bike_rentals_project.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Bike Rental Prediction Project"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This project investigates communal bike rentals in Washington, D.C. Many cities have bike stations where people can rent bikes by the hour or day. This dataset contains 17380 rows, where each row represents the number of bike rentals for a single hour in a given day. The dataset contains the following columns:\n",
    "\n",
    "instant - A unique sequential ID number for each row\n",
    "\n",
    "dteday - The date of the rentals\n",
    "\n",
    "season - The season in which the rentals occurred\n",
    "\n",
    "yr - The year the rentals occurred\n",
    "\n",
    "mnth - The month the rentals occurred\n",
    "\n",
    "hr - The hour the rentals occurred\n",
    "\n",
    "holiday - Whether or not the day was a holiday\n",
    "\n",
    "weekday - The day of the week (as a number, 0 to 7)\n",
    "\n",
    "workingday - Whether or not the day was a working day\n",
    "\n",
    "weathersit - The weather (as a categorical variable)\n",
    "\n",
    "temp - The temperature, on a 0-1 scale\n",
    "\n",
    "atemp - The adjusted temperature\n",
    "\n",
    "hum - The humidity, on a 0-1 scale\n",
    "\n",
    "windspeed - The wind speed, on a 0-1 scale\n",
    "\n",
    "casual - The number of casual riders (people who hadn't \n",
    "previously signed up with the bike sharing program)\n",
    "\n",
    "registered - The number of registered riders (people who had already signed up)\n",
    "\n",
    "cnt - The total number of bike rentals (casual + registered)\n",
    "\n",
    "The aim of the project is to predict the number of bike rentals in a given hour, using the cnt column. The project will utilize different machine learning models and compare the results. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import libraries and functions\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "pd.set_option(\"display.max_columns\", None)\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "from sklearn.metrics import mean_absolute_error\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.metrics import roc_auc_score\n",
    "\n",
    "from sklearn import linear_model\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "from sklearn.ensemble import RandomForestRegressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>instant</th>\n",
       "      <th>dteday</th>\n",
       "      <th>season</th>\n",
       "      <th>yr</th>\n",
       "      <th>mnth</th>\n",
       "      <th>hr</th>\n",
       "      <th>holiday</th>\n",
       "      <th>weekday</th>\n",
       "      <th>workingday</th>\n",
       "      <th>weathersit</th>\n",
       "      <th>temp</th>\n",
       "      <th>atemp</th>\n",
       "      <th>hum</th>\n",
       "      <th>windspeed</th>\n",
       "      <th>casual</th>\n",
       "      <th>registered</th>\n",
       "      <th>cnt</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2011-01-01</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.2879</td>\n",
       "      <td>0.81</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>13</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>2011-01-01</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.2727</td>\n",
       "      <td>0.80</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8</td>\n",
       "      <td>32</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>2011-01-01</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.2727</td>\n",
       "      <td>0.80</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5</td>\n",
       "      <td>27</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>2011-01-01</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.2879</td>\n",
       "      <td>0.75</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>10</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>2011-01-01</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.2879</td>\n",
       "      <td>0.75</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   instant      dteday  season  yr  mnth  hr  holiday  weekday  workingday  \\\n",
       "0        1  2011-01-01       1   0     1   0        0        6           0   \n",
       "1        2  2011-01-01       1   0     1   1        0        6           0   \n",
       "2        3  2011-01-01       1   0     1   2        0        6           0   \n",
       "3        4  2011-01-01       1   0     1   3        0        6           0   \n",
       "4        5  2011-01-01       1   0     1   4        0        6           0   \n",
       "\n",
