Mission213Solution.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\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</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</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</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</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</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       3          13   16  \n",
       "1           1  0.22  0.2727  0.80          0       8          32   40  \n",
       "2           1  0.22  0.2727  0.80          0       5          27   32  \n",
       "3           1  0.24  0.2879  0.75          0       3          10   13  \n",
       "4           1  0.24  0.2879  0.75          0       0           1    1  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas\n",
    "\n",
    "bike_rentals = pandas.read_csv(\"bike_rental_hour.csv\")\n",
    "bike_rentals.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 6972.,  3705.,  2659.,  1660.,   987.,   663.,   369.,   188.,\n",
       "          139.,    37.]),\n",
       " array([   1. ,   98.6,  196.2,  293.8,  391.4,  489. ,  586.6,  684.2,\n",
       "         781.8,  879.4,  977. ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "f/kcbWp173Q/CexK8t+BQ8BPJ3ma6ZuHRWeAM1X1/bb9TQYhcXbK5uNvA/+pqv5XVV0A/j3wd5m+\n",
       "ebjcSn4uzrT6TZfVX3VeJiUUfgDMJPlAkrXAQ8DRMY/phkoS4CvAiar64tCuowwuqNH+PDJU/3CS\n",
       "tUm2ADMMLiC9o1XV56tqc1VtAR4GfqeqdjNl87Coqs4CryW5u1V9AngJ+BbTNR8ngY8kWdd+Vj4B\n",
       "nGD65uFyK/q5aP+e3mh3sAXYPdTnysZ9hX3oqvrPMLgD5xSwf9zjWYXj/SiDNfQXgRfaYydwO/Ad\n",
       "4BXgOWD9UJ/Pt/k5CfzDcR/DDZiTn+LS3UfTPA9/C/g+8J8Z/A/5tmmcD+CXGQTicQYXVW+Zpnlg\n",
       "cOb8R8CbDK65/ty1HD+wrc3hKeBLS72uH16TJHWTsnwkSZoAhoIkqTMUJEmdoSBJ6gwFSVJnKEiS\n",
       "OkNBktQZCpKk7v8BIgy2anPl5soAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10790ef28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.hist(bike_rentals[\"cnt\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "instant       0.278379\n",
       "season        0.178056\n",
       "yr            0.250495\n",
       "mnth          0.120638\n",
       "hr            0.394071\n",
       "holiday      -0.030927\n",
       "weekday       0.026900\n",
       "workingday    0.030284\n",
       "weathersit   -0.142426\n",
       "temp          0.404772\n",
       "atemp         0.400929\n",
       "hum          -0.322911\n",
       "windspeed     0.093234\n",
       "casual        0.694564\n",
       "registered    0.972151\n",
       "cnt           1.000000\n",
       "Name: cnt, dtype: float64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bike_rentals.corr()[\"cnt\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def assign_label(hour):\n",
    "    if hour >=0 and hour < 6:\n",
    "        return 4\n",
    "    elif hour >=6 and hour < 12:\n",
    "        return 1\n",
    "    elif hour >= 12 and hour < 18:\n",
    "        return 2\n",
    "    elif hour >= 18 and hour <=24:\n",
    "        return 3\n",
    "\n",
    "bike_rentals[\"time_label\"] = bike_rentals[\"hr\"].apply(assign_label)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Error metric\n",
    "\n",
    "The mean squared error metric makes the most sense to evaluate our error.  MSE works on continuous numeric data, which fits our data quite well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "train = bike_rentals.sample(frac=.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "test = bike_rentals.loc[~bike_rentals.index.isin(train.index)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, normalize=False)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "predictors = list(train.columns)\n",
    "predictors.remove(\"cnt\")\n",
    "predictors.remove(\"casual\")\n",
    "predictors.remove(\"registered\")\n",
    "predictors.remove(\"dteday\")\n",
    "\n",
    "reg = LinearRegression()\n",
    "\n",
    "reg.fit(train[predictors], train[\"cnt\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16586.154698429491"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy\n",
    "predictions = reg.predict(test[predictors])\n",
    "\n",
    "numpy.mean((predictions - test[\"cnt\"]) ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -75.31906346,  144.15652539,  125.29713548, ...,  167.94469909,\n",
