numeric_methods/numerical_methods.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rusty Bargain used car sales service is developing an app to attract new customers. In that app, you can quickly find out the market value of your car. You have access to historical data: technical specifications, trim versions, and prices. You need to build the model to determine the value. \n",
    "\n",
    "Rusty Bargain is interested in:\n",
    "\n",
    "- the quality of the prediction;\n",
    "- the speed of the prediction;\n",
    "- the time required for training\n",
    "\n",
    "---\n",
    "Features\n",
    "\n",
    "- DateCrawled — date profile was downloaded from the database\n",
    "- VehicleType — vehicle body type\n",
    "- RegistrationYear — vehicle registration year\n",
    "- Gearbox — gearbox type\n",
    "- Power — power (hp)\n",
    "- Model — vehicle model\n",
    "- Mileage — mileage (measured in km due to dataset's regional specifics)\n",
    "- RegistrationMonth — vehicle registration month\n",
    "- FuelType — fuel type\n",
    "- Brand — vehicle brand\n",
    "- NotRepaired — vehicle repaired or not\n",
    "- DateCreated — date of profile creation\n",
    "- NumberOfPictures — number of vehicle pictures\n",
    "- PostalCode — postal code of profile owner (user)\n",
    "- LastSeen — date of the last activity of the user\n",
    "\n",
    "Target\n",
    "- Price — price (Euro)\n",
    "\n",
    "Analysis done January 2022"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data preparation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import libraries\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import time\n",
    "import lightgbm as lgb\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.ensemble import RandomForestRegressor\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "from catboost import CatBoostRegressor\n",
    "from sklearn.model_selection import cross_val_score\n",
    "from sklearn.metrics import make_scorer\n",
    "from sklearn.model_selection import RandomizedSearchCV\n",
    "\n",
    "import random\n",
    "random_state=42\n",
    "random.seed(random_state)\n",
    "np.random.seed(random_state)\n",
    "\n",
    "# import sys and insert code to ignore warnings \n",
    "import sys\n",
    "if not sys.warnoptions:\n",
    "    import warnings\n",
    "    warnings.simplefilter(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Helper functions__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# function for timing execution of cell [refrence](https://stackoverflow.com/questions/52738709/how-to-store-time-values-in-a-variable-in-jupyter)\n",
    "# couldn't get it to work though...\n",
    "def exec_time(start, end): \n",
    "   diff_time = end - start\n",
    "   m, s = divmod(diff_time, 60)\n",
    "   h, m = divmod(m, 60)\n",
    "   s,m,h = int(round(s, 0)), int(round(m, 0)), int(round(h, 0))\n",
    "   print(\"time: \" + \"{0:02d}:{1:02d}:{2:02d}\".format(h, m, s))\n",
    "\n",
    "# function for displaying outlier statistics for column\n",
    "def outlier_stats(data):\n",
    "    data_mean, data_std = np.mean(data), np.std(data)\n",
    "    cut_off = data_std * 3\n",
    "    lower, upper = data_mean - cut_off, data_mean + cut_off\n",
    "    outliers = [x for x in data if x < lower or x > upper]\n",
    "    outliers_removed = [x for x in data if x >= lower and x <= upper]   \n",
    "    outliers_stats = pd.Series(outliers)\n",
    "    return outliers_stats.describe()\n",
    "\n",
    "# function for displaying count and percent of missing values if column object or int64\n",
    "def missing_stats(df):\n",
    "    print(\"\\nColumns Missing Values\")\n",
    "    df_missing = pd.concat([df.dtypes, df.isnull().sum(), df.isnull().sum() / (len(df)*.01)], axis=1)\n",
    "    df_missing.columns = ['type', 'cnt', 'pct']\n",
    "    print(df_missing)\n",
    "    df.describe(include=['object', 'int64'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# load data\n",
    "df = pd.read_csv('/datasets/car_data.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>DateCrawled</th>\n",
       "      <th>Price</th>\n",
       "      <th>VehicleType</th>\n",
       "      <th>RegistrationYear</th>\n",
       "      <th>Gearbox</th>\n",
       "      <th>Power</th>\n",
       "      <th>Model</th>\n",
       "      <th>Mileage</th>\n",
       "      <th>RegistrationMonth</th>\n",
       "      <th>FuelType</th>\n",
       "      <th>Brand</th>\n",
       "      <th>NotRepaired</th>\n",
       "      <th>DateCreated</th>\n",
       "      <th>NumberOfPictures</th>\n",
       "      <th>PostalCode</th>\n",
       "      <th>LastSeen</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>24/03/2016 11:52</td>\n",
       "      <td>480</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1993</td>\n",
       "      <td>manual</td>\n",
       "      <td>0</td>\n",
       "      <td>golf</td>\n",
       "      <td>150000</td>\n",
       "      <td>0</td>\n",
       "      <td>petrol</td>\n",
       "      <td>volkswagen</td>\n",
       "      <td>NaN</td>\n",
       "      <td>24/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>70435</td>\n",
       "      <td>07/04/2016 03:16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>24/03/2016 10:58</td>\n",
       "      <td>18300</td>\n",
       "      <td>coupe</td>\n",
       "      <td>2011</td>\n",
       "      <td>manual</td>\n",
       "      <td>190</td>\n",
       "      <td>NaN</td>\n",
       "      <td>125000</td>\n",
       "      <td>5</td>\n",
       "      <td>gasoline</td>\n",
       "      <td>audi</td>\n",
       "      <td>yes</td>\n",
       "      <td>24/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>66954</td>\n",
       "      <td>07/04/2016 01:46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>14/03/2016 12:52</td>\n",
       "      <td>9800</td>\n",
       "      <td>suv</td>\n",
       "      <td>2004</td>\n",
       "      <td>auto</td>\n",
       "      <td>163</td>\n",
       "      <td>grand</td>\n",
       "      <td>125000</td>\n",
       "      <td>8</td>\n",
       "      <td>gasoline</td>\n",
       "      <td>jeep</td>\n",
       "      <td>NaN</td>\n",
       "      <td>14/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>90480</td>\n",
       "      <td>05/04/2016 12:47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>17/03/2016 16:54</td>\n",
       "      <td>1500</td>\n",
       "      <td>small</td>\n",
       "      <td>2001</td>\n",
       "      <td>manual</td>\n",
       "      <td>75</td>\n",
       "      <td>golf</td>\n",
       "      <td>150000</td>\n",
       "      <td>6</td>\n",
       "      <td>petrol</td>\n",
       "      <td>volkswagen</td>\n",
       "      <td>no</td>\n",
       "      <td>17/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>91074</td>\n",
       "      <td>17/03/2016 17:40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>31/03/2016 17:25</td>\n",
       "      <td>3600</td>\n",
       "      <td>small</td>\n",
       "      <td>2008</td>\n",
       "      <td>manual</td>\n",
       "      <td>69</td>\n",
       "      <td>fabia</td>\n",
       "      <td>90000</td>\n",
       "      <td>7</td>\n",
       "      <td>gasoline</td>\n",
       "      <td>skoda</td>\n",
       "      <td>no</td>\n",
       "      <td>31/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>60437</td>\n",
       "      <td>06/04/2016 10:17</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        DateCrawled  Price VehicleType  RegistrationYear Gearbox  Power  \\\n",
       "0  24/03/2016 11:52    480         NaN              1993  manual      0   \n",
       "1  24/03/2016 10:58  18300       coupe              2011  manual    190   \n",
       "2  14/03/2016 12:52   9800         suv              2004    auto    163   \n",
       "3  17/03/2016 16:54   1500       small              2001  manual     75   \n",
       "4  31/03/2016 17:25   3600       small              2008  manual     69   \n",
       "\n",
       "   Model  Mileage  RegistrationMonth  FuelType       Brand NotRepaired  \\\n",
       "0   golf   150000                  0    petrol  volkswagen         NaN   \n",
       "1    NaN   125000                  5  gasoline        audi         yes   \n",
       "2  grand   125000                  8  gasoline        jeep         NaN   \n",
       "3   golf   150000                  6    petrol  volkswagen          no   \n",
       "4  fabia    90000                  7  gasoline       skoda          no   \n",
       "\n",
       "        DateCreated  NumberOfPictures  PostalCode          LastSeen  \n",
       "0  24/03/2016 00:00                 0       70435  07/04/2016 03:16  \n",
       "1  24/03/2016 00:00                 0       66954  07/04/2016 01:46  \n",
       "2  14/03/2016 00:00                 0       90480  05/04/2016 12:47  \n",
       "3  17/03/2016 00:00                 0       91074  17/03/2016 17:40  \n",
       "4  31/03/2016 00:00                 0       60437  06/04/2016 10:17  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# inspect data\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(354369, 16)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "original_no_rows = df.shape[0]\n",
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "262"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.duplicated().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Columns Missing Values\n",
      "                     type    cnt        pct\n",
      "DateCrawled        object      0   0.000000\n",
      "Price               int64      0   0.000000\n",
      "VehicleType        object  37490  10.579368\n",
      "RegistrationYear    int64      0   0.000000\n",
      "Gearbox            object  19833   5.596709\n",
      "Power               int64      0   0.000000\n",
      "Model              object  19705   5.560588\n",
      "Mileage             int64      0   0.000000\n",
      "RegistrationMonth   int64      0   0.000000\n",
      "FuelType           object  32895   9.282697\n",
      "Brand              object      0   0.000000\n",
      "NotRepaired        object  71154  20.079070\n",
      "DateCreated        object      0   0.000000\n",
      "NumberOfPictures    int64      0   0.000000\n",
      "PostalCode          int64      0   0.000000\n",
      "LastSeen           object      0   0.000000\n"
     ]
    }
   ],
   "source": [
    "missing_stats(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Rename columns to lowercase for consistency__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['date_crawled', 'price', 'vehicle_type', 'registration_year', 'gearbox',\n",
       "       'power', 'model', 'milage', 'registration_month', 'fuel_type', 'brand',\n",
       "       'not_repaired', 'date_created', 'num_pictures', 'postal_code',\n",
       "       'last_seen'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df.rename(columns={'DateCrawled': 'date_crawled', 'Price': 'price', 'VehicleType': 'vehicle_type', \n",
    "                        'RegistrationYear': 'registration_year', 'Gearbox': 'gearbox', 'Power': 'power', \n",
    "                        'Model': 'model','Mileage': 'milage', 'RegistrationMonth': 'registration_month', \n",
    "                        'FuelType': 'fuel_type', 'Brand': 'brand','NotRepaired': 'not_repaired', \n",
    "                        'DateCreated': 'date_created', 'NumberOfPictures': 'num_pictures', \n",
    "                        'PostalCode': 'postal_code', 'LastSeen': 'last_seen', })\n",
    "\n",
    "df.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Initial findings__\n",
    "\n",
    "- 354369 rows by 16 columns/features, all listed as int64 or object\n",
    "- 262 duplicate rows --> delete\n",
    "- 5 features have missing rows --> investigate\n",
    "- Not all features will be useful in analysis --> investigate\n",
    "- Some dates are listed as objects --> chg datatype or delete feature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(354107, 16)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# drop duplicate rows\n",
    "df = df.drop_duplicates() \n",
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>date_crawled</th>\n",
       "      <th>price</th>\n",
       "      <th>vehicle_type</th>\n",
       "      <th>registration_year</th>\n",
       "      <th>gearbox</th>\n",
       "      <th>power</th>\n",
       "      <th>model</th>\n",
       "      <th>milage</th>\n",
       "      <th>registration_month</th>\n",
       "      <th>fuel_type</th>\n",
       "      <th>brand</th>\n",
       "      <th>not_repaired</th>\n",
       "      <th>date_created</th>\n",
       "      <th>num_pictures</th>\n",
       "      <th>postal_code</th>\n",
       "      <th>last_seen</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>count</td>\n",
       "      <td>354107</td>\n",
       "      <td>354107.000000</td>\n",
       "      <td>316623</td>\n",
       "      <td>354107.000000</td>\n",
       "      <td>334277</td>\n",
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       "      <td>321218</td>\n",
       "      <td>354107</td>\n",
       "      <td>282962</td>\n",
       "      <td>354107</td>\n",
       "      <td>354107.0</td>\n",
       "      <td>354107.000000</td>\n",
       "      <td>354107</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>unique</td>\n",
       "      <td>15470</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>250</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7</td>\n",
       "      <td>40</td>\n",
       "      <td>2</td>\n",
       "      <td>109</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18592</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>top</td>\n",
       "      <td>05/03/2016 14:25</td>\n",
       "      <td>NaN</td>\n",
       "      <td>sedan</td>\n",
       "      <td>NaN</td>\n",
       "      <td>manual</td>\n",
       "      <td>NaN</td>\n",
       "      <td>golf</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>petrol</td>\n",
       "      <td>volkswagen</td>\n",
       "      <td>no</td>\n",
       "      <td>03/04/2016 00:00</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>07/04/2016 07:16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>freq</td>\n",
       "      <td>66</td>\n",
       "      <td>NaN</td>\n",
       "      <td>91399</td>\n",
       "      <td>NaN</td>\n",
       "      <td>268034</td>\n",
       "      <td>NaN</td>\n",
       "      <td>29215</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>216161</td>\n",
       "      <td>76960</td>\n",
       "      <td>246927</td>\n",
       "      <td>13705</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mean</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4416.433287</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2004.235355</td>\n",
       "      <td>NaN</td>\n",
       "      <td>110.089651</td>\n",
       "      <td>NaN</td>\n",
       "      <td>128211.811684</td>\n",
       "      <td>5.714182</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>50507.145030</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>std</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4514.338584</td>\n",
       "      <td>NaN</td>\n",
       "      <td>90.261168</td>\n",
       "      <td>NaN</td>\n",
       "      <td>189.914972</td>\n",
       "      <td>NaN</td>\n",
       "      <td>37906.590101</td>\n",
       "      <td>3.726682</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>25784.212094</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>min</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5000.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1067.000000</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>25%</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1050.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1999.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>69.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>125000.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>30165.000000</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>50%</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2700.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2003.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>105.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>150000.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>49406.000000</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>75%</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6400.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2008.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>143.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>150000.000000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>71083.000000</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>max</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20000.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9999.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20000.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>150000.000000</td>\n",
       "      <td>12.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>99998.000000</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            date_crawled          price vehicle_type  registration_year  \\\n",
       "count             354107  354107.000000       316623      354107.000000   \n",
       "unique             15470            NaN            8                NaN   \n",
       "top     05/03/2016 14:25            NaN        sedan                NaN   \n",