       "   weathersit  temp   atemp   hum  windspeed  casual  registered  cnt  \n",
       "0           1  0.24  0.2879  0.81        0.0       3          13   16  \n",
       "1           1  0.22  0.2727  0.80        0.0       8          32   40  \n",
       "2           1  0.22  0.2727  0.80        0.0       5          27   32  \n",
       "3           1  0.24  0.2879  0.75        0.0       3          10   13  \n",
       "4           1  0.24  0.2879  0.75        0.0       0           1    1  "
      ]
     },
     "execution_count": 286,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# read csv file into a dataframe\n",
    "bike_rentals = pd.read_csv(\"bike_rental_hour.csv\")\n",
    "# explore first few rows of the data\n",
    "bike_rentals.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f787ccb1f60>"
      ]
     },
     "execution_count": 287,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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XKuZCGxEVB7vdjrS0NEyfPl1ZamltbUV2djYSEhKQk5ODtrY2Zf/S0lI4HA4kJSWhpqZG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\nByIiCsHiQEREIVgciIgoxP8DhA3uh4fN+48AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f787ce513c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# explore the distribution of the cnt column\n",
    "br_hist = bike_rentals[\"cnt\"].hist()\n",
    "br_hist.set_title(\"Count Distribution\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly the distribution of bike rentals is heavily skewed to the right. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 288,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "weekday       0.026900\n",
       "workingday    0.030284\n",
       "holiday       0.030927\n",
       "windspeed     0.093234\n",
       "mnth          0.120638\n",
       "weathersit    0.142426\n",
       "season        0.178056\n",
       "yr            0.250495\n",
       "instant       0.278379\n",
       "hum           0.322911\n",
       "hr            0.394071\n",
       "atemp         0.400929\n",
       "temp          0.404772\n",
       "casual        0.694564\n",
       "registered    0.972151\n",
       "cnt           1.000000\n",
       "Name: cnt, dtype: float64"
      ]
     },
     "execution_count": 288,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# explore correlations to cnt\n",
    "corr_values = bike_rentals.corr()[\"cnt\"].abs().sort_values()\n",
    "corr_values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to obtain better information from the hour (hr) column, I will write a function to group the hours into morning, afternoon, evening, and night. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "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>instant</th>\n",
       "      <th>dteday</th>\n",
       "      <th>season</th>\n",
       "      <th>yr</th>\n",
       "      <th>mnth</th>\n",
       "      <th>hr</th>\n",
       "      <th>holiday</th>\n",
       "      <th>weekday</th>\n",
       "      <th>workingday</th>\n",
       "      <th>weathersit</th>\n",
       "      <th>temp</th>\n",
       "      <th>atemp</th>\n",
       "      <th>hum</th>\n",
       "      <th>windspeed</th>\n",
       "      <th>casual</th>\n",
       "      <th>registered</th>\n",
       "      <th>cnt</th>\n",
       "      <th>time_label</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2011-01-01</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.2879</td>\n",
       "      <td>0.81</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>13</td>\n",
       "      <td>16</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>2011-01-01</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.2727</td>\n",
       "      <td>0.80</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8</td>\n",
       "      <td>32</td>\n",
       "      <td>40</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>2011-01-01</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.2727</td>\n",
       "      <td>0.80</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5</td>\n",
       "      <td>27</td>\n",
       "      <td>32</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>2011-01-01</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.2879</td>\n",
       "      <td>0.75</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>10</td>\n",
       "      <td>13</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>2011-01-01</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.2879</td>\n",
       "      <td>0.75</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   instant      dteday  season  yr  mnth  hr  holiday  weekday  workingday  \\\n",
