n",
    "plt.xlim([3000,12000])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Insights from the graph suggest that the lowest rmse values for k ranging from 1 to 9 with an interval of 2 is <b>highway-mpg</b> at a value of k=9. One explanation of this can be the correlation of the feature with the price, but that is just surface level.\n",
    "\n",
    "One more thing we can do is get the values of prices and predicted prices from the function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'normalized-losses': {1: 8730.931714690953,\n",
       "  3: 9132.30052644129,\n",
       "  5: 8246.797180940934,\n",
       "  7: 7731.286208857365,\n",
       "  9: 7382.18225802066},\n",
       " 'wheel-base': {1: 8106.735021520181,\n",
       "  3: 9004.470600946595,\n",
       "  5: 9649.74827452917,\n",
       "  7: 8782.02059619916,\n",
       "  9: 8508.592019851796},\n",
       " 'length': {1: 9999.119164359023,\n",
       "  3: 9250.708547608927,\n",
       "  5: 8827.576764096792,\n",
       "  7: 8596.352373651833,\n",
       "  9: 7668.679953322082},\n",
       " 'width': {1: 9323.779007222787,\n",
       "  3: 6172.68035697483,\n",
       "  5: 6819.524241906653,\n",
       "  7: 6294.841265873941,\n",
       "  9: 6213.0835771632455},\n",
       " 'height': {1: 14585.02008290746,\n",
       "  3: 11541.107590752637,\n",
       "  5: 10888.31474142904,\n",
       "  7: 10069.64622778205,\n",
       "  9: 9363.597059413903},\n",
       " 'curb-weight': {1: 7134.817057235699,\n",
       "  3: 6206.820624217271,\n",
       "  5: 5981.5961011543495,\n",
       "  7: 5782.7881790408455,\n",
       "  9: 5533.505423344071},\n",
       " 'engine-size': {1: 5651.403465742561,\n",
       "  3: 5300.943874056778,\n",
       "  5: 4821.1058157726975,\n",
       "  7: 4647.882332451139,\n",
       "  9: 4347.223520912874},\n",
       " 'compression-rate': {1: 7943.535650306552,\n",
       "  3: 7958.722038617806,\n",
       "  5: 7931.911082144877,\n",
       "  7: 7901.86620122549,\n",
       "  9: 7675.120829137446},\n",
       " 'city-mpg': {1: 5342.394696387088,\n",
       "  3: 5337.692712205836,\n",
       "  5: 4826.908842041854,\n",
       "  7: 4715.809125499923,\n",
       "  9: 4876.643198777047},\n",
       " 'highway-mpg': {1: 5183.629569272964,\n",
       "  3: 4422.164723521852,\n",
       "  5: 4702.996454439048,\n",
       "  7: 4134.4322929464,\n",
       "  9: 4005.144829631212},\n",
       " 'bore': {1: 13260.434706421334,\n",
       "  3: 13937.578952105645,\n",
       "  5: 13323.697665030348,\n",
       "  7: 11168.162356041874,\n",
       "  9: 10245.380178704436},\n",
       " 'stroke': {1: 10860.227110212589,\n",
       "  3: 12120.859578407262,\n",
       "  5: 9192.843085497168,\n",
       "  7: 7236.034133269646,\n",
       "  9: 8070.7205876278385},\n",
       " 'horsepower': {1: 5839.48447462536,\n",
       "  3: 6018.613933836798,\n",
       "  5: 4996.5931612626255,\n",
       "  7: 4512.342179772446,\n",
       "  9: 4024.580862528612},\n",
       " 'peak-rpm': {1: 9959.588750506267,\n",
       "  3: 9659.414445887018,\n",
       "  5: 9659.574802371517,\n",
       "  7: 9492.37968884411,\n",
       "  9: 9398.094376956205}}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rmse_uni_k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  7: [24658.571428571428,\n",
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       "  9: [22927.11111111111,\n",
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       "   12632.714285714286,\n",
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       "   11337.555555555555,\n",
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       "   30094.0,\n",
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       "   11337.555555555555,\n",
       "   11337.555555555555,\n",
       "   11337.555555555555,\n",
       "   9687.0,\n",
       "   9687.0,\n",
       "   11337.555555555555,\n",
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       "   11337.555555555555,\n",
       "   11337.555555555555,\n",
       "   11337.555555555555,\n",
       "   11337.555555555555,\n",
       "   26613.333333333332,\n",
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       "   26613.333333333332,\n",
       "   26613.333333333332,\n",
       "   26613.333333333332,\n",
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       "   8054.555555555556,\n",
       "   8054.555555555556,\n",
       "   11337.555555555555,\n",
       "   8410.111111111111,\n",
       "   11337.555555555555,\n",
       "   8410.111111111111,\n",
       "   8410.111111111111,\n",
       "   30094.0,\n",
       "   10198.777777777777,\n",
       "   10198.777777777777,\n",
       "   10198.777777777777,\n",
       "   10198.777777777777,\n",
       "   30094.0,\n",