       "freq                  66            NaN        91399                NaN   \n",
       "mean                 NaN    4416.433287          NaN        2004.235355   \n",
       "std                  NaN    4514.338584          NaN          90.261168   \n",
       "min                  NaN       0.000000          NaN        1000.000000   \n",
       "25%                  NaN    1050.000000          NaN        1999.000000   \n",
       "50%                  NaN    2700.000000          NaN        2003.000000   \n",
       "75%                  NaN    6400.000000          NaN        2008.000000   \n",
       "max                  NaN   20000.000000          NaN        9999.000000   \n",
       "\n",
       "       gearbox          power   model         milage  registration_month  \\\n",
       "count   334277  354107.000000  334406  354107.000000       354107.000000   \n",
       "unique       2            NaN     250            NaN                 NaN   \n",
       "top     manual            NaN    golf            NaN                 NaN   \n",
       "freq    268034            NaN   29215            NaN                 NaN   \n",
       "mean       NaN     110.089651     NaN  128211.811684            5.714182   \n",
       "std        NaN     189.914972     NaN   37906.590101            3.726682   \n",
       "min        NaN       0.000000     NaN    5000.000000            0.000000   \n",
       "25%        NaN      69.000000     NaN  125000.000000            3.000000   \n",
       "50%        NaN     105.000000     NaN  150000.000000            6.000000   \n",
       "75%        NaN     143.000000     NaN  150000.000000            9.000000   \n",
       "max        NaN   20000.000000     NaN  150000.000000           12.000000   \n",
       "\n",
       "       fuel_type       brand not_repaired      date_created  num_pictures  \\\n",
       "count     321218      354107       282962            354107      354107.0   \n",
       "unique         7          40            2               109           NaN   \n",
       "top       petrol  volkswagen           no  03/04/2016 00:00           NaN   \n",
       "freq      216161       76960       246927             13705           NaN   \n",
       "mean         NaN         NaN          NaN               NaN           0.0   \n",
       "std          NaN         NaN          NaN               NaN           0.0   \n",
       "min          NaN         NaN          NaN               NaN           0.0   \n",
       "25%          NaN         NaN          NaN               NaN           0.0   \n",
       "50%          NaN         NaN          NaN               NaN           0.0   \n",
       "75%          NaN         NaN          NaN               NaN           0.0   \n",
       "max          NaN         NaN          NaN               NaN           0.0   \n",
       "\n",
       "          postal_code         last_seen  \n",
       "count   354107.000000            354107  \n",
       "unique            NaN             18592  \n",
       "top               NaN  07/04/2016 07:16  \n",
       "freq              NaN               653  \n",
       "mean     50507.145030               NaN  \n",
       "std      25784.212094               NaN  \n",
       "min       1067.000000               NaN  \n",
       "25%      30165.000000               NaN  \n",
       "50%      49406.000000               NaN  \n",
       "75%      71083.000000               NaN  \n",
       "max      99998.000000               NaN  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# investigate columns\n",
    "df.describe(include=['object', 'int64'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Initial observations__ \n",
    "- date_crawled, date_created and last_seen indicate these listing are from 2016\n",
    "- The latest year possible in registration_year is 2016 --> delete rows > 2016\n",
    "- date_crawled, date_created and last_seen are not useful for analysis --> delete columns\n",
    "- num_pictures only has 0.0, not useful for analysis --> delete column\n",
    "- postal_code has objects less than 5 digits long --> investigate and delete rows or postal_code column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>date_crawled</th>\n",
       "      <th>price</th>\n",
       "      <th>vehicle_type</th>\n",
       "      <th>registration_year</th>\n",
       "      <th>gearbox</th>\n",
       "      <th>power</th>\n",
       "      <th>model</th>\n",
       "      <th>milage</th>\n",
       "      <th>registration_month</th>\n",
       "      <th>fuel_type</th>\n",
       "      <th>brand</th>\n",
       "      <th>not_repaired</th>\n",
       "      <th>date_created</th>\n",
       "      <th>num_pictures</th>\n",
       "      <th>postal_code</th>\n",
       "      <th>last_seen</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>22</td>\n",
       "      <td>23/03/2016 14:52</td>\n",
       "      <td>2900</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2018</td>\n",
       "      <td>manual</td>\n",
       "      <td>90</td>\n",
       "      <td>meriva</td>\n",
       "      <td>150000</td>\n",
       "      <td>5</td>\n",
       "      <td>petrol</td>\n",
       "      <td>opel</td>\n",
       "      <td>no</td>\n",
       "      <td>23/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>49716</td>\n",
       "      <td>31/03/2016 01:16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>26</td>\n",
       "      <td>10/03/2016 19:38</td>\n",
       "      <td>5555</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2017</td>\n",
       "      <td>manual</td>\n",
       "      <td>125</td>\n",
       "      <td>c4</td>\n",
       "      <td>125000</td>\n",
       "      <td>4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>citroen</td>\n",
       "      <td>no</td>\n",
       "      <td>10/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>31139</td>\n",
       "      <td>16/03/2016 09:16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>48</td>\n",
       "      <td>25/03/2016 14:40</td>\n",
       "      <td>7750</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2017</td>\n",
       "      <td>manual</td>\n",
       "      <td>80</td>\n",
       "      <td>golf</td>\n",
       "      <td>100000</td>\n",
       "      <td>1</td>\n",
       "      <td>petrol</td>\n",
       "      <td>volkswagen</td>\n",
       "      <td>NaN</td>\n",
       "      <td>25/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>48499</td>\n",
       "      <td>31/03/2016 21:47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>51</td>\n",
       "      <td>07/03/2016 18:57</td>\n",
       "      <td>2000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2017</td>\n",
       "      <td>manual</td>\n",
       "      <td>90</td>\n",
       "      <td>punto</td>\n",
       "      <td>150000</td>\n",
       "      <td>11</td>\n",
       "      <td>gasoline</td>\n",
       "      <td>fiat</td>\n",
       "      <td>yes</td>\n",
       "      <td>07/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>66115</td>\n",
       "      <td>07/03/2016 18:57</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>57</td>\n",
       "      <td>10/03/2016 20:53</td>\n",
       "      <td>2399</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2018</td>\n",
       "      <td>manual</td>\n",
       "      <td>64</td>\n",
       "      <td>other</td>\n",
       "      <td>125000</td>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "      <td>seat</td>\n",
       "      <td>no</td>\n",
       "      <td>10/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>33397</td>\n",
       "      <td>25/03/2016 10:17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>354112</td>\n",
       "      <td>11/03/2016 15:49</td>\n",
       "      <td>3600</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2017</td>\n",
       "      <td>manual</td>\n",
       "      <td>86</td>\n",
       "      <td>transit</td>\n",
       "      <td>150000</td>\n",
       "      <td>5</td>\n",
       "      <td>gasoline</td>\n",
       "      <td>ford</td>\n",
       "      <td>NaN</td>\n",
       "      <td>11/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>32339</td>\n",
       "      <td>12/03/2016 05:45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>354140</td>\n",
       "      <td>29/03/2016 16:47</td>\n",
       "      <td>1000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2017</td>\n",
       "      <td>manual</td>\n",
       "      <td>101</td>\n",
       "      <td>a4</td>\n",
       "      <td>150000</td>\n",
       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>audi</td>\n",
       "      <td>NaN</td>\n",
       "      <td>29/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>38315</td>\n",
       "      <td>06/04/2016 02:44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>354203</td>\n",
       "      <td>17/03/2016 00:56</td>\n",
       "      <td>2140</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2018</td>\n",
       "      <td>manual</td>\n",
       "      <td>80</td>\n",
       "      <td>fiesta</td>\n",
       "      <td>150000</td>\n",
       "      <td>6</td>\n",
       "      <td>NaN</td>\n",
       "      <td>ford</td>\n",
       "      <td>no</td>\n",
       "      <td>17/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>44866</td>\n",
       "      <td>29/03/2016 15:45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>354253</td>\n",
       "      <td>25/03/2016 09:37</td>\n",
       "      <td>1250</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2018</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>corsa</td>\n",
       "      <td>150000</td>\n",
       "      <td>0</td>\n",
       "      <td>petrol</td>\n",
       "      <td>opel</td>\n",
       "      <td>NaN</td>\n",
       "      <td>25/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>45527</td>\n",
       "      <td>06/04/2016 07:46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>354289</td>\n",
       "      <td>05/03/2016 14:55</td>\n",
       "      <td>5000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2017</td>\n",
       "      <td>manual</td>\n",
       "      <td>120</td>\n",
       "      <td>other</td>\n",
       "      <td>150000</td>\n",
       "      <td>7</td>\n",
       "      <td>NaN</td>\n",
       "      <td>citroen</td>\n",
       "      <td>yes</td>\n",
       "      <td>05/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>15518</td>\n",
       "      <td>05/04/2016 11:48</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>14529 rows × 16 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            date_crawled  price vehicle_type  registration_year gearbox  \\\n",
       "22      23/03/2016 14:52   2900          NaN               2018  manual   \n",
       "26      10/03/2016 19:38   5555          NaN               2017  manual   \n",
       "48      25/03/2016 14:40   7750          NaN               2017  manual   \n",
       "51      07/03/2016 18:57   2000          NaN               2017  manual   \n",
       "57      10/03/2016 20:53   2399          NaN               2018  manual   \n",
       "...                  ...    ...          ...                ...     ...   \n",
       "354112  11/03/2016 15:49   3600          NaN               2017  manual   \n",
       "354140  29/03/2016 16:47   1000          NaN               2017  manual   \n",
       "354203  17/03/2016 00:56   2140          NaN               2018  manual   \n",
       "354253  25/03/2016 09:37   1250          NaN               2018     NaN   \n",
       "354289  05/03/2016 14:55   5000          NaN               2017  manual   \n",
       "\n",
       "        power    model  milage  registration_month fuel_type       brand  \\\n",
       "22         90   meriva  150000                   5    petrol        opel   \n",
       "26        125       c4  125000                   4       NaN     citroen   \n",
       "48         80     golf  100000                   1    petrol  volkswagen   \n",
       "51         90    punto  150000                  11  gasoline        fiat   \n",
       "57         64    other  125000                   3       NaN        seat   \n",
       "...       ...      ...     ...                 ...       ...         ...   \n",
       "354112     86  transit  150000                   5  gasoline        ford   \n",
       "354140    101       a4  150000                   9       NaN        audi   \n",
       "354203     80   fiesta  150000                   6       NaN        ford   \n",
       "354253      0    corsa  150000                   0    petrol        opel   \n",
       "354289    120    other  150000                   7       NaN     citroen   \n",
       "\n",
       "       not_repaired      date_created  num_pictures  postal_code  \\\n",
       "22               no  23/03/2016 00:00             0        49716   \n",
       "26               no  10/03/2016 00:00             0        31139   \n",
       "48              NaN  25/03/2016 00:00             0        48499   \n",
       "51              yes  07/03/2016 00:00             0        66115   \n",
       "57               no  10/03/2016 00:00             0        33397   \n",
       "...             ...               ...           ...          ...   \n",
       "354112          NaN  11/03/2016 00:00             0        32339   \n",
       "354140          NaN  29/03/2016 00:00             0        38315   \n",
       "354203           no  17/03/2016 00:00             0        44866   \n",
       "354253          NaN  25/03/2016 00:00             0        45527   \n",
       "354289          yes  05/03/2016 00:00             0        15518   \n",
       "\n",
       "               last_seen  \n",
       "22      31/03/2016 01:16  \n",
       "26      16/03/2016 09:16  \n",
       "48      31/03/2016 21:47  \n",
       "51      07/03/2016 18:57  \n",
       "57      25/03/2016 10:17  \n",
       "...                  ...  \n",
       "354112  12/03/2016 05:45  \n",
       "354140  06/04/2016 02:44  \n",
       "354203  29/03/2016 15:45  \n",
       "354253  06/04/2016 07:46  \n",
       "354289  05/04/2016 11:48  \n",
       "\n",
       "[14529 rows x 16 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.query('registration_year > 2016')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.04099963597267255"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "14529/354369"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>date_crawled</th>\n",
       "      <th>price</th>\n",
       "      <th>vehicle_type</th>\n",
       "      <th>registration_year</th>\n",
       "      <th>gearbox</th>\n",
       "      <th>power</th>\n",
       "      <th>model</th>\n",
       "      <th>milage</th>\n",
       "      <th>registration_month</th>\n",
       "      <th>fuel_type</th>\n",
       "      <th>brand</th>\n",
       "      <th>not_repaired</th>\n",
       "      <th>date_created</th>\n",
       "      <th>num_pictures</th>\n",
       "      <th>postal_code</th>\n",
       "      <th>last_seen</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>15</td>\n",
       "      <td>11/03/2016 21:39</td>\n",
       "      <td>450</td>\n",
       "      <td>small</td>\n",
       "      <td>1910</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>ka</td>\n",
       "      <td>5000</td>\n",
       "      <td>0</td>\n",
       "      <td>petrol</td>\n",
       "      <td>ford</td>\n",
       "      <td>NaN</td>\n",
       "      <td>11/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>24148</td>\n",
       "      <td>19/03/2016 08:46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>622</td>\n",
       "      <td>16/03/2016 16:55</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1111</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5000</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>opel</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>44628</td>\n",
       "      <td>20/03/2016 16:44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1928</td>\n",
       "      <td>25/03/2016 15:58</td>\n",
       "      <td>7000</td>\n",
       "      <td>suv</td>\n",
       "      <td>1945</td>\n",
       "      <td>manual</td>\n",
       "      <td>48</td>\n",
       "      <td>other</td>\n",
       "      <td>150000</td>\n",
       "      <td>2</td>\n",
       "      <td>petrol</td>\n",
       "      <td>volkswagen</td>\n",
       "      <td>no</td>\n",
       "      <td>25/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>58135</td>\n",
       "      <td>25/03/2016 15:58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2273</td>\n",
       "      <td>15/03/2016 21:44</td>\n",
       "      <td>1800</td>\n",
       "      <td>convertible</td>\n",
       "      <td>1925</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5000</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>sonstige_autos</td>\n",
       "      <td>no</td>\n",
       "      <td>15/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>79288</td>\n",
       "      <td>07/04/2016 05:15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3333</td>\n",
       "      <td>15/03/2016 21:36</td>\n",
       "      <td>10500</td>\n",
       "      <td>sedan</td>\n",
       "      <td>1955</td>\n",
       "      <td>manual</td>\n",
       "      <td>30</td>\n",
       "      <td>other</td>\n",
       "      <td>60000</td>\n",
       "      <td>0</td>\n",
       "      <td>petrol</td>\n",
       "      <td>ford</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>53498</td>\n",