       "0        1  2011-01-01       1   0     1   0        0        6           0   \n",
       "1        2  2011-01-01       1   0     1   1        0        6           0   \n",
       "2        3  2011-01-01       1   0     1   2        0        6           0   \n",
       "3        4  2011-01-01       1   0     1   3        0        6           0   \n",
       "4        5  2011-01-01       1   0     1   4        0        6           0   \n",
       "\n",
       "   weathersit  temp   atemp   hum  windspeed  casual  registered  cnt  \\\n",
       "0           1  0.24  0.2879  0.81        0.0       3          13   16   \n",
       "1           1  0.22  0.2727  0.80        0.0       8          32   40   \n",
       "2           1  0.22  0.2727  0.80        0.0       5          27   32   \n",
       "3           1  0.24  0.2879  0.75        0.0       3          10   13   \n",
       "4           1  0.24  0.2879  0.75        0.0       0           1    1   \n",
       "\n",
       "   time_label  \n",
       "0           4  \n",
       "1           4  \n",
       "2           4  \n",
       "3           4  \n",
       "4           4  "
      ]
     },
     "execution_count": 289,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create function to group hours\n",
    "def assign_label(x):\n",
    "    if x >= 0 and x < 6:\n",
    "        return 4\n",
    "    elif x >=6  and x < 12:\n",
    "        return 1\n",
    "    elif x >= 12 and x < 18:\n",
    "        return 2\n",
    "    elif x >= 18 and x <= 24:\n",
    "        return 3\n",
    "    \n",
    "bike_rentals['time_label'] = bike_rentals['hr'].apply(assign_label)\n",
    "bike_rentals.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Divide data into training and test sets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given the heavy right skew of the \"cnt\" (count) column, the target column, I will use mean absolute error as the error metric."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 290,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# use sample method to select rows for training and test sets\n",
    "train = bike_rentals.sample(frac=0.8) \n",
    "test = bike_rentals.loc[~bike_rentals.index.isin(train.index)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear regression model\n",
    "Create list of predictor columns to be used in training and predictions. This will exclude 'casual' and 'registered', as 'cnt' is derived from them. \"Instant\" and \"dteday\" also will be removed, as they don't add any meaningful predictive value. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 291,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# predictor columns\n",
    "cols = ['season', 'yr', 'mnth', 'hr',\n",
    "        'holiday', 'weekday', 'workingday', 'weathersit',\n",
    "       'temp', 'atemp', 'hum', 'windspeed']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 292,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "106.23469429727929"
      ]
     },
     "execution_count": 292,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# instantiate linear model\n",
    "lr = linear_model.LinearRegression()\n",
    "# fit model on train \n",
    "fit = lr.fit(train[cols], train[\"cnt\"])\n",
    "# make predictions on test\n",
    "predictions = lr.predict(test[cols])\n",
    "# calculate mean absolute error on test predictions        \n",
    "mae = mean_absolute_error(test[\"cnt\"],  predictions)\n",
    "mae\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a large error, perhaps related to the heavily skewed distribution of 'cnt'. Perhaps methods that do not rely on normal distributions will produce lower error."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Decision tree model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 293,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAE for train: 0.013090699848953464\n",
      "MAE for test: 35.01884349827388\n"
     ]
    }
   ],
   "source": [
    "# instantiate the decision tree model\n",
    "reg = DecisionTreeRegressor(random_state=1)\n",
    "# fit the model\n",
    "reg.fit(train[cols], train['cnt'])\n",
    "# make predictions on train\n",
    "train_predictions = reg.predict(train[cols])\n",
    "# make predictions on test\n",
    "test_predictions = reg.predict(test[cols])\n",
    "# calculate error for train and test sets\n",
    "dt_train_mae = mean_absolute_error(train[\"cnt\"],  train_predictions)\n",
    "dt_test_mae = mean_absolute_error(test[\"cnt\"],  test_predictions)\n",
    "\n",
    "print('MAE for train: {}'.format(dt_train_mae))\n",