       "   10198.777777777777,\n",
       "   17833.69541182974,\n",
       "   17833.69541182974,\n",
       "   17833.69541182974,\n",
       "   17833.69541182974,\n",
       "   13974.888888888889,\n",
       "   13974.888888888889,\n",
       "   17833.69541182974,\n",
       "   18354.139856274185,\n",
       "   10198.777777777777,\n",
       "   11337.555555555555,\n",
       "   17833.69541182974]}}"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# many predictions will be the same as this is an univariate model and rows with the same feature will have the \n",
    "# same value\n",
    "predictions_uni_k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "   22625.0]}}"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# these values dont depend on the model training unlike the predictions\n",
    "# these values are used to calucalte the rmse values\n",
    "prices_uni_k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('highway-mpg', 4489.6735739622945),\n",
       " ('engine-size', 4953.71180178721),\n",
       " ('city-mpg', 5019.88971498235),\n",
       " ('horsepower', 5078.322922405168),\n",
       " ('curb-weight', 6127.905476998447),\n",
       " ('width', 6964.781689828291),\n",
       " ('compression-rate', 7882.231160286434),\n",
       " ('normalized-losses', 8244.69957779024),\n",
       " ('wheel-base', 8810.31330260938),\n",
       " ('length', 8868.48736060773),\n",
       " ('stroke', 9496.1368990029),\n",
       " ('peak-rpm', 9633.810412913024),\n",
       " ('height', 11289.537140457018),\n",
       " ('bore', 12387.050771660728)]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculating mean rmse values for each column rmse of 5 k values\n",
    "#sorting the values which tells us the order of feature selection\n",
    "import statistics\n",
    "mean_rmse = {}\n",
    "for i,j in rmse_uni_k.items():\n",
    "    mean_rmse[i] = statistics.mean(j.values())\n",
    "rmse_sorted =  sorted(mean_rmse.items(), key=lambda item: item[1])\n",
    "rmse_sorted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "highway-mpg           4489.673574\n",
       "engine-size           4953.711802\n",
       "city-mpg              5019.889715\n",
       "horsepower            5078.322922\n",
       "curb-weight           6127.905477\n",
       "width                 6964.781690\n",
       "compression-rate      7882.231160\n",
       "normalized-losses     8244.699578\n",
       "wheel-base            8810.313303\n",
       "length                8868.487361\n",
       "stroke                9496.136899\n",
       "peak-rpm              9633.810413\n",
       "height               11289.537140\n",
       "bore                 12387.050772\n",
       "dtype: float64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_index = []\n",
    "sorted_values = []\n",
    "for i in rmse_sorted:\n",
    "    sorted_index.append(i[0])\n",
    "    sorted_values.append(i[1])\n",
    "rmse_sorted = pd.Series(sorted_values, index = sorted_index)\n",
    "rmse_sorted"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multivariate KNN\n",
    "\n",
    "For multivariate Regression we will do the following\n",
    "- Use the best 2 features from the previous step to train and test a multivariate k-nearest neighbors model using the default k value.\n",
    "- Use the best 3 features from the previous step to train and test a multivariate k-nearest neighbors model using the default k value.\n",
    "- Use the best 4 features from the previous step to train and test a multivariate k-nearest neighbors model using the default k value.\n",
    "- Use the best 5 features from the previous step to train and test a multivariate k-nearest neighbors model using the default k value.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def knn_train_test(train_feature, target_col, df):\n",
    "    knn = KNeighborsRegressor()\n",
    "    np.random.seed(4)\n",
    "        \n",
    "    # Randomize order of rows in data frame.\n",
    "    shuffled_index = np.random.permutation(df.index)\n",
    "    rand_df = df.reindex(shuffled_index)\n",
    "    train_df = df.iloc[:int(len(df)/2),:]\n",
    "    test_df = df.iloc[int(len(df)/2):,:]\n",
    "    knn.fit(train_df[train_feature],train_df[target_col])\n",
    "    predictions = knn.predict(test_df[train_feature])\n",
    "    mse = mean_squared_error(test_df[target_col],predictions)\n",
    "    rmse = np.sqrt(mse)\n",
    "    return rmse\n",
    "\n",
    "rmse_multi = {}\n",
    "\n",
    "for i in range(2,6):\n",
    "    rmse_multi[i] = knn_train_test(sorted_index[:i],'price',numeric_cars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{2: 4670.18786324807,\n",
       " 3: 4346.318321065622,\n",
       " 4: 3973.7999954994466,\n",