       "      <td>07/04/2016 08:16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>351299</td>\n",
       "      <td>09/03/2016 21:56</td>\n",
       "      <td>5500</td>\n",
       "      <td>bus</td>\n",
       "      <td>1956</td>\n",
       "      <td>manual</td>\n",
       "      <td>37</td>\n",
       "      <td>NaN</td>\n",
       "      <td>60000</td>\n",
       "      <td>4</td>\n",
       "      <td>petrol</td>\n",
       "      <td>sonstige_autos</td>\n",
       "      <td>no</td>\n",
       "      <td>09/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>1900</td>\n",
       "      <td>06/04/2016 02:17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>351682</td>\n",
       "      <td>12/03/2016 00:57</td>\n",
       "      <td>11500</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1800</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16</td>\n",
       "      <td>other</td>\n",
       "      <td>5000</td>\n",
       "      <td>6</td>\n",
       "      <td>petrol</td>\n",
       "      <td>fiat</td>\n",
       "      <td>NaN</td>\n",
       "      <td>11/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>16515</td>\n",
       "      <td>05/04/2016 19:47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>353531</td>\n",
       "      <td>16/03/2016 21:56</td>\n",
       "      <td>6000</td>\n",
       "      <td>sedan</td>\n",
       "      <td>1937</td>\n",
       "      <td>manual</td>\n",
       "      <td>38</td>\n",
       "      <td>other</td>\n",
       "      <td>5000</td>\n",
       "      <td>0</td>\n",
       "      <td>petrol</td>\n",
       "      <td>mercedes_benz</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>23936</td>\n",
       "      <td>30/03/2016 18:47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>353961</td>\n",
       "      <td>17/03/2016 13:54</td>\n",
       "      <td>200</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1910</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5000</td>\n",
       "      <td>0</td>\n",
       "      <td>petrol</td>\n",
       "      <td>sonstige_autos</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>42289</td>\n",
       "      <td>31/03/2016 22:46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>354316</td>\n",
       "      <td>07/03/2016 19:58</td>\n",
       "      <td>3300</td>\n",
       "      <td>coupe</td>\n",
       "      <td>1957</td>\n",
       "      <td>manual</td>\n",
       "      <td>40</td>\n",
       "      <td>other</td>\n",
       "      <td>100000</td>\n",
       "      <td>11</td>\n",
       "      <td>petrol</td>\n",
       "      <td>trabant</td>\n",
       "      <td>no</td>\n",
       "      <td>07/03/2016 00:00</td>\n",
       "      <td>0</td>\n",
       "      <td>10317</td>\n",
       "      <td>08/03/2016 06:45</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>390 rows × 16 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            date_crawled  price vehicle_type  registration_year gearbox  \\\n",
       "15      11/03/2016 21:39    450        small               1910     NaN   \n",
       "622     16/03/2016 16:55      0          NaN               1111     NaN   \n",
       "1928    25/03/2016 15:58   7000          suv               1945  manual   \n",
       "2273    15/03/2016 21:44   1800  convertible               1925     NaN   \n",
       "3333    15/03/2016 21:36  10500        sedan               1955  manual   \n",
       "...                  ...    ...          ...                ...     ...   \n",
       "351299  09/03/2016 21:56   5500          bus               1956  manual   \n",
       "351682  12/03/2016 00:57  11500          NaN               1800     NaN   \n",
       "353531  16/03/2016 21:56   6000        sedan               1937  manual   \n",
       "353961  17/03/2016 13:54    200          NaN               1910     NaN   \n",
       "354316  07/03/2016 19:58   3300        coupe               1957  manual   \n",
       "\n",
       "        power  model  milage  registration_month fuel_type           brand  \\\n",
       "15          0     ka    5000                   0    petrol            ford   \n",
       "622         0    NaN    5000                   0       NaN            opel   \n",
       "1928       48  other  150000                   2    petrol      volkswagen   \n",
       "2273        0    NaN    5000                   1       NaN  sonstige_autos   \n",
       "3333       30  other   60000                   0    petrol            ford   \n",
       "...       ...    ...     ...                 ...       ...             ...   \n",
       "351299     37    NaN   60000                   4    petrol  sonstige_autos   \n",
       "351682     16  other    5000                   6    petrol            fiat   \n",
       "353531     38  other    5000                   0    petrol   mercedes_benz   \n",
       "353961      0    NaN    5000                   0    petrol  sonstige_autos   \n",
       "354316     40  other  100000                  11    petrol         trabant   \n",
       "\n",
       "       not_repaired      date_created  num_pictures  postal_code  \\\n",
       "15              NaN  11/03/2016 00:00             0        24148   \n",
       "622             NaN  16/03/2016 00:00             0        44628   \n",
       "1928             no  25/03/2016 00:00             0        58135   \n",
       "2273             no  15/03/2016 00:00             0        79288   \n",
       "3333            NaN  15/03/2016 00:00             0        53498   \n",
       "...             ...               ...           ...          ...   \n",
       "351299           no  09/03/2016 00:00             0         1900   \n",
       "351682          NaN  11/03/2016 00:00             0        16515   \n",
       "353531          NaN  16/03/2016 00:00             0        23936   \n",
       "353961          NaN  17/03/2016 00:00             0        42289   \n",
       "354316           no  07/03/2016 00:00             0        10317   \n",
       "\n",
       "               last_seen  \n",
       "15      19/03/2016 08:46  \n",
       "622     20/03/2016 16:44  \n",
       "1928    25/03/2016 15:58  \n",
       "2273    07/04/2016 05:15  \n",
       "3333    07/04/2016 08:16  \n",
       "...                  ...  \n",
       "351299  06/04/2016 02:17  \n",
       "351682  05/04/2016 19:47  \n",
       "353531  30/03/2016 18:47  \n",
       "353961  31/03/2016 22:46  \n",
       "354316  08/03/2016 06:45  \n",
       "\n",
       "[390 rows x 16 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.query('registration_year < 1959')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0011005477341415305"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "390/354369"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Since it is unlikely that we have many legitimate cars with registration dates less then 1960, we will eliminate those rows along with the rows of vehicles with a registration year > 2016, which would be impossible since the data was collected in 2016.__"
   ]
  },
  {
   "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>date_crawled</th>\n",
       "      <th>price</th>\n",
       "      <th>vehicle_type</th>\n",
       "      <th>registration_year</th>\n",
       "      <th>gearbox</th>\n",
       "      <th>power</th>\n",
       "      <th>model</th>\n",
       "      <th>milage</th>\n",
       "      <th>registration_month</th>\n",
       "      <th>fuel_type</th>\n",
       "      <th>brand</th>\n",
       "      <th>not_repaired</th>\n",
       "      <th>date_created</th>\n",
       "      <th>num_pictures</th>\n",
       "      <th>postal_code</th>\n",
       "      <th>last_seen</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Empty DataFrame\n",
       "Columns: [date_crawled, price, vehicle_type, registration_year, gearbox, power, model, milage, registration_month, fuel_type, brand, not_repaired, date_created, num_pictures, postal_code, last_seen]\n",
       "Index: []"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df.loc[df['registration_year'] <= 2016]\n",
    "df = df.loc[df['registration_year'] >1959]\n",
    "df.query('registration_year > 2016' and 'registration_year < 1960')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pct of rows with postal_codes < 10000 0.05119178195284766\n"
     ]
    }
   ],
   "source": [
    "df_bad_code = df.query('postal_code <10000') \n",
    "print('Pct of rows with postal_codes < 10000', df_bad_code.shape[0]/df.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>price</th>\n",
       "      <th>registration_year</th>\n",
       "      <th>power</th>\n",
       "      <th>milage</th>\n",
       "      <th>registration_month</th>\n",
       "      <th>num_pictures</th>\n",
       "      <th>postal_code</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>price</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.453728</td>\n",
       "      <td>0.161802</td>\n",
       "      <td>-0.337630</td>\n",
       "      <td>0.107351</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.075679</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>registration_year</td>\n",
       "      <td>0.453728</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.050668</td>\n",
       "      <td>-0.225518</td>\n",
       "      <td>0.073391</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.034969</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>power</td>\n",
       "      <td>0.161802</td>\n",
       "      <td>0.050668</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.024620</td>\n",
       "      <td>0.042747</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.021350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>milage</td>\n",
       "      <td>-0.337630</td>\n",
       "      <td>-0.225518</td>\n",
       "      <td>0.024620</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.008051</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.008220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>registration_month</td>\n",
       "      <td>0.107351</td>\n",
       "      <td>0.073391</td>\n",
       "      <td>0.042747</td>\n",
       "      <td>0.008051</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.013036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>num_pictures</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>postal_code</td>\n",
       "      <td>0.075679</td>\n",
       "      <td>0.034969</td>\n",
       "      <td>0.021350</td>\n",
       "      <td>-0.008220</td>\n",
       "      <td>0.013036</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       price  registration_year     power    milage  \\\n",
       "price               1.000000           0.453728  0.161802 -0.337630   \n",
       "registration_year   0.453728           1.000000  0.050668 -0.225518   \n",
       "power               0.161802           0.050668  1.000000  0.024620   \n",
       "milage             -0.337630          -0.225518  0.024620  1.000000   \n",
       "registration_month  0.107351           0.073391  0.042747  0.008051   \n",
       "num_pictures             NaN                NaN       NaN       NaN   \n",
       "postal_code         0.075679           0.034969  0.021350 -0.008220   \n",
       "\n",
       "                    registration_month  num_pictures  postal_code  \n",
       "price                         0.107351           NaN     0.075679  \n",
       "registration_year             0.073391           NaN     0.034969  \n",
       "power                         0.042747           NaN     0.021350  \n",
       "milage                        0.008051           NaN    -0.008220  \n",
       "registration_month            1.000000           NaN     0.013036  \n",
       "num_pictures                       NaN           NaN          NaN  \n",
       "postal_code                   0.013036           NaN     1.000000  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__We note a little over half a percent of the rows have an obviously inaccurate postal code so deleting those rows is one choice. However, the correlation between price and postal_code is fairly low, so we will drop the postal_code column instead__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(339156, 16)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(339156, 11)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(df.shape)\n",
    "df.drop(columns=['date_crawled', 'date_created', 'last_seen', 'num_pictures', 'postal_code'], inplace=True)\n",
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Columns Missing Values\n",
      "                      type    cnt        pct\n",
      "price                int64      0   0.000000\n",
      "vehicle_type        object  22835   6.732890\n",
      "registration_year    int64      0   0.000000\n",
      "gearbox             object  17774   5.240656\n",
      "power                int64      0   0.000000\n",
      "model               object  17459   5.147779\n",
      "milage               int64      0   0.000000\n",
      "registration_month   int64      0   0.000000\n",
      "fuel_type           object  27131   7.999564\n",
      "brand               object      0   0.000000\n",
      "not_repaired        object  64613  19.051115\n"
     ]
    }
   ],
   "source": [
    "missing_stats(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Observations with updated list__\n",
    "- price has outliers --> investigate outliers\n",
    "- vehicle_type has missing values --> fillin related to model\n",
    "- registration_year --> handled earlier\n",
    "- gearbox has missing values --> investigate and fillin \n",
    "- power values vary widely --> [research online](https://www.autolist.com/guides/average-car-horsepower), investigate\n",
    "- __model has missing values --> investigate (first since will use for fill ins)__\n",
    "- milage no missing values, given values look reasonable --> keep as is\n",
    "- registration_month has some values of zero --> investigate\n",
    "- fuel_type, not sure how there are 7 unique values --> investigate\n",
    "- brand (make) has no missing values --> keep as is\n",
    "- not_repaired indicates if vehicle repaired or not --> investigate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "golf                  27593\n",
       "other                 23711\n",
       "3er                   19206\n",
       "NaN                   17459\n",
       "polo                  12441\n",
       "                      ...  \n",
       "kalina                    6\n",
       "serie_3                   4\n",
       "rangerover                3\n",
       "serie_1                   2\n",
       "range_rover_evoque        2\n",
       "Name: model, Length: 251, dtype: int64"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['model'].value_counts(dropna=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.051477786033565676"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['model'].isnull().sum()/len(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>price</th>\n",
       "      <th>vehicle_type</th>\n",
       "      <th>registration_year</th>\n",
       "      <th>gearbox</th>\n",
       "      <th>power</th>\n",
       "      <th>model</th>\n",
       "      <th>milage</th>\n",
       "      <th>registration_month</th>\n",
       "      <th>fuel_type</th>\n",
       "      <th>brand</th>\n",
       "      <th>not_repaired</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>18300</td>\n",
       "      <td>coupe</td>\n",
       "      <td>2011</td>\n",
       "      <td>manual</td>\n",
       "      <td>190</td>\n",
       "      <td>NaN</td>\n",
       "      <td>125000</td>\n",
       "      <td>5</td>\n",
       "      <td>gasoline</td>\n",
       "      <td>audi</td>\n",
       "      <td>yes</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>59</td>\n",
       "      <td>1</td>\n",
       "      <td>suv</td>\n",
       "      <td>1994</td>\n",
       "      <td>manual</td>\n",
       "      <td>286</td>\n",
       "      <td>NaN</td>\n",
       "      <td>150000</td>\n",
       "      <td>11</td>\n",
       "      <td>NaN</td>\n",
       "      <td>sonstige_autos</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>81</td>\n",
       "      <td>350</td>\n",
       "      <td>small</td>\n",
       "      <td>1997</td>\n",
       "      <td>manual</td>\n",
       "      <td>54</td>\n",
       "      <td>NaN</td>\n",
       "      <td>150000</td>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "      <td>fiat</td>\n",
       "      <td>yes</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>115</td>\n",
       "      <td>0</td>\n",
       "      <td>small</td>\n",
       "      <td>1999</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5000</td>\n",
       "      <td>0</td>\n",
       "      <td>petrol</td>\n",
       "      <td>volkswagen</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>135</td>\n",
       "      <td>1450</td>\n",
       "      <td>sedan</td>\n",
       "      <td>1992</td>\n",
       "      <td>manual</td>\n",
       "      <td>136</td>\n",
       "      <td>NaN</td>\n",
       "      <td>150000</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>audi</td>\n",
       "      <td>no</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     price vehicle_type  registration_year gearbox  power model  milage  \\\n",
       "1    18300        coupe               2011  manual    190   NaN  125000   \n",
       "59       1          suv               1994  manual    286   NaN  150000   \n",