    "print('MAE for test: {}'.format(dt_test_mae))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the decision tree regressor model resulted in the error going down dramatically. The mean absolute error went from 105 using linear regression to 35 with the decision tree model. However, the decision tree model clearly results in overfitting, as the error using the train set was only 0.01. Now I will adjust the minimum sample leaf parameter to try to correct this. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 294,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAE for train: 20.481449418819054\n",
      "MAE for test: 32.009482140573915\n"
     ]
    }
   ],
   "source": [
    "reg = DecisionTreeRegressor(random_state=1, min_samples_leaf=5)\n",
    "# fit the model\n",
    "reg.fit(train[cols], train['cnt'])\n",
    "# make predictions on train\n",
    "train_predictions = reg.predict(train[cols])\n",
    "# make predictions on test\n",
    "test_predictions = reg.predict(test[cols])\n",
    "# calculate error for train and test sets\n",
    "dt_train_mae = mean_absolute_error(train[\"cnt\"],  train_predictions)\n",
    "dt_test_mae = mean_absolute_error(test[\"cnt\"],  test_predictions)\n",
    "\n",
    "print('MAE for train: {}'.format(dt_train_mae))\n",
    "print('MAE for test: {}'.format(dt_test_mae))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 295,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAE for train: 10.65511040782565\n",
      "MAE for test: 32.97899884925201\n"
     ]
    }
   ],
   "source": [
    "reg = DecisionTreeRegressor(random_state=1, min_samples_leaf=2)\n",
    "# fit the model\n",
    "reg.fit(train[cols], train['cnt'])\n",
    "# make predictions on train\n",
    "train_predictions = reg.predict(train[cols])\n",
    "# make predictions on test\n",
    "test_predictions = reg.predict(test[cols])\n",
    "# calculate error for train and test sets\n",
    "dt_train_mae = mean_absolute_error(train[\"cnt\"],  train_predictions)\n",
    "dt_test_mae = mean_absolute_error(test[\"cnt\"],  test_predictions)\n",
    "\n",
    "print('MAE for train: {}'.format(dt_train_mae))\n",
    "print('MAE for test: {}'.format(dt_test_mae))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 296,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAE for train: 26.200837985646324\n",
      "MAE for test: 31.891712888631233\n"
     ]
    }
   ],
   "source": [
    "reg = DecisionTreeRegressor(random_state=1, min_samples_leaf=10)\n",
    "# fit the model\n",
    "reg.fit(train[cols], train['cnt'])\n",
    "# make predictions on train\n",
    "train_predictions = reg.predict(train[cols])\n",
    "# make predictions on test\n",
    "test_predictions = reg.predict(test[cols])\n",
    "# calculate error for train and test sets\n",
    "dt_train_mae = mean_absolute_error(train[\"cnt\"],  train_predictions)\n",
    "dt_test_mae = mean_absolute_error(test[\"cnt\"],  test_predictions)\n",
    "\n",
    "print('MAE for train: {}'.format(dt_train_mae))\n",
    "print('MAE for test: {}'.format(dt_test_mae))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Setting the minimum samples leaf = 10 decreases the overfitting while maintaining predictive accuracy. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Random forest model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 297,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAE for train: 25.481906794938602\n",
      "MAE for test: 28.33339911472002\n"
     ]
    }
   ],
   "source": [
    "rf = RandomForestRegressor(n_estimators=150, random_state=1, min_samples_leaf=10)\n",
    "\n",
    "rf.fit(train[cols], train[\"cnt\"])\n",
    "\n",
    "train_predictions = rf.predict(train[cols])\n",
    "test_predictions = rf.predict(test[cols])\n",
    "\n",
    "rf_train_mae = mean_absolute_error(train[\"cnt\"],  train_predictions)\n",
    "rf_test_mae = mean_absolute_error(test[\"cnt\"],  test_predictions)\n",
    "\n",
    "print('MAE for train: {}'.format(rf_train_mae))\n",
    "print('MAE for test: {}'.format(rf_test_mae))\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the random forest method reduced the error on the test set and also reduced the discrepancy between the error in the train and test sets. There was less overfitting with random forest. Overall, the predictive accuracy improved dramatically using decision trees and then random forest as compared to linear regression. The non-normality of the distribution of the target variable, as well as the ability to capture interactions with decision tree/random forest models, probably explains why these models performed better. \n"
   ]
  }
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