       " 5: 4189.144032530089}"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rmse_multi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the top 3 models are containing 3,4 and 5 features\n",
    "def knn_train_test_k(train_feature, target_col, df,k):\n",
    "    knn = KNeighborsRegressor(n_neighbors = k)\n",
    "    np.random.seed(1)\n",
    "        \n",
    "    # Randomize order of rows in data frame.\n",
    "    shuffled_index = np.random.permutation(df.index)\n",
    "    rand_df = df.reindex(shuffled_index)\n",
    "    train_df = df.iloc[:int(len(df)/2),:]\n",
    "    test_df = df.iloc[int(len(df)/2):,:]\n",
    "    knn.fit(train_df[train_feature],train_df[target_col])\n",
    "    predictions = knn.predict(test_df[train_feature])\n",
    "    mse = mean_squared_error(test_df[target_col],predictions)\n",
    "    rmse = np.sqrt(mse)\n",
    "    return rmse\n",
    "\n",
    "rmse_multi_k = {}\n",
    "k = [i for i in range(1,26)]\n",
    "for i in range(2,6):\n",
    "    d = {}\n",
    "    for j in k:\n",
    "        d[j] = knn_train_test_k(sorted_index[:i],'price',numeric_cars,j)\n",
    "        plt.scatter\n",
    "    rmse_multi_k[i] = d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       " 3: {1: 5637.582774530638,\n",
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       " 5: {1: 4899.686063789857,\n",
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       "  23: 3693.8473031477492,\n",
       "  24: 3672.81619309122,\n",
       "  25: 3658.2677849814213}}"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rmse_multi_k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_items([(2, {1: 4609.470216141888, 2: 4659.988774369158, 3: 4612.02173801327, 4: 4514.613104125041, 5: 4670.18786324807, 6: 4140.443291763167, 7: 3866.6778867562525, 8: 3829.7926622019704, 9: 3727.430383708687, 10: 3579.7436117270945, 11: 3449.605284544298, 12: 3399.495726261016, 13: 3442.323031807465, 14: 3494.8497015070575, 15: 3561.603619813081, 16: 3616.919197355503, 17: 3601.475661543099, 18: 3643.5010924580074, 19: 3627.373272301764, 20: 3666.7241758578593, 21: 3696.8367350316666, 22: 3687.1610781540426, 23: 3605.0020996127855, 24: 3530.534331757233, 25: 3564.776014001351}), (3, {1: 5637.582774530638, 2: 4738.67230650477, 3: 4390.540061873881, 4: 4369.026761793873, 5: 4346.318321065622, 6: 4127.839832020747, 7: 3866.0455675004964, 8: 3729.2590969669923, 9: 3635.0847079461973, 10: 3652.311361608205, 11: 3686.61979799408, 12: 3673.8166469181947, 13: 3673.9390184349927, 14: 3723.1540059661156, 15: 3731.098703972646, 16: 3752.170513883767, 17: 3700.668867566034, 18: 3683.272567239796, 19: 3684.5047491455125, 20: 3709.5751661330355, 21: 3719.525879812698, 22: 3794.2903950729597, 23: 3737.6141478897757, 24: 3651.501806438952, 25: 3682.471709732075}), (4, {1: 4422.678623819221, 2: 4674.77548397212, 3: 4538.221965443251, 4: 4110.381708210674, 5: 3973.7999954994466, 6: 3881.042445980396, 7: 3873.1236057308197, 8: 3791.3292426194457, 9: 3800.28551359632, 10: 3842.0541605446497, 11: 3970.0197427842536, 12: 3926.799674186446, 13: 3818.4654735555273, 14: 3745.6148946697876, 15: 3710.5789574145974, 16: 3675.023382715854, 17: 3658.024202244065, 18: 3680.8514444422076, 19: 3686.007476416339, 20: 3710.8838882560613, 21: 3682.8682288565597, 22: 3674.0006791267265, 23: 3674.392466963343, 24: 3675.8172188241856, 25: 3668.623243950804}), (5, {1: 4899.686063789857, 2: 4832.477010333464, 3: 4793.243577668765, 4: 4686.948268916227, 5: 4189.144032530089, 6: 4246.1705707082265, 7: 4281.233063035377, 8: 4231.197458181218, 9: 4069.5096761135533, 10: 3913.3298879966273, 11: 3814.2851266938346, 12: 3725.789017222331, 13: 3688.7309905605707, 14: 3657.1869372002698, 15: 3626.2494436862603, 16: 3596.2671223674947, 17: 3653.6682191623127, 18: 3747.3095102452767, 19: 3707.569994173309, 20: 3723.29298175034, 21: 3703.022925976065, 22: 3700.788161056696, 23: 3693.8473031477492, 24: 3672.81619309122, 25: 3658.2677849814213})])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rmse_multi_k.items()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "for i,j in rmse_multi_k.items():\n",
    "    x = list(j.keys())\n",
    "    y = list(j.values())\n",
    "    plt.plot(x,y,label = f'{i} features')\n",
    "plt.xlabel('k value')\n",
    "plt.ylabel('RMSE')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 2 best features, the k for min value is 12\n",
      "For 3 best features, the k for min value is 9\n",
      "For 4 best features, the k for min value is 17\n",
      "For 5 best features, the k for min value is 16\n"
     ]
    }
   ],
   "source": [
    "for i,j in rmse_multi_k.items():\n",
    "    m = min(j,key = j.get)\n",
    "    print(f'For {i} best features, the k for min value is {m}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}