       "81     350        small               1997  manual     54   NaN  150000   \n",
       "115      0        small               1999     NaN      0   NaN    5000   \n",
       "135   1450        sedan               1992  manual    136   NaN  150000   \n",
       "\n",
       "     registration_month fuel_type           brand not_repaired  \n",
       "1                     5  gasoline            audi          yes  \n",
       "59                   11       NaN  sonstige_autos          NaN  \n",
       "81                    3       NaN            fiat          yes  \n",
       "115                   0    petrol      volkswagen          NaN  \n",
       "135                   0       NaN            audi           no  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.loc[df['model'].isnull()].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__model has 251 unique values and a little over half a percent are null. It is unlikely we can make wise replacements for the missing values, so we will remove those rows with missing the model value.__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(339156, 11)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(321697, 11)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(df.shape)\n",
    "df.dropna(subset=['model'], inplace=True) \n",
    "df.shape               "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['model'].isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count     4467.000000\n",
       "mean     19247.173942\n",
       "std        572.356100\n",
       "min      18247.000000\n",
       "25%      18800.000000\n",
       "50%      19200.000000\n",
       "75%      19900.000000\n",
       "max      20000.000000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "outlier_stats(df.price)"
   ]
  },
  {
   "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>price</th>\n",
       "      <th>vehicle_type</th>\n",
       "      <th>registration_year</th>\n",
       "      <th>gearbox</th>\n",
       "      <th>power</th>\n",
       "      <th>model</th>\n",
       "      <th>milage</th>\n",
       "      <th>registration_month</th>\n",
       "      <th>fuel_type</th>\n",
       "      <th>brand</th>\n",
       "      <th>not_repaired</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>sedan</td>\n",
       "      <td>1980</td>\n",
       "      <td>manual</td>\n",
       "      <td>50</td>\n",
       "      <td>other</td>\n",
       "      <td>40000</td>\n",
       "      <td>7</td>\n",
       "      <td>petrol</td>\n",
       "      <td>volkswagen</td>\n",
       "      <td>no</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>40</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1990</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>corsa</td>\n",
       "      <td>150000</td>\n",
       "      <td>1</td>\n",
       "      <td>petrol</td>\n",
       "      <td>opel</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>152</td>\n",
       "      <td>0</td>\n",
       "      <td>bus</td>\n",
       "      <td>2004</td>\n",
       "      <td>manual</td>\n",
       "      <td>101</td>\n",
       "      <td>meriva</td>\n",
       "      <td>150000</td>\n",
       "      <td>10</td>\n",
       "      <td>lpg</td>\n",
       "      <td>opel</td>\n",
       "      <td>yes</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>154</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2006</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>other</td>\n",
       "      <td>5000</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>fiat</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>231</td>\n",
       "      <td>0</td>\n",
       "      <td>wagon</td>\n",
       "      <td>2001</td>\n",
       "      <td>manual</td>\n",
       "      <td>115</td>\n",
       "      <td>mondeo</td>\n",
       "      <td>150000</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>ford</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>354205</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2000</td>\n",
       "      <td>manual</td>\n",
       "      <td>65</td>\n",
       "      <td>corsa</td>\n",
       "      <td>150000</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>opel</td>\n",
       "      <td>yes</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>354238</td>\n",
       "      <td>0</td>\n",
       "      <td>small</td>\n",
       "      <td>2002</td>\n",
       "      <td>manual</td>\n",
       "      <td>60</td>\n",
       "      <td>fiesta</td>\n",
       "      <td>150000</td>\n",
       "      <td>3</td>\n",
       "      <td>petrol</td>\n",
       "      <td>ford</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>354248</td>\n",
       "      <td>0</td>\n",
       "      <td>small</td>\n",
       "      <td>1999</td>\n",
       "      <td>manual</td>\n",
       "      <td>53</td>\n",
       "      <td>swift</td>\n",
       "      <td>150000</td>\n",
       "      <td>3</td>\n",
       "      <td>petrol</td>\n",
       "      <td>suzuki</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>354277</td>\n",
       "      <td>0</td>\n",
       "      <td>small</td>\n",
       "      <td>1999</td>\n",
       "      <td>manual</td>\n",
       "      <td>37</td>\n",
       "      <td>arosa</td>\n",
       "      <td>150000</td>\n",
       "      <td>7</td>\n",
       "      <td>petrol</td>\n",
       "      <td>seat</td>\n",
       "      <td>yes</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>354364</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2005</td>\n",
       "      <td>manual</td>\n",
       "      <td>0</td>\n",
       "      <td>colt</td>\n",
       "      <td>150000</td>\n",
       "      <td>7</td>\n",
       "      <td>petrol</td>\n",
       "      <td>mitsubishi</td>\n",
       "      <td>yes</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>7993 rows × 11 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        price vehicle_type  registration_year gearbox  power   model  milage  \\\n",
       "7           0        sedan               1980  manual     50   other   40000   \n",
       "40          0          NaN               1990     NaN      0   corsa  150000   \n",
       "152         0          bus               2004  manual    101  meriva  150000   \n",
       "154         0          NaN               2006     NaN      0   other    5000   \n",
       "231         0        wagon               2001  manual    115  mondeo  150000   \n",
       "...       ...          ...                ...     ...    ...     ...     ...   \n",
       "354205      0          NaN               2000  manual     65   corsa  150000   \n",
       "354238      0        small               2002  manual     60  fiesta  150000   \n",
       "354248      0        small               1999  manual     53   swift  150000   \n",
       "354277      0        small               1999  manual     37   arosa  150000   \n",
       "354364      0          NaN               2005  manual      0    colt  150000   \n",
       "\n",
       "        registration_month fuel_type       brand not_repaired  \n",
       "7                        7    petrol  volkswagen           no  \n",
       "40                       1    petrol        opel          NaN  \n",
       "152                     10       lpg        opel          yes  \n",
       "154                      0       NaN        fiat          NaN  \n",
       "231                      0       NaN        ford          NaN  \n",
       "...                    ...       ...         ...          ...  \n",
       "354205                   0       NaN        opel          yes  \n",
       "354238                   3    petrol        ford          NaN  \n",
       "354248                   3    petrol      suzuki          NaN  \n",
       "354277                   7    petrol        seat          yes  \n",
       "354364                   7    petrol  mitsubishi          yes  \n",
       "\n",
       "[7993 rows x 11 columns]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.query('price == 0')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__There are almost 8000 rows where the price is 0. This may be clerical error or it may reflect vehicles junked or given for free. Either way, these will not be useful for our analysis. We will keep the rows with higher outlier values as some cars may have gone for an impressive amount.__"
   ]
  },
  {
   "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>price</th>\n",
       "      <th>vehicle_type</th>\n",
       "      <th>registration_year</th>\n",
       "      <th>gearbox</th>\n",
       "      <th>power</th>\n",
       "      <th>model</th>\n",
       "      <th>milage</th>\n",
       "      <th>registration_month</th>\n",
       "      <th>fuel_type</th>\n",
       "      <th>brand</th>\n",
       "      <th>not_repaired</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Empty DataFrame\n",
       "Columns: [price, vehicle_type, registration_year, gearbox, power, model, milage, registration_month, fuel_type, brand, not_repaired]\n",
       "Index: []"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df.loc[df['price'] != 0]\n",
    "df.query('price == 0')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sedan          86217\n",
       "small          74809\n",
       "wagon          61646\n",
       "bus            27400\n",
       "convertible    19001\n",
       "NaN            16217\n",
       "coupe          14743\n",
       "suv            11041\n",
       "other           2630\n",
       "Name: vehicle_type, dtype: int64"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['vehicle_type'].value_counts(dropna=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sedan          93980\n",
       "small          79416\n",
       "wagon          63377\n",
       "bus            28920\n",
       "convertible    19154\n",
       "coupe          14955\n",
       "suv            11272\n",
       "other           2630\n",
       "Name: vehicle_type, dtype: int64"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['vehicle_type'].fillna(df.groupby('model')['vehicle_type'].\n",
    "                          transform(lambda x:x.value_counts().index[0]), inplace=True)\n",
    "df['vehicle_type'].value_counts(dropna=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "manual    240670\n",
       "auto       60188\n",
       "NaN        12846\n",
       "Name: gearbox, dtype: int64"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['gearbox'].value_counts(dropna=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__gearbox is missing about 4% of the values and we will replace those based on model since the gearbox is usally consistent with models.__ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "manual    252002\n",
       "auto       61702\n",
       "Name: gearbox, dtype: int64"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['gearbox'].fillna(df.groupby('model')['gearbox']\\\n",
    "                          .transform(lambda x:x.value_counts().index[0]), inplace=True)\n",
    "df['gearbox'].value_counts(dropna=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count      270.000000\n",
       "mean      3716.562963\n",
       "std       4484.265366\n",
       "min        671.000000\n",
       "25%       1149.500000\n",
       "50%       1612.500000\n",
       "75%       4237.500000\n",
       "max      20000.000000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "outlier_stats(df.power)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__We discover a small number of outliers in the power column and will delete those.__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(313704, 11)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(313434, 11)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(df.shape)\n",
    "df = df.loc[df['power'] <= 670]\n",
    "df.shape "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['power'].isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3     31568\n",
       "6     28522\n",
       "4     26538\n",
       "5     26437\n",
       "0     24734\n",
       "7     24652\n",
       "10    23937\n",
       "11    22226\n",
       "12    22024\n",
       "9     21924\n",
       "1     20953\n",
       "8     20552\n",
       "2     19367\n",
       "Name: registration_month, dtype: int64"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['registration_month'].value_counts()"
   ]
  },
  {
   "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>price</th>\n",
       "      <th>registration_year</th>\n",
       "      <th>power</th>\n",
       "      <th>milage</th>\n",
       "      <th>registration_month</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>price</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.485168</td>\n",
       "      <td>0.492910</td>\n",
       "      <td>-0.367805</td>\n",
       "      <td>0.085502</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>registration_year</td>\n",
       "      <td>0.485168</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.152706</td>\n",
       "      <td>-0.273744</td>\n",
       "      <td>0.058507</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>power</td>\n",
       "      <td>0.492910</td>\n",
       "      <td>0.152706</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.073695</td>\n",
       "      <td>0.098254</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>milage</td>\n",
       "      <td>-0.367805</td>\n",
       "      <td>-0.273744</td>\n",
       "      <td>0.073695</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.003873</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>registration_month</td>\n",
       "      <td>0.085502</td>\n",
       "      <td>0.058507</td>\n",
       "      <td>0.098254</td>\n",
       "      <td>-0.003873</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       price  registration_year     power    milage  \\\n",
       "price               1.000000           0.485168  0.492910 -0.367805   \n",
       "registration_year   0.485168           1.000000  0.152706 -0.273744   \n",
       "power               0.492910           0.152706  1.000000  0.073695   \n",
       "milage             -0.367805          -0.273744  0.073695  1.000000   \n",
       "registration_month  0.085502           0.058507  0.098254 -0.003873   \n",
       "\n",
       "                    registration_month  \n",
       "price                         0.085502  \n",
       "registration_year             0.058507  \n",
       "power                         0.098254  \n",
       "milage                       -0.003873  \n",
       "registration_month            1.000000  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Once again we find a weak relationship between registration_month and price, but it would be better to keep the column and rows for overall data integrity. The months are fairly evenly divided so we could randomly distribute the NA values with values of 1:12 to indicate months.__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11    26388\n",
       "3     26325\n",
       "2     26291\n",
       "8     26165\n",
       "5     26144\n",
       "10    26111\n",
       "7     26094\n",
       "9     26053\n",
       "1     26037\n",
       "4     25968\n",
       "12    25960\n",
       "6     25898\n",
       "Name: registration_month, dtype: int64"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['registration_month'] = df['registration_month'].apply(lambda v: random.choice([1,2,3,4,5,6,7,8,9,10,11,12]))\n",
    "df['registration_month'].value_counts(dropna=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "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>price</th>\n",
       "      <th>vehicle_type</th>\n",
       "      <th>registration_year</th>\n",
       "      <th>gearbox</th>\n",
       "      <th>power</th>\n",
       "      <th>model</th>\n",
       "      <th>milage</th>\n",
       "      <th>registration_month</th>\n",
       "      <th>fuel_type</th>\n",
       "      <th>brand</th>\n",
       "      <th>not_repaired</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Empty DataFrame\n",
       "Columns: [price, vehicle_type, registration_year, gearbox, power, model, milage, registration_month, fuel_type, brand, not_repaired]\n",
       "Index: []"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.query('registration_month == 0')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "petrol      196403\n",
       "gasoline     92275\n",
       "NaN          19160\n",
       "lpg           4711\n",
       "cng            511\n",
       "hybrid         198\n",
       "other          113\n",
       "electric        63\n",
       "Name: fuel_type, dtype: int64"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['fuel_type'].value_counts(dropna=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__We will fill in the missing values using the influence of model since usually the fuel type is consistent with model.__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "petrol      212129\n",
       "gasoline     95709\n",
       "lpg           4711\n",
       "cng            511\n",
       "hybrid         198\n",
       "other          113\n",
       "electric        63\n",
       "Name: fuel_type, dtype: int64"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['fuel_type'].fillna(df.groupby('model')['fuel_type']\\\n",
    "                          .transform(lambda x:x.value_counts().index[0]), inplace=True)\n",