       "        181.44415684,  165.3047817 ])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "actual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4          1\n",
       "10        36\n",
       "16        93\n",
       "24        17\n",
       "36        75\n",
       "39        76\n",
       "40        65\n",
       "45         9\n",
       "48         2\n",
       "52        64\n",
       "68        12\n",
       "72         2\n",
       "76       179\n",
       "80        78\n",
       "81        97\n",
       "87       112\n",
       "88        54\n",
       "90        35\n",
       "92         6\n",
       "109      169\n",
       "111       89\n",
       "112       43\n",
       "113       42\n",
       "115       11\n",
       "122      219\n",
       "133      112\n",
       "138       17\n",
       "144       84\n",
       "146      134\n",
       "147       63\n",
       "        ... \n",
       "17232     34\n",
       "17243     31\n",
       "17245      8\n",
       "17255     32\n",
       "17265     45\n",
       "17269     75\n",
       "17280     63\n",
       "17289     51\n",
       "17291    239\n",
       "17292    191\n",
       "17298    225\n",
       "17301    213\n",
       "17302    128\n",
       "17304     92\n",
       "17309     19\n",
       "17311      3\n",
       "17312      3\n",
       "17315     44\n",
       "17316     49\n",
       "17327     66\n",
       "17339     33\n",
       "17340     74\n",
       "17343    144\n",
       "17346    138\n",
       "17348    123\n",
       "17349    125\n",
       "17351     72\n",
       "17353     36\n",
       "17354     49\n",
       "17373    122\n",
       "Name: cnt, dtype: int64"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test[\"cnt\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Error\n",
    "\n",
    "The error is very high, which may be due to the fact that the data has a few extremely high rental counts, but otherwise mostly low counts.  Larger errors are penalized more with MSE, which leads to a higher total error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeRegressor(compute_importances=None, criterion='mse',\n",
       "           max_depth=None, max_features=None, max_leaf_nodes=None,\n",
       "           min_density=None, min_samples_leaf=5, min_samples_split=2,\n",
       "           random_state=None, splitter='best')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "reg = DecisionTreeRegressor(min_samples_leaf=5)\n",
    "\n",
    "reg.fit(train[predictors], train[\"cnt\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2644.2820429330714"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictions = reg.predict(test[predictors])\n",
    "\n",
    "numpy.mean((predictions - test[\"cnt\"]) ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2964.7288070579207"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg = DecisionTreeRegressor(min_samples_leaf=2)\n",
    "\n",
    "reg.fit(train[predictors], train[\"cnt\"])\n",
    "\n",
    "predictions = reg.predict(test[predictors])\n",
    "\n",
    "numpy.mean((predictions - test[\"cnt\"]) ** 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Decision tree error\n",
    "\n",
    "By taking the nonlinear predictors into account, the decision tree regressor appears to have much higher accuracy than linear regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestRegressor(bootstrap=True, compute_importances=None,\n",
       "           criterion='mse', max_depth=None, max_features='auto',\n",
       "           max_leaf_nodes=None, min_density=None, min_samples_leaf=5,\n",
       "           min_samples_split=2, n_estimators=10, n_jobs=1, oob_score=False,\n",
       "           random_state=None, verbose=0)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.ensemble import RandomForestRegressor\n",
    "\n",
    "reg = RandomForestRegressor(min_samples_leaf=5)\n",
    "reg.fit(train[predictors], train[\"cnt\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1911.9827104170736"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictions = reg.predict(test[predictors])\n",
    "\n",
    "numpy.mean((predictions - test[\"cnt\"]) ** 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Random forest error\n",
    "\n",
    "By removing some of the sources of overfitting, the random forest accuracy is improved over the decision tree accuracy."
   ]
  }
 ],
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