    "df['fuel_type'].value_counts(dropna=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "no     229472\n",
       "NaN     53015\n",
       "yes     30947\n",
       "Name: not_repaired, dtype: int64"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['not_repaired'].value_counts(dropna=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Since no is the most common value, we will replace the missing values with no.__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "no     282487\n",
       "yes     30947\n",
       "Name: not_repaired, dtype: int64"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['not_repaired'].fillna('no', inplace=True)\n",
    "df['not_repaired'].value_counts(dropna=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Now we will check to for any missed missing values, reset the index, and look at the percentage of the original data we deleted.__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Columns Missing Values\n",
      "                      type  cnt  pct\n",
      "price                int64    0  0.0\n",
      "vehicle_type        object    0  0.0\n",
      "registration_year    int64    0  0.0\n",
      "gearbox             object    0  0.0\n",
      "power                int64    0  0.0\n",
      "model               object    0  0.0\n",
      "milage               int64    0  0.0\n",
      "registration_month   int64    0  0.0\n",
      "fuel_type           object    0  0.0\n",
      "brand               object    0  0.0\n",
      "not_repaired        object    0  0.0\n"
     ]
    }
   ],
   "source": [
    "missing_stats(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "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>price</th>\n",
       "      <th>vehicle_type</th>\n",
       "      <th>registration_year</th>\n",
       "      <th>gearbox</th>\n",
       "      <th>power</th>\n",
       "      <th>model</th>\n",
       "      <th>milage</th>\n",
       "      <th>registration_month</th>\n",
       "      <th>fuel_type</th>\n",
       "      <th>brand</th>\n",
       "      <th>not_repaired</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>480</td>\n",
       "      <td>sedan</td>\n",
       "      <td>1993</td>\n",
       "      <td>manual</td>\n",
       "      <td>0</td>\n",
       "      <td>golf</td>\n",
       "      <td>150000</td>\n",
       "      <td>11</td>\n",
       "      <td>petrol</td>\n",
       "      <td>volkswagen</td>\n",
       "      <td>no</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>9800</td>\n",
       "      <td>suv</td>\n",
       "      <td>2004</td>\n",
       "      <td>auto</td>\n",
       "      <td>163</td>\n",
       "      <td>grand</td>\n",
       "      <td>125000</td>\n",
       "      <td>2</td>\n",
       "      <td>gasoline</td>\n",
       "      <td>jeep</td>\n",
       "      <td>no</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>1500</td>\n",
       "      <td>small</td>\n",
       "      <td>2001</td>\n",
       "      <td>manual</td>\n",
       "      <td>75</td>\n",
       "      <td>golf</td>\n",
       "      <td>150000</td>\n",
       "      <td>1</td>\n",
       "      <td>petrol</td>\n",
       "      <td>volkswagen</td>\n",
       "      <td>no</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>3600</td>\n",
       "      <td>small</td>\n",
       "      <td>2008</td>\n",
       "      <td>manual</td>\n",
       "      <td>69</td>\n",
       "      <td>fabia</td>\n",
       "      <td>90000</td>\n",
       "      <td>12</td>\n",
       "      <td>gasoline</td>\n",
       "      <td>skoda</td>\n",
       "      <td>no</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>650</td>\n",
       "      <td>sedan</td>\n",
       "      <td>1995</td>\n",
       "      <td>manual</td>\n",
       "      <td>102</td>\n",
       "      <td>3er</td>\n",
       "      <td>150000</td>\n",
       "      <td>5</td>\n",
       "      <td>petrol</td>\n",
       "      <td>bmw</td>\n",
       "      <td>yes</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   price vehicle_type  registration_year gearbox  power  model  milage  \\\n",
       "0    480        sedan               1993  manual      0   golf  150000   \n",
       "2   9800          suv               2004    auto    163  grand  125000   \n",
       "3   1500        small               2001  manual     75   golf  150000   \n",
       "4   3600        small               2008  manual     69  fabia   90000   \n",
       "5    650        sedan               1995  manual    102    3er  150000   \n",
       "\n",
       "   registration_month fuel_type       brand not_repaired  \n",
       "0                  11    petrol  volkswagen           no  \n",
       "2                   2  gasoline        jeep           no  \n",
       "3                   1    petrol  volkswagen           no  \n",
       "4                  12  gasoline       skoda           no  \n",
       "5                   5    petrol         bmw          yes  "
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>index</th>\n",
       "      <th>price</th>\n",
       "      <th>vehicle_type</th>\n",
       "      <th>registration_year</th>\n",
       "      <th>gearbox</th>\n",
       "      <th>power</th>\n",
       "      <th>model</th>\n",
       "      <th>milage</th>\n",
       "      <th>registration_month</th>\n",
       "      <th>fuel_type</th>\n",
       "      <th>brand</th>\n",
       "      <th>not_repaired</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>480</td>\n",
       "      <td>sedan</td>\n",
       "      <td>1993</td>\n",
       "      <td>manual</td>\n",
       "      <td>0</td>\n",
       "      <td>golf</td>\n",
       "      <td>150000</td>\n",
       "      <td>11</td>\n",
       "      <td>petrol</td>\n",
       "      <td>volkswagen</td>\n",
       "      <td>no</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>9800</td>\n",
       "      <td>suv</td>\n",
       "      <td>2004</td>\n",
       "      <td>auto</td>\n",
       "      <td>163</td>\n",
       "      <td>grand</td>\n",
       "      <td>125000</td>\n",
       "      <td>2</td>\n",
       "      <td>gasoline</td>\n",
       "      <td>jeep</td>\n",
       "      <td>no</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1500</td>\n",
       "      <td>small</td>\n",
       "      <td>2001</td>\n",
       "      <td>manual</td>\n",
       "      <td>75</td>\n",
       "      <td>golf</td>\n",
       "      <td>150000</td>\n",
       "      <td>1</td>\n",
       "      <td>petrol</td>\n",
       "      <td>volkswagen</td>\n",
       "      <td>no</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>3600</td>\n",
       "      <td>small</td>\n",
       "      <td>2008</td>\n",
       "      <td>manual</td>\n",
       "      <td>69</td>\n",
       "      <td>fabia</td>\n",
       "      <td>90000</td>\n",
       "      <td>12</td>\n",
       "      <td>gasoline</td>\n",
       "      <td>skoda</td>\n",
       "      <td>no</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>650</td>\n",
       "      <td>sedan</td>\n",
       "      <td>1995</td>\n",
       "      <td>manual</td>\n",
       "      <td>102</td>\n",
       "      <td>3er</td>\n",
       "      <td>150000</td>\n",
       "      <td>5</td>\n",
       "      <td>petrol</td>\n",
       "      <td>bmw</td>\n",
       "      <td>yes</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   index  price vehicle_type  registration_year gearbox  power  model  milage  \\\n",
       "0      0    480        sedan               1993  manual      0   golf  150000   \n",
       "1      2   9800          suv               2004    auto    163  grand  125000   \n",
       "2      3   1500        small               2001  manual     75   golf  150000   \n",
       "3      4   3600        small               2008  manual     69  fabia   90000   \n",
       "4      5    650        sedan               1995  manual    102    3er  150000   \n",
       "\n",
       "   registration_month fuel_type       brand not_repaired  \n",
       "0                  11    petrol  volkswagen           no  \n",
       "1                   2  gasoline        jeep           no  \n",
       "2                   1    petrol  volkswagen           no  \n",
       "3                  12  gasoline       skoda           no  \n",
       "4                   5    petrol         bmw          yes  "
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# resetting the DataFrame index\n",
    "df = df.reset_index()\n",
    "df.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8844848166741448"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df)/original_no_rows"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Summary of data preparation__\n",
    "- We dropped several columns, 'date_crawled', 'date_created', 'last_seen', 'num_pictures', 'postal_code', that will not be useful for our analysis.\n",
    "- We eliminated rows where the registration_year > 2016 (the year of the data) or < 1960 (unlikely).\n",
    "- We eliminated rows where the price = 0.\n",
    "- We eliminated the rows where a value for model was missing.\n",
    "- We filled in missing rows in vehicle_type, gearbox, fuel_type, power based on model.\n",
    "- We changed the zero values in registration_month to a randomly assigned # (1-12).\n",
    "- We replaced the NaN values in not_repaired with 'no'.\n",
    "- We verified that no missing values remain.\n",
    "- We note our preparation eliminated almost 12% of the data, but feel confident in the deletion choices."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "# change into categories for lightBGM and CatBoost\n",
    "categories = ['vehicle_type', 'gearbox', 'model', 'fuel_type', 'brand', 'not_repaired']\n",
    "for col in categories:\n",
    "    df[col] = df[col].astype('category')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create feature and target variables\n",
    "target = df['price']\n",
    "features = df.drop(['price'], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "# use one hot encoding to turn the categories into numeric\n",
    "features_ohe = pd.get_dummies(features, drop_first=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train target and features and percentage\n",
      " (188060,) (188060, 307) pct 0.5999987238142639\n",
      "Valid target and features and percentage\n",
      " (62687,) (62687, 307) pct 0.20000063809286803\n",
      "Test target and features and percentage\n",
      " (62687,) (62687, 307) pct 0.20000063809286803\n"
     ]
    }
   ],
   "source": [
    "# divide data with OHE into 3 groups using 3:1:1 (60%, 20%, 20%) ratio\n",
    "features_train, features_valid, target_train, target_valid = train_test_split(\n",
    "    features_ohe, target, test_size=0.4, random_state = 12345)\n",
    "features_valid, features_test, target_valid, target_test = train_test_split(\n",
    "    features_valid, target_valid, test_size=0.5, shuffle = False)\n",
    "print('Train target and features and percentage\\n', target_train.shape, features_train.shape,\n",
    "      'pct', (len(target_train)/len(df)))\n",
    "print('Valid target and features and percentage\\n', target_valid.shape, features_valid.shape,\n",
    "      'pct', (len(target_valid)/len(df)))\n",
    "print('Test target and features and percentage\\n', target_test.shape, features_test.shape,\n",
    "      'pct', (len(target_test)/len(df)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train target and features and percentage\n",
      " (188060,) (188060, 11) pct 0.5999987238142639\n",
      "Valid target and features and percentage\n",
      " (62687,) (62687, 11) pct 0.20000063809286803\n",
      "Test target and features and percentage\n",
      " (62687,) (62687, 11) pct 0.20000063809286803\n"
     ]
    }
   ],
   "source": [
    "# divide data without OHE into 3 groups using 3:1:1 (60%, 20%, 20%) ratio\n",
    "features_train_2, features_valid_2, target_train_2, target_valid_2 = train_test_split(\n",
    "    features, target, test_size=0.4, random_state = 12345)\n",
    "features_valid_2, features_test_2, target_valid_2, target_test_2 = train_test_split(\n",
    "    features_valid_2, target_valid_2, test_size=0.5, shuffle = False)\n",
    "\n",
    "print('Train target and features and percentage\\n', target_train_2.shape, features_train_2.shape,\n",
    "      'pct', (len(target_train_2)/len(df)))\n",
    "print('Valid target and features and percentage\\n', target_valid_2.shape, features_valid_2.shape,\n",
    "      'pct', (len(target_valid_2)/len(df)))\n",
    "print('Test target and features and percentage\\n', target_test_2.shape, features_test_2.shape,\n",
    "      'pct', (len(target_test_2)/len(df)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up rmse calculation\n",
    "def find_rmse(target_test, predictions):\n",
    "    return round(mean_squared_error(target_test, predictions) ** 0.5, 2)\n",
    "rmse = make_scorer(find_rmse, greater_is_better=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Note on timing cells. We used %%time to find the total time elapsed in each cell. However, we wanted to save the time values in variables and discovered %%time does not allow that. Therefore, we manually timed training time and prediction time and took note that their total matched closely with the %%time.__\n",
    "\n",
    "__Looking at base models__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Linear Regression - Sanity Check\n",
      "RMSE: 2673.154220556299 Training time: 19.875536680221558 Prediction time: 0.2535219192504883\n",
      "CPU times: user 15.7 s, sys: 4.5 s, total: 20.2 s\n",
      "Wall time: 20.2 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# linear regression with default parameters\n",
    "lr_model = LinearRegression()\n",
    "\n",
    "start = time.time()\n",
    "lr_model.fit(features_train, target_train)\n",
    "end = time.time()\n",
    "lrtt = end - start\n",
    "\n",
    "start = time.time()\n",
    "predicted_valid = lr_model.predict(features_valid)\n",
    "end = time.time()\n",
    "lrpt = end - start\n",
    "\n",
    "lr_rmse_calc = mean_squared_error(target_valid, predicted_valid)**0.5\n",
    "\n",
    "print('Linear Regression - Sanity Check')\n",
    "print('RMSE:', lr_rmse_calc, 'Training time:', lrtt, 'Prediction time:', lrpt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Random Forest Regressor\n",
      "RMSE: 1727.9087596013774 Training time: 60.69512057304382 Prediction time: 0.6225581169128418\n",
      "CPU times: user 1min, sys: 139 ms, total: 1min\n",
      "Wall time: 1min 1s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# random forest regressor with default parameters\n",
    "rf_model = RandomForestRegressor(random_state=42)\n",
    "\n",
    "start = time.time()\n",
    "rf_model.fit(features_train, target_train)\n",
    "end = time.time()\n",
    "rftt = end - start\n",
    "\n",
    "start = time.time()\n",
    "predicted_valid = rf_model.predict(features_valid)\n",
    "end = time.time()\n",
    "rfpt = end - start\n",
    "\n",
    "rf_rmse_calc = mean_squared_error(target_valid, predicted_valid)**0.5\n",
    "\n",
    "print('Random Forest Regressor')\n",
    "print('RMSE:', rf_rmse_calc, 'Training time:', rftt, 'Prediction time:', rfpt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LightGBM with OHE\n",
      "RMSE: 1707.641861082534 Training time: 10.578785419464111 Prediction time: 1.1029925346374512\n",
      "CPU times: user 11.2 s, sys: 351 ms, total: 11.6 s\n",
      "Wall time: 11.7 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# lightGBM with OHE \n",
    "lg_model = lgb.LGBMRegressor(random_state=42)\n",
    "\n",
    "start = time.time()\n",
    "lg_model.fit(features_train, target_train)\n",
    "end = time.time()\n",
    "lgohett = end - start\n",
    "\n",
    "start = time.time()\n",
    "predicted_valid = lg_model.predict(features_valid)\n",
    "end = time.time()\n",
    "lgohept = end - start\n",
    "\n",
    "lgohe_rmse_calc = mean_squared_error(target_valid, predicted_valid)**0.5\n",
    "\n",
    "print('LightGBM with OHE')\n",
    "print('RMSE:', lgohe_rmse_calc, 'Training time:', lgohett, 'Prediction time:', lgohept)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LightGBM without OHE\n",
      "RMSE: 1643.351067294688 Training time: 8.479040384292603 Prediction time: 0.9047174453735352\n",
      "CPU times: user 9.2 s, sys: 43.4 ms, total: 9.24 s\n",
      "Wall time: 9.39 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# lightGBM without OHE \n",
    "lg_model_2 = lgb.LGBMRegressor(random_state=42)\n",
    "\n",
    "start = time.time()\n",
    "lg_model_2.fit(features_train_2, target_train_2, categorical_feature=categories)\n",
    "end = time.time()\n",
    "lgtt = end - start\n",
    "\n",
    "start = time.time()\n",
    "predicted_valid = lg_model_2.predict(features_valid_2)\n",
    "end = time.time()\n",
    "lgpt = end - start\n",
    "\n",
    "lg_rmse_calc = mean_squared_error(target_valid_2, predicted_valid)**0.5\n",
    "\n",
    "print('LightGBM without OHE')\n",
    "print('RMSE:', lg_rmse_calc, 'Training time:', lgtt, 'Prediction time:', lgpt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "999:\tlearn: 1670.5789370\ttotal: 2m 26s\tremaining: 0us\n",
      "CatBoost with OHE\n",
      "RMSE: 1703.817876905744 Training time: 153.08609819412231 Prediction time: 0.21335506439208984\n",
      "CPU times: user 2min 13s, sys: 16.5 s, total: 2min 29s\n",
      "Wall time: 2min 33s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# CatBoost with OHE \n",
    "cb_model = CatBoostRegressor(random_state=42)\n",
    "\n",
    "start = time.time()\n",
    "cb_model.fit(features_train, target_train)\n",
    "end = time.time()\n",
    "cbohett = end - start\n",
    "\n",
    "start = time.time()\n",
    "predicted_valid = cb_model.predict(features_valid)\n",
    "end = time.time()\n",
    "cbohept = end - start\n",
    "\n",
    "cbohe_rmse_calc = mean_squared_error(target_valid, predicted_valid)**0.5\n",
    "\n",
    "print('CatBoost with OHE')\n",
    "print('RMSE:', cbohe_rmse_calc, 'Training time:', cbohett, 'Prediction time:', cbohept)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "997:\tlearn: 1636.5701431\ttotal: 8m 16s\tremaining: 996ms\n",
      "998:\tlearn: 1636.4409173\ttotal: 8m 17s\tremaining: 498ms\n",
      "999:\tlearn: 1636.3651039\ttotal: 8m 18s\tremaining: 0us\n",
      "CatBoost without OHE\n",
      "RMSE: 1683.0274262756113 Training time: 501.59921288490295 Prediction time: 0.4114964008331299\n",
      "CPU times: user 7min 28s, sys: 48.7 s, total: 8min 17s\n",
      "Wall time: 8min 22s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# CatBoost without OHE \n",
    "cb_model = CatBoostRegressor(random_state=42)\n",
    "\n",
    "start = time.time()\n",
    "cb_model.fit(features_train_2, target_train_2, cat_features=categories)\n",
    "end = time.time()\n",
    "cbtt = end - start\n",
    "\n",
    "start = time.time()\n",
    "predicted_valid = cb_model.predict(features_valid_2)\n",
    "end = time.time()\n",
    "cbpt = end - start\n",
    "\n",
    "cb_rmse_calc = mean_squared_error(target_valid_2, predicted_valid)**0.5\n",
    "\n",
    "print('CatBoost without OHE')\n",
    "print('RMSE:', cb_rmse_calc, 'Training time:', cbtt, 'Prediction time:', cbpt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Linear Regression - Sanity Check\n",
      "RMSE: 2673.154220556299 Training time: 19.875536680221558 Prediction time: 0.2535219192504883\n",
      "\n",
      "Random Forest Regressor\n",
      "RMSE: 1727.9087596013774 Training time: 60.69512057304382 Prediction time: 0.6225581169128418\n",
      "\n",
      "LightGBM with OHE\n",
      "RMSE: 1707.641861082534 Training time: 10.578785419464111 Prediction time: 1.1029925346374512\n",
      "\n",
      "LightGBM without OHE\n",
      "RMSE: 1643.351067294688 Training time: 8.479040384292603 Prediction time: 0.9047174453735352\n",
      "\n",
      "CatBoost with OHE\n",
      "RMSE: 1703.817876905744 Training time: 153.08609819412231 Prediction time: 0.21335506439208984\n",
      "\n",
      "CatBoost without OHE\n",
      "RMSE: 1683.0274262756113 Training time: 501.59921288490295 Prediction time: 0.4114964008331299\n"
     ]
    }
   ],
   "source": [
    "print('Linear Regression - Sanity Check')\n",
    "print('RMSE:', lr_rmse_calc, 'Training time:', lrtt, 'Prediction time:', lrpt)\n",
    "print('\\nRandom Forest Regressor')\n",
    "print('RMSE:', rf_rmse_calc, 'Training time:', rftt, 'Prediction time:', rfpt)\n",
    "print('\\nLightGBM with OHE')\n",
    "print('RMSE:', lgohe_rmse_calc, 'Training time:', lgohett, 'Prediction time:', lgohept)\n",
    "print('\\nLightGBM without OHE')\n",
    "print('RMSE:', lg_rmse_calc, 'Training time:', lgtt, 'Prediction time:', lgpt)\n",
    "print('\\nCatBoost with OHE')\n",
    "print('RMSE:', cbohe_rmse_calc, 'Training time:', cbohett, 'Prediction time:', cbohept)\n",
    "print('\\nCatBoost without OHE')\n",
    "print('RMSE:', cb_rmse_calc, 'Training time:', cbtt, 'Prediction time:', cbpt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__We note the RMSE and the times required for training and prediction__\n",
    "\n",
    "- All the models perform better on RMSE (goodness of fit) than linear regression, which we expected.\n",
    "- LightGBM without One Hot Encoding provides the best RMSE, but all the values besides linear regression are pretty close.\n",
    "- The training times of the base models range from around 20 seconds with LightGBM to just over 500 seconds with CatBoost.\n",
    "- The prediction times of the base models range from around .2 seconds (CatBoost) to close to 1.2 with LightGBM w/OHE.\n",
    "- Since the model needs to be trained once, the prediction time is actually more relevant for running multiple predictions. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Tuning hyperparameters__\n",
    "\n",
    "- We will look at n_estimators with RandomForestRegressor\n",
    "- We will tune parameters of CatBoost and LightGBM using both with and without OHE since there is variable performance [LightGBMdoc](https://lightgbm.readthedocs.io/en/latest/Advanced-Topics.html), [CatBoost](https://catboost.ai/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting 5 folds for each of 4 candidates, totalling 20 fits\n",
      "[CV] n_estimators=10 .................................................\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[CV] ................. n_estimators=10, score=-1772.600, total=  48.5s\n",
      "[CV] n_estimators=10 .................................................\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:   48.5s remaining:    0.0s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[CV] ................. n_estimators=10, score=-1711.530, total=  47.8s\n",
      "[CV] n_estimators=10 .................................................\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done   2 out of   2 | elapsed:  1.6min remaining:    0.0s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[CV] ................. n_estimators=10, score=-1736.270, total=  48.7s\n",
      "[CV] n_estimators=10 .................................................\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done   3 out of   3 | elapsed:  2.4min remaining:    0.0s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[CV] ................. n_estimators=10, score=-1717.170, total=  48.1s\n",
      "[CV] n_estimators=10 .................................................\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done   4 out of   4 | elapsed:  3.2min remaining:    0.0s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[CV] ................. n_estimators=10, score=-1741.730, total=  48.8s\n",
      "[CV] n_estimators=15 .................................................\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done   5 out of   5 | elapsed:  4.0min remaining:    0.0s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[CV] ................. n_estimators=15, score=-1744.790, total= 1.2min\n",
      "[CV] n_estimators=15 .................................................\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done   6 out of   6 | elapsed:  5.2min remaining:    0.0s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[CV] ................. n_estimators=15, score=-1686.140, total= 1.2min\n",
      "[CV] n_estimators=15 .................................................\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done   7 out of   7 | elapsed:  6.4min remaining:    0.0s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[CV] ................. n_estimators=15, score=-1710.780, total= 1.2min\n",
      "[CV] n_estimators=15 .................................................\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done   8 out of   8 | elapsed:  7.6min remaining:    0.0s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[CV] ................. n_estimators=15, score=-1692.710, total= 1.2min\n",
      "[CV] n_estimators=15 .................................................\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done   9 out of   9 | elapsed:  8.8min remaining:    0.0s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[CV] ................. n_estimators=15, score=-1719.410, total= 1.2min\n",
      "[CV] n_estimators=20 .................................................\n",
      "[CV] ................. n_estimators=20, score=-1729.780, total= 1.6min\n",
      "[CV] n_estimators=20 .................................................\n",
      "[CV] ................. n_estimators=20, score=-1676.970, total= 1.6min\n",
      "[CV] n_estimators=20 .................................................\n",
      "[CV] ................. n_estimators=20, score=-1704.250, total= 1.6min\n",
      "[CV] n_estimators=20 .................................................\n",
      "[CV] ................. n_estimators=20, score=-1678.980, total= 1.6min\n",
      "[CV] n_estimators=20 .................................................\n",
      "[CV] ................. n_estimators=20, score=-1708.880, total= 1.6min\n",
      "[CV] n_estimators=25 .................................................\n",
      "[CV] ................. n_estimators=25, score=-1722.470, total= 2.2min\n",
      "[CV] n_estimators=25 .................................................\n",
      "[CV] ................. n_estimators=25, score=-1668.740, total= 2.1min\n",
      "[CV] n_estimators=25 .................................................\n",
      "[CV] ................. n_estimators=25, score=-1694.250, total= 2.0min\n",
      "[CV] n_estimators=25 .................................................\n",
      "[CV] ................. n_estimators=25, score=-1669.860, total= 2.4min\n",
      "[CV] n_estimators=25 .................................................\n",
      "[CV] ................. n_estimators=25, score=-1700.940, total= 2.1min\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done  20 out of  20 | elapsed: 28.7min finished\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best parameters: {'n_estimators': 25}\n",
      "RMSE: 1681.12\n",
      "CPU times: user 30min 46s, sys: 1.88 s, total: 30min 48s\n",
      "Wall time: 31min 22s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "rf_model = RandomForestRegressor(random_state=42)\n",
    "params = { 'n_estimators': range(10, 30, 5) }\n",
    "\n",
    "best_model = RandomizedSearchCV(rf_model, params, scoring=rmse, cv=5, verbose=10)\n",
    "best_model.fit(features_train, target_train)  \n",
    "print('Best parameters:', best_model.best_params_)\n",
    "\n",
    "predictions = best_model.best_estimator_.predict(features_valid)\n",
    "print('RMSE:', round(mean_squared_error(target_valid, predictions) ** 0.5, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Tuning for Random Forest Regressor__\n",
    "\n",
    "__Print and copy results so we don't run use another 30 minute block by running the code__\n",
    "\n",
    "Fitting 5 folds for each of 4 candidates, totalling 20 fits\n",
    "[CV] n_estimators=10 .................................................\n",
    "[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.\n",
    "[CV] ................. n_estimators=10, score=-1772.600, total=  49.3s\n",
    "[CV] n_estimators=10 .................................................\n",
    "[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:   49.3s remaining:    0.0s\n",
    "[CV] ................. n_estimators=10, score=-1711.530, total=  49.8s\n",
    "[CV] n_estimators=10 .................................................\n",
    "[Parallel(n_jobs=1)]: Done   2 out of   2 | elapsed:  1.7min remaining:    0.0s\n",
    "[CV] ................. n_estimators=10, score=-1736.270, total=  49.9s\n",
    "[CV] n_estimators=10 .................................................\n",
    "[Parallel(n_jobs=1)]: Done   3 out of   3 | elapsed:  2.5min remaining:    0.0s\n",
    "[CV] ................. n_estimators=10, score=-1717.170, total=  49.5s\n",
    "[CV] n_estimators=10 .................................................\n",
    "[Parallel(n_jobs=1)]: Done   4 out of   4 | elapsed:  3.3min remaining:    0.0s\n",
    "[CV] ................. n_estimators=10, score=-1741.730, total=  48.3s\n",
    "[CV] n_estimators=15 .................................................\n",
    "[Parallel(n_jobs=1)]: Done   5 out of   5 | elapsed:  4.1min remaining:    0.0s\n",
    "[CV] ................. n_estimators=15, score=-1744.790, total= 1.2min\n",
    "[CV] n_estimators=15 .................................................\n",
    "[Parallel(n_jobs=1)]: Done   6 out of   6 | elapsed:  5.3min remaining:    0.0s\n",
    "[CV] ................. n_estimators=15, score=-1686.140, total= 1.2min\n",
    "[CV] n_estimators=15 .................................................\n",
    "[Parallel(n_jobs=1)]: Done   7 out of   7 | elapsed:  6.6min remaining:    0.0s\n",
    "[CV] ................. n_estimators=15, score=-1710.780, total= 1.2min\n",
    "[CV] n_estimators=15 .................................................\n",
    "[Parallel(n_jobs=1)]: Done   8 out of   8 | elapsed:  7.7min remaining:    0.0s\n",
    "[CV] ................. n_estimators=15, score=-1692.710, total= 1.2min\n",
    "[CV] n_estimators=15 .................................................\n",
    "[Parallel(n_jobs=1)]: Done   9 out of   9 | elapsed:  8.9min remaining:    0.0s\n",
    "[CV] ................. n_estimators=15, score=-1719.410, total= 1.2min\n",
    "[CV] n_estimators=20 .................................................\n",
    "[CV] ................. n_estimators=20, score=-1729.780, total= 1.6min\n",
    "[CV] n_estimators=20 .................................................\n",
    "[CV] ................. n_estimators=20, score=-1676.970, total= 1.6min\n",
    "[CV] n_estimators=20 .................................................\n",
    "[CV] ................. n_estimators=20, score=-1704.250, total= 1.6min\n",
    "[CV] n_estimators=20 .................................................\n",
    "[CV] ................. n_estimators=20, score=-1678.980, total= 1.6min\n",
    "[CV] n_estimators=20 .................................................\n",
    "[CV] ................. n_estimators=20, score=-1708.880, total= 1.6min\n",
    "[CV] n_estimators=25 .................................................\n",
    "[CV] ................. n_estimators=25, score=-1722.470, total= 2.0min\n",
    "[CV] n_estimators=25 .................................................\n",
    "[CV] ................. n_estimators=25, score=-1668.740, total= 2.1min\n",
    "[CV] n_estimators=25 .................................................\n",
    "[CV] ................. n_estimators=25, score=-1694.250, total= 2.0min\n",
    "[CV] n_estimators=25 .................................................\n",
    "[CV] ................. n_estimators=25, score=-1669.860, total= 2.0min\n",
    "[CV] n_estimators=25 .................................................\n",
    "[CV] ................. n_estimators=25, score=-1700.940, total= 2.0min\n",
    "[Parallel(n_jobs=1)]: Done  20 out of  20 | elapsed: 28.1min finished\n",
    "Best parameters: {'n_estimators': 25}\n",
    "RMSE: 1681.06\n",
    "CPU times: user 30min 16s, sys: 2.41 s, total: 30min 19s\n",
    "Wall time: 30min 45s\n",
    "\n",
    "Best parameters: {'n_estimators': 25}\n",
    "\n",
    "RMSE: 1681.06\n",
    "\n",
    "CPU times: user 30min 16s, sys: 2.41 s, total: 30min 19s\n",
    "\n",
    "Wall time: 30min 45s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting 5 folds for each of 10 candidates, totalling 50 fits\n",
      "[CV] n_estimators=10, learning_rate=0.25 .............................\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.\n"
     ]
    },
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      "[CV]  n_estimators=10, learning_rate=0.25, score=-2082.430, total=   4.2s\n",
      "[CV] n_estimators=10, learning_rate=0.25 .............................\n"
     ]
    },
    {
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      "[CV]  n_estimators=10, learning_rate=0.25, score=-2065.370, total=   3.8s\n",
      "[CV] n_estimators=10, learning_rate=0.25 .............................\n"
     ]
    },
    {
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      "[CV]  n_estimators=10, learning_rate=0.25, score=-2064.070, total=   4.0s\n",
      "[CV] n_estimators=10, learning_rate=0.25 .............................\n"
     ]
    },
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      "[CV]  n_estimators=10, learning_rate=0.25, score=-2063.230, total=   3.9s\n",
      "[CV] n_estimators=10, learning_rate=0.25 .............................\n"
     ]
    },
    {
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      "[CV]  n_estimators=10, learning_rate=0.25, score=-2084.950, total=   4.0s\n",
      "[CV] n_estimators=15, learning_rate=0.5 ..............................\n"
     ]
    },
    {
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      "[CV] n_estimators=15, learning_rate=0.5 ..............................\n"
     ]
    },
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      "[CV] n_estimators=15, learning_rate=0.5 ..............................\n"
     ]
    },
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      "[CV] n_estimators=15, learning_rate=0.5 ..............................\n"
     ]
    },
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      "[CV] n_estimators=15, learning_rate=0.5 ..............................\n"
     ]
    },
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      "[CV]  n_estimators=15, learning_rate=0.5, score=-1885.590, total=   5.2s\n",
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      "[CV]  n_estimators=20, learning_rate=0.25, score=-1909.020, total=   6.4s\n",
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      "[CV]  n_estimators=20, learning_rate=0.25, score=-1891.540, total=   6.2s\n",
      "[CV] n_estimators=20, learning_rate=0.25 .............................\n",
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      "[CV] n_estimators=20, learning_rate=0.25 .............................\n",
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      "[CV] n_estimators=20, learning_rate=0.5 ..............................\n",
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      "[CV] n_estimators=20, learning_rate=0.5 ..............................\n",
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      "[CV]  n_estimators=20, learning_rate=0.5, score=-1830.860, total=   6.1s\n",
      "[CV] n_estimators=20, learning_rate=0.5 ..............................\n",
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      "[CV]  n_estimators=20, learning_rate=0.5, score=-1818.670, total=   6.1s\n",
      "[CV] n_estimators=20, learning_rate=0.5 ..............................\n",
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      "[CV] n_estimators=20, learning_rate=0.5 ..............................\n",
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      "[CV] n_estimators=25, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=25, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=25, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=10, learning_rate=0.5 ..............................\n",
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      "[CV] n_estimators=10, learning_rate=0.5 ..............................\n",
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      "[CV] n_estimators=10, learning_rate=0.5 ..............................\n",
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      "[CV] n_estimators=10, learning_rate=0.5 ..............................\n",
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      "[CV] n_estimators=15, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=15, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=15, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=20, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=20, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=20, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=20, learning_rate=0.75 .............................\n",
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      "[CV]  n_estimators=20, learning_rate=0.75, score=-1803.040, total=   6.1s\n",
      "[CV] n_estimators=20, learning_rate=0.75 .............................\n",
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      "[CV]  n_estimators=20, learning_rate=0.75, score=-1836.430, total=   6.1s\n",
      "[CV] n_estimators=15, learning_rate=0.25 .............................\n",
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      "[CV]  n_estimators=15, learning_rate=0.25, score=-1962.760, total=   5.0s\n",
      "[CV] n_estimators=15, learning_rate=0.25 .............................\n",
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     ]
    },
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      "CatBoost without OHE\n",
      "Best parameters: {'n_estimators': 25, 'learning_rate': 0.75}\n",
      "RMSE: 1792.03\n",
      "CPU times: user 3min 31s, sys: 22.8 s, total: 3min 54s\n",
      "Wall time: 4min 51s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# CatBoost without OHE\n",
    "cb_model_2 = CatBoostRegressor(random_state=42)\n",
    "params = { 'n_estimators': range(10, 30, 5), 'learning_rate': [.25, .5, .75] }\n",
    "\n",
    "best_model = RandomizedSearchCV(cb_model_2, params, scoring=rmse, cv=5, verbose=10)\n",
    "best_model.fit(features_train_2, target_train_2, cat_features=categories) \n",
    "predictions = best_model.best_estimator_.predict(features_valid_2)\n",
    "\n",
    "print('CatBoost without OHE')\n",
    "print('Best parameters:', best_model.best_params_)\n",
    "print('RMSE:', round(mean_squared_error(target_valid_2, predictions) ** 0.5, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Tuning for CatBoost without OHE__\n",
    "\n",
    "CatBoost without OHE\n",
    "\n",
    "Best parameters: {'n_estimators': 25, 'learning_rate': 0.75}\n",
    "\n",
    "RMSE: 1787.49\n",
    "\n",
    "CPU times: user 3min 42s, sys: 27.7 s, total: 4min 10s\n",
    "\n",
    "Wall time: 5min 8s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting 5 folds for each of 10 candidates, totalling 50 fits\n",
      "[CV] n_estimators=10, learning_rate=0.75 .............................\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.\n"
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      "[CV] n_estimators=10, learning_rate=0.75 .............................\n"
     ]
    },
    {
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      "[CV] n_estimators=10, learning_rate=0.75 .............................\n"
     ]
    },
    {
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      "[CV] n_estimators=10, learning_rate=0.75 .............................\n"
     ]
    },
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      "[CV] n_estimators=10, learning_rate=0.75 .............................\n"
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      "[CV]  n_estimators=15, learning_rate=0.75, score=-1868.320, total=   7.5s\n",
      "[CV] n_estimators=15, learning_rate=0.75 .............................\n"
     ]
    },
    {
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      "[Parallel(n_jobs=1)]: Done   8 out of   8 | elapsed:   56.9s remaining:    0.0s\n"
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      "[CV]  n_estimators=15, learning_rate=0.75, score=-1836.100, total=   7.6s\n",
      "[CV] n_estimators=15, learning_rate=0.75 .............................\n"
     ]
    },
    {
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      "[CV]  n_estimators=15, learning_rate=0.5, score=-1896.860, total=   7.8s\n",
      "[CV] n_estimators=15, learning_rate=0.5 ..............................\n",
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      "[CV]  n_estimators=15, learning_rate=0.5, score=-1890.080, total=   7.6s\n",
      "[CV] n_estimators=15, learning_rate=0.5 ..............................\n",
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      "[CV]  n_estimators=15, learning_rate=0.5, score=-1874.090, total=   8.0s\n",
      "[CV] n_estimators=15, learning_rate=0.5 ..............................\n",
      "0:\tlearn: 3254.0322062\ttotal: 47.7ms\tremaining: 668ms\n",
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      "14:\tlearn: 1884.1630501\ttotal: 1.83s\tremaining: 0us\n",
      "[CV]  n_estimators=15, learning_rate=0.5, score=-1895.500, total=   7.4s\n",
      "[CV] n_estimators=10, learning_rate=0.5 ..............................\n",
      "0:\tlearn: 3246.7078833\ttotal: 76.4ms\tremaining: 688ms\n",
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      "9:\tlearn: 1962.1322503\ttotal: 1.18s\tremaining: 0us\n",
      "[CV]  n_estimators=10, learning_rate=0.5, score=-1999.480, total=   7.2s\n",
      "[CV] n_estimators=10, learning_rate=0.5 ..............................\n",
      "0:\tlearn: 3260.4048698\ttotal: 78.3ms\tremaining: 705ms\n",
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      "[CV]  n_estimators=10, learning_rate=0.5, score=-1970.130, total=   6.7s\n",
      "[CV] n_estimators=10, learning_rate=0.5 ..............................\n",
      "0:\tlearn: 3276.6782381\ttotal: 62.4ms\tremaining: 562ms\n",
      "1:\tlearn: 2662.0988431\ttotal: 166ms\tremaining: 663ms\n",
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      "9:\tlearn: 1961.0428666\ttotal: 1.25s\tremaining: 0us\n",
      "[CV]  n_estimators=10, learning_rate=0.5, score=-1959.350, total=   6.8s\n",
      "[CV] n_estimators=10, learning_rate=0.5 ..............................\n",
      "0:\tlearn: 3256.9473510\ttotal: 86.1ms\tremaining: 775ms\n",
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      "9:\tlearn: 1965.1027906\ttotal: 1.18s\tremaining: 0us\n",
      "[CV]  n_estimators=10, learning_rate=0.5, score=-1951.310, total=   7.0s\n",
      "[CV] n_estimators=10, learning_rate=0.5 ..............................\n",
      "0:\tlearn: 3254.0322062\ttotal: 59ms\tremaining: 531ms\n",
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      "[CV]  n_estimators=10, learning_rate=0.5, score=-1973.070, total=   6.9s\n",
      "[CV] n_estimators=25, learning_rate=0.75 .............................\n",
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      "[CV]  n_estimators=25, learning_rate=0.75, score=-1818.200, total=   8.7s\n",
      "[CV] n_estimators=25, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=20, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=25, learning_rate=0.25 .............................\n",
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      "[CV] n_estimators=25, learning_rate=0.25 .............................\n",
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      "[CV] n_estimators=25, learning_rate=0.25 .............................\n",
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      "[CV] n_estimators=25, learning_rate=0.25 .............................\n",
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      "[CV] n_estimators=10, learning_rate=0.25 .............................\n",
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      "[CV] n_estimators=10, learning_rate=0.25 .............................\n",
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      "[CV] n_estimators=10, learning_rate=0.25 .............................\n",
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      "[CV] n_estimators=10, learning_rate=0.25 .............................\n",
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      "[CV] n_estimators=10, learning_rate=0.25 .............................\n",
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      "[CV] n_estimators=20, learning_rate=0.25 .............................\n",
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     ]
    },
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      "CatBoost with OHE\n",
      "Best parameters: {'n_estimators': 25, 'learning_rate': 0.75}\n",
      "RMSE: 1814.42\n",
      "CPU times: user 5min 13s, sys: 27.8 s, total: 5min 41s\n",
      "Wall time: 6min 37s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# CatBoost with OHE\n",
    "cb_model = CatBoostRegressor(random_state=42)\n",
    "params = { 'n_estimators': range(10, 30, 5), 'learning_rate': [.25, .5, .75] }\n",
    "\n",
    "best_model = RandomizedSearchCV(cb_model, params, scoring=rmse, cv=5, verbose=10)\n",
    "best_model.fit(features_train, target_train) \n",
    "predictions = best_model.best_estimator_.predict(features_valid)\n",
    "\n",
    "print('CatBoost with OHE')\n",
    "print('Best parameters:', best_model.best_params_)\n",
    "print('RMSE:', round(mean_squared_error(target_valid, predictions) ** 0.5, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Tuning for CatBoost with OHE__\n",
    "\n",
    "CatBoost with OHE\n",
    "\n",
    "Best parameters: {'n_estimators': 25, 'learning_rate': 0.75}\n",
    "\n",
    "RMSE: 1814.42\n",
    "\n",
    "CPU times: user 5min 24s, sys: 27.8 s, total: 5min 52s\n",
    "\n",
    "Wall time: 6min 46s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting 5 folds for each of 10 candidates, totalling 50 fits\n",
      "[CV] n_estimators=20, learning_rate=0.25 .............................\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.\n"
     ]
    },
    {
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      "[CV]  n_estimators=20, learning_rate=0.25, score=-1819.550, total=  47.8s\n",
      "[CV] n_estimators=20, learning_rate=0.25 .............................\n"
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      "[CV] n_estimators=10, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=10, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=15, learning_rate=0.25 .............................\n",
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      "[CV] n_estimators=15, learning_rate=0.5 ..............................\n",
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      "[CV] n_estimators=15, learning_rate=0.5 ..............................\n",
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      "[CV] n_estimators=15, learning_rate=0.5 ..............................\n",
      "[CV]  n_estimators=15, learning_rate=0.5, score=-1775.360, total=   4.2s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done  50 out of  50 | elapsed: 22.9min finished\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LightGBM with OHE\n",
      "Best parameters: {'n_estimators': 25, 'learning_rate': 0.5}\n",
      "RMSE: 1731.09\n",
      "CPU times: user 22min 25s, sys: 20.5 s, total: 22min 45s\n",
      "Wall time: 22min 56s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# LIghtGBM with OHE\n",
    "lg_model = lgb.LGBMRegressor(random_state=42)\n",
    "params = { 'n_estimators': range(10, 30, 5), 'learning_rate': [.25, .5, .75] }\n",
    "\n",
    "best_model = RandomizedSearchCV(lg_model, params, scoring=rmse, cv=5, verbose=10)\n",
    "best_model.fit(features_train, target_train) \n",
    "predictions = best_model.best_estimator_.predict(features_valid)\n",
    "\n",
    "print('LightGBM with OHE')\n",
    "print('Best parameters:', best_model.best_params_)\n",
    "print('RMSE:', round(mean_squared_error(target_valid, predictions) ** 0.5, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Tuning for LightGBM with OHE__\n",
    "\n",
    "LightGBM with OHE\n",
    "\n",
    "Best parameters: {'n_estimators': 25, 'learning_rate': 0.5}\n",
    "\n",
    "RMSE: 1731.08\n",
    "\n",
    "CPU times: user 3min 14s, sys: 14.1 s, total: 3min 28s\n",
    "\n",
    "Wall time: 3min 30s\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting 5 folds for each of 10 candidates, totalling 50 fits\n",
      "[CV] n_estimators=20, learning_rate=0.25 .............................\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[CV]  n_estimators=20, learning_rate=0.25, score=-1722.390, total=   3.1s\n",
      "[CV] n_estimators=20, learning_rate=0.25 .............................\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    3.1s remaining:    0.0s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
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      "[CV]  n_estimators=20, learning_rate=0.25, score=-1692.810, total=   2.1s\n",
      "[CV] n_estimators=20, learning_rate=0.25 .............................\n"
     ]
    },
    {
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     "output_type": "stream",
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      "[Parallel(n_jobs=1)]: Done   2 out of   2 | elapsed:    5.2s remaining:    0.0s\n"
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      "[CV]  n_estimators=20, learning_rate=0.25, score=-1700.010, total=   2.0s\n",
      "[CV] n_estimators=20, learning_rate=0.25 .............................\n"
     ]
    },
    {
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     "output_type": "stream",
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      "[Parallel(n_jobs=1)]: Done   3 out of   3 | elapsed:    7.2s remaining:    0.0s\n"
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    {
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      "[CV]  n_estimators=20, learning_rate=0.25, score=-1682.490, total=   2.1s\n",
      "[CV] n_estimators=20, learning_rate=0.25 .............................\n"
     ]
    },
    {
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      "[Parallel(n_jobs=1)]: Done   4 out of   4 | elapsed:    9.4s remaining:    0.0s\n"
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      "[CV]  n_estimators=20, learning_rate=0.25, score=-1704.770, total=   2.3s\n",
      "[CV] n_estimators=10, learning_rate=0.25 .............................\n"
     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done   5 out of   5 | elapsed:   11.7s remaining:    0.0s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[CV]  n_estimators=10, learning_rate=0.25, score=-1860.680, total=   1.5s\n",
      "[CV] n_estimators=10, learning_rate=0.25 .............................\n"
     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done   6 out of   6 | elapsed:   13.2s remaining:    0.0s\n"
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      "[CV]  n_estimators=10, learning_rate=0.25, score=-1837.940, total=   1.4s\n",
      "[CV] n_estimators=10, learning_rate=0.25 .............................\n"
     ]
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      "[CV]  n_estimators=10, learning_rate=0.25, score=-1833.680, total=   1.4s\n",
      "[CV] n_estimators=10, learning_rate=0.25 .............................\n"
     ]
    },
    {
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      "[CV]  n_estimators=10, learning_rate=0.25, score=-1827.030, total=   1.5s\n",
      "[CV] n_estimators=10, learning_rate=0.25 .............................\n"
     ]
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      "[CV]  n_estimators=10, learning_rate=0.25, score=-1842.050, total=   1.5s\n",
      "[CV] n_estimators=15, learning_rate=0.5 ..............................\n",
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      "[CV] n_estimators=25, learning_rate=0.25 .............................\n",
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      "[CV] n_estimators=25, learning_rate=0.25 .............................\n",
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      "[CV] n_estimators=25, learning_rate=0.25 .............................\n",
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      "[CV] n_estimators=20, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=15, learning_rate=0.25 .............................\n",
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      "[CV] n_estimators=15, learning_rate=0.25 .............................\n",
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      "[CV] n_estimators=15, learning_rate=0.25 .............................\n",
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      "[CV] n_estimators=15, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=15, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=15, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=15, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=15, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=10, learning_rate=0.5 ..............................\n",
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      "[CV] n_estimators=10, learning_rate=0.5 ..............................\n",
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      "[CV] n_estimators=25, learning_rate=0.75 .............................\n",
      "[CV]  n_estimators=25, learning_rate=0.75, score=-1742.300, total=   3.8s\n",
      "[CV] n_estimators=25, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=25, learning_rate=0.75 .............................\n",
      "[CV]  n_estimators=25, learning_rate=0.75, score=-1735.380, total=   2.2s\n",
      "[CV] n_estimators=25, learning_rate=0.75 .............................\n",
      "[CV]  n_estimators=25, learning_rate=0.75, score=-1721.240, total=   2.2s\n",
      "[CV] n_estimators=25, learning_rate=0.75 .............................\n",
      "[CV]  n_estimators=25, learning_rate=0.75, score=-1725.040, total=   2.2s\n",
      "[CV] n_estimators=10, learning_rate=0.75 .............................\n",
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      "[CV] n_estimators=10, learning_rate=0.75 .............................\n",
      "[CV]  n_estimators=10, learning_rate=0.75, score=-1796.250, total=   1.4s\n",
      "[CV] n_estimators=10, learning_rate=0.75 .............................\n",
      "[CV]  n_estimators=10, learning_rate=0.75, score=-1800.600, total=   1.2s\n",
      "[CV] n_estimators=10, learning_rate=0.75 .............................\n",
      "[CV]  n_estimators=10, learning_rate=0.75, score=-1770.670, total=   1.3s\n",
      "[CV] n_estimators=10, learning_rate=0.75 .............................\n",
      "[CV]  n_estimators=10, learning_rate=0.75, score=-1788.290, total=   1.6s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done  50 out of  50 | elapsed:  1.6min finished\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LightGBM without OHE\n",
      "Best parameters: {'n_estimators': 25, 'learning_rate': 0.25}\n",
      "RMSE: 1693.93\n",
      "CPU times: user 1min 42s, sys: 372 ms, total: 1min 42s\n",
      "Wall time: 1min 43s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# LightGBM without OHE\n",
    "lg_model_2 = lgb.LGBMRegressor(random_state=42)\n",
    "params = { 'n_estimators': range(10, 30, 5), 'learning_rate': [.25, .5, .75] }\n",
    "\n",
    "best_model = RandomizedSearchCV(lg_model_2, params, scoring=rmse, cv=5, verbose=10)\n",
    "best_model.fit(features_train_2, target_train_2, categorical_feature=categories)  \n",
    "predictions = best_model.best_estimator_.predict(features_valid_2)\n",
    "\n",
    "print('LightGBM without OHE')\n",
    "print('Best parameters:', best_model.best_params_)\n",
    "print('RMSE:', round(mean_squared_error(target_valid_2, predictions) ** 0.5, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Tuning for LightGBM without OHE__\n",
    "\n",
    "LightGBM without OHE\n",
    "\n",
    "Best parameters: {'n_estimators': 25, 'learning_rate': 0.25}\n",
    "\n",
    "RMSE: 1693.92\n",
    "\n",
    "CPU times: user 4min 59s, sys: 960 ms, total: 5min\n",
    "\n",
    "Wall time: 5min 3s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Fit models with best parameters__\n",
    "\n",
    "- We will use the combined data from the train and valid datasets because that gives us a slightly better RMSE score (we compared previously).\n",
    "- We will compare tuned and untuned versions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Random Forest Regressor with test data\n",
      "RMSE: 1660.958400832672 Training time: 220.39202785491943 Prediction time: 1.481811285018921\n",
      "CPU times: user 3min 37s, sys: 331 ms, total: 3min 37s\n",
      "Wall time: 3min 41s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# random forest regressor with test data\n",
    "# Best parameters: {'n_estimators': 25}\n",
    "rf_test = RandomForestRegressor(random_state=42, n_estimators = 25)\n",
    "\n",
    "start = time.time()\n",
    "# fit with train and valid data\n",
    "rf_test.fit(pd.concat([features_train, features_valid]), pd.concat([target_train, target_valid]))\n",
    "end = time.time()\n",
    "test_rftt = end - start\n",
    "\n",
    "start = time.time()\n",
    "test_pred = rf_test.predict(features_test)\n",
    "end = time.time()\n",
    "test_rfpt = end - start\n",
    "\n",
    "test_rf_rmse_calc = mean_squared_error(target_test, test_pred)**0.5\n",
    "\n",
    "print('Random Forest Regressor with test data')\n",
    "print('RMSE:', test_rf_rmse_calc, 'Training time:', test_rftt, 'Prediction time:', test_rfpt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0:\tlearn: 2799.7902845\ttotal: 41.6ms\tremaining: 999ms\n",
      "1:\tlearn: 2392.2788678\ttotal: 242ms\tremaining: 2.78s\n",
      "2:\tlearn: 2242.0372998\ttotal: 438ms\tremaining: 3.21s\n",
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      "24:\tlearn: 1776.1357221\ttotal: 4.42s\tremaining: 0us\n",
      "CatBoost with OHE with test data\n",
      "RMSE: 1792.644534898325 Training time: 11.937709331512451 Prediction time: 0.015808820724487305\n",
      "CPU times: user 9.83 s, sys: 928 ms, total: 10.8 s\n",
      "Wall time: 12 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# CatBoost with OHE with test data\n",
    "# Best parameters: {'n_estimators': 25, 'learning_rate': 0.75}\n",
    "cb_test = CatBoostRegressor(random_state=42, n_estimators=25, learning_rate=0.75)\n",
    "\n",
    "start = time.time()\n",
    "# use combined train and valid datasets to fit on\n",
    "cb_test.fit(pd.concat([features_train, features_valid]), pd.concat([target_train, target_valid]))\n",
    "end = time.time()\n",
    "test_cbohett = end - start\n",
    "\n",
    "start = time.time()\n",
    "test_pred = cb_test.predict(features_test)\n",
    "end = time.time()\n",
    "test_cbohept = end - start\n",
    "\n",
    "test_cbohe_rmse_calc = mean_squared_error(target_test, test_pred)**0.5\n",
    "\n",
    "print('CatBoost with OHE with test data')\n",
    "print('RMSE:', test_cbohe_rmse_calc, 'Training time:', test_cbohett, 'Prediction time:', test_cbohept)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "24:\tlearn: 1774.7724777\ttotal: 8.57s\tremaining: 0us\n",
      "CatBoost without OHE with test data\n",
      "RMSE: 1790.8160057257508 Training time: 10.462419748306274 Prediction time: 0.058998823165893555\n",
      "CPU times: user 8.57 s, sys: 908 ms, total: 9.48 s\n",
      "Wall time: 10.5 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# CatBoost without initial one hot encoding\n",
    "# Best parameters: {'n_estimators': 25, 'learning_rate': 0.75}\n",
    "\n",
    "start = time.time()\n",
    "# use combined train and valid datasets to fit on\n",
    "cb_test_2 = CatBoostRegressor(random_state=42, n_estimators=25, learning_rate=0.75)\n",
    "cb_test_2.fit(pd.concat([features_train_2, features_valid_2]), pd.concat([target_train_2, target_valid_2]), cat_features=categories)\n",
    "end = time.time()\n",
    "test_cbtt = end - start\n",
    "\n",
    "start = time.time()\n",
    "test_pred = cb_test_2.predict(features_test_2)\n",
    "end = time.time()\n",
    "test_cbpt = end - start\n",
    "\n",
    "test_cb_rmse=mean_squared_error(target_test, test_pred)**0.5\n",
    "\n",
    "print('CatBoost without OHE with test data')\n",
    "print('RMSE:',test_cb_rmse, 'Training time:', test_cbtt, 'Prediction time:', test_cbpt) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LightGBM with OHE with test data\n",
      "RMSE: 1726.3591713044495 Training time: 5.873456001281738 Prediction time: 0.5961816310882568\n",
      "CPU times: user 6.02 s, sys: 391 ms, total: 6.41 s\n",
      "Wall time: 6.47 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# lightGBM with OHE with test data\n",
    "# Best parameters: {'n_estimators': 25, 'learning_rate': 0.5}\n",
    "lgohe_test = lgb.LGBMRegressor(random_state=42, n_estimators=25, learning_rate=0.5)\n",
    "\n",
    "start = time.time()\n",
    "# fit model on combined data from train and valid\n",
    "lgohe_test.fit(pd.concat([features_train, features_valid]), pd.concat([target_train, target_valid]))\n",
    "end = time.time()\n",
    "test_lgohett = end - start\n",
    "\n",
    "start = time.time()\n",
    "test_pred = lgohe_test.predict(features_test)\n",
    "end = time.time()\n",
    "test_lgohept = end - start\n",
    "\n",
    "test_lgohe_rmse_calc = mean_squared_error(target_test, test_pred)**0.5\n",
    "\n",
    "print('LightGBM with OHE with test data')\n",
    "print('RMSE:', test_lgohe_rmse_calc, 'Training time:', test_lgohett, 'Prediction time:', test_lgohept)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LightGBM without OHE\n",
      "RMSE: 1680.7187262024022 Training time: 3.1926093101501465 Prediction time: 0.29376220703125\n",
      "CPU times: user 3.46 s, sys: 5.31 ms, total: 3.46 s\n",
      "Wall time: 3.49 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# lightGBM without OHE with test data\n",
    "# Best parameters: {'n_estimators': 25, 'learning_rate': 0.25}\n",
    "lg_test = lgb.LGBMRegressor(random_state=42, n_estimators=25, learning_rate=0.25)\n",
    "\n",
    "start = time.time()\n",
    "# fit on combined data from train and valid\n",
    "lg_test.fit(pd.concat([features_train_2, features_valid_2]), pd.concat([target_train_2, target_valid_2]), categorical_feature=categories)\n",
    "end = time.time()\n",
    "test_lgtt = end - start\n",
    "\n",
    "start = time.time()\n",
    "test_pred = lg_test.predict(features_test_2)\n",
    "end = time.time()\n",
    "test_lgpt = end - start\n",
    "\n",
    "test_lg_rmse_calc = mean_squared_error(target_test_2, test_pred)**0.5\n",
    "\n",
    "print('LightGBM without OHE')\n",
    "print('RMSE:', test_lg_rmse_calc, 'Training time:', test_lgtt, 'Prediction time:', test_lgpt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Linear Regression - Sanity Check on test data\n",
      "RMSE: 2669.1918845974697 Prediction time: 0.1891636848449707\n"
     ]
    }
   ],
   "source": [
    "# linear regression base model with test data\n",
    "start = time.time()\n",
    "predicted_test = lr_model.predict(features_test)\n",
    "end = time.time()\n",
    "test_lrpt = end - start\n",
    "\n",
    "test_lr_rmse_calc = mean_squared_error(target_test, predicted_test)**0.5\n",
    "\n",
    "print('Linear Regression - Sanity Check on test data')\n",
    "print('RMSE:', test_lr_rmse_calc, 'Prediction time:', test_lrpt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results with test data of base models\n",
      "\n",
      "Random Forest Regressor\n",
      "RMSE: 1727.9087596013774 Training time: 60.69512057304382 Prediction time: 0.6225581169128418\n",
      "\n",
      "LightGBM with OHE\n",
      "RMSE: 1707.641861082534 Training time: 10.578785419464111 Prediction time: 1.1029925346374512\n",
      "\n",
      "LightGBM without OHE\n",
      "RMSE: 1643.351067294688 Training time: 8.479040384292603 Prediction time: 0.9047174453735352\n",
      "\n",
      "CatBoost with OHE\n",
      "RMSE: 1703.817876905744 Training time: 153.08609819412231 Prediction time: 0.21335506439208984\n",
      "\n",
      "CatBoost without OHE\n",
      "RMSE: 1683.0274262756113 Training time: 501.59921288490295 Prediction time: 0.4114964008331299\n",
      "\n",
      "Linear Regression - Sanity Check\n",
      "RMSE: 2673.154220556299 Training time: 19.875536680221558 Prediction time: 0.2535219192504883\n"
     ]
    }
   ],
   "source": [
    "print('Results with test data of base models\\n')\n",
    "\n",
    "print('Random Forest Regressor')\n",
    "print('RMSE:', rf_rmse_calc, 'Training time:', rftt, 'Prediction time:', rfpt)\n",
    "print('\\nLightGBM with OHE')\n",
    "print('RMSE:', lgohe_rmse_calc, 'Training time:', lgohett, 'Prediction time:', lgohept)\n",
    "print('\\nLightGBM without OHE')\n",
    "print('RMSE:', lg_rmse_calc, 'Training time:', lgtt, 'Prediction time:', lgpt)\n",
    "print('\\nCatBoost with OHE')\n",
    "print('RMSE:', cbohe_rmse_calc, 'Training time:', cbohett, 'Prediction time:', cbohept)\n",
    "print('\\nCatBoost without OHE')\n",
    "print('RMSE:', cb_rmse_calc, 'Training time:', cbtt, 'Prediction time:', cbpt)\n",
    "print('\\nLinear Regression - Sanity Check')\n",
    "print('RMSE:', lr_rmse_calc, 'Training time:', lrtt, 'Prediction time:', lrpt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results with test data of tuned models\n",
      "\n",
      "Random Forest Regressor with test data\n",
      "RMSE: 1660.958400832672 Training time: 220.39202785491943 Prediction time: 1.481811285018921\n",
      "\n",
      "CatBoost with OHE with test data\n",
      "RMSE: 1792.644534898325 Training time: 11.937709331512451 Prediction time: 0.015808820724487305\n",
      "\n",
      "CatBoost without OHE with test data\n",
      "RMSE: 1790.8160057257508 Training time: 10.462419748306274 Prediction time: 0.058998823165893555\n",
      "\n",
      "LightGBM with OHE with test data\n",
      "RMSE: 1726.3591713044495 Training time: 5.873456001281738 Prediction time: 0.5961816310882568\n",
      "\n",
      "LightGBM without OHE\n",
      "RMSE: 1680.7187262024022 Training time: 3.1926093101501465 Prediction time: 0.29376220703125\n",
      "\n",
      "Linear Regression - Sanity Check on test data\n",
      "RMSE: 2669.1918845974697 Prediction time: 0.1891636848449707\n"
     ]
    }
   ],
   "source": [
    "print('Results with test data of tuned models\\n')\n",
    "\n",
    "print('Random Forest Regressor with test data')\n",
    "print('RMSE:', test_rf_rmse_calc, 'Training time:', test_rftt, 'Prediction time:', test_rfpt)\n",
    "\n",
    "print('\\nCatBoost with OHE with test data')\n",
    "print('RMSE:', test_cbohe_rmse_calc, 'Training time:', test_cbohett, 'Prediction time:', test_cbohept)\n",
    "\n",
    "print('\\nCatBoost without OHE with test data')\n",
    "print('RMSE:',test_cb_rmse, 'Training time:', test_cbtt, 'Prediction time:', test_cbpt)\n",
    "\n",
    "print('\\nLightGBM with OHE with test data')\n",
    "print('RMSE:', test_lgohe_rmse_calc, 'Training time:', test_lgohett, 'Prediction time:', test_lgohept)\n",
    "\n",
    "print('\\nLightGBM without OHE')\n",
    "print('RMSE:', test_lg_rmse_calc, 'Training time:', test_lgtt, 'Prediction time:', test_lgpt)\n",
    "\n",
    "print('\\nLinear Regression - Sanity Check on test data')\n",
    "print('RMSE:', test_lr_rmse_calc, 'Prediction time:', test_lrpt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__We were tasked with finding the RMSE, the training time and the prediction time__\n",
    "\n",
    "\n",
    "- Tuning the Random Forest Regressor model did improve the goodness of fit as evidenced by a lower RMSE, but tuning also more than doubled the time for predictions and training.\n",
    "- The RMSE for CatBoost and LightGBM did not benefit from my implementation of performance tuning.\n",
    "- However, tuning the parameters decreased the prediction time dramatically.\n",
    "- The best RMSE for both tuned and untuned models is LightGBM without OHE. This matches nicely with [documentation of LightGBM](https://lightgbm.readthedocs.io/en/latest/Advanced-Topics.html). It states LightGBM \"offers good accuracy with integer-encoded categorical features. LightGBM applies Fisher (1958) to find the optimal split over categories as described here. This often performs better than one-hot encoding.\"\n",
    "- LightGBM, both with and without OHE, had the fastest prediction speeds. CatBoost had the slowest.\n",
    "- LightGBM had lower prediction times, and tuning the model lowered them further.\n",
    "- While the tuned Random Forest Regressor has the lowest RMSE, it also has the highest prediction time, over double of the second longest. The slight gains in RMSE over LIghtGBM without OHE doesn't compensate for the large increase in prediction time.\n",
    "\n",
    "__Recommendation__\n",
    "\n",
    "- We recommend the tuned LightGBM without One Hot Encoding. It has the 3rd lowest RMSE scores, but also has a fast training time, just over 11 seconds, and an impressive prediction time of about 1/5th of a second."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Timing cells](https://stackoverflow.com/questions/52738709/how-to-store-time-values-in-a-variable-in-jupyter)\n",
    "\n",
    "[simple function to time execution of cell](https://stackoverflow.com/questions/52738709/how-to-store-time-values-in-a-variable-in-jupyter)\n",
    "\n",
    "[LightGBM often performs better without OHE](https://lightgbm.readthedocs.io/en/latest/Advanced-Topics.html)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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