exercises/bikes.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear regression and regularization\n",
    "This is a subset of a UCI dataset that contains the hourly and daily count of rental bikes between years 2011 and 2012 in Capital bikeshare system with the corresponding weather and seasonal information.\n",
    " - [Dataset info](https://archive.ics.uci.edu/ml/datasets/bike+sharing+dataset)\n",
    " \n",
    "Our task will be to predict the number of bikes rented in a given day.\n",
    " \n",
    "### Data description\n",
    " - season: 1 - spring, 2 - summer, 3 - fall, 4 - winter\n",
    " - yr: 0 - 2011, 1 - 2012\n",
    " - mnth: Month, from 1  to 12\n",
    " - holiday: 0 - not a holiday, 1 - holiday\n",
    " - weekday: Day of the week, from 0 to 6\n",
    " - workingday: 0 - non working day, 1 - working day\n",
    " - weathersit: weather from 1 (clear day) to 4 (heavy rain)\n",
    " - temp: Temperature (degrees Celsius)\n",
    " - atemp: \"Feels like\" temperature\n",
    " - hum: Humididty\n",
    " - windspeed(mph)\n",
    " - windspeed(ms)\n",
    " - cnt: number of bikes rented this day"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import sklearn\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('bikes_rent.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>season</th>\n",
       "      <th>yr</th>\n",
       "      <th>mnth</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(mph)</th>\n",
       "      <th>windspeed(ms)</th>\n",
       "      <th>cnt</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>14.110847</td>\n",
       "      <td>18.18125</td>\n",
       "      <td>80.5833</td>\n",
       "      <td>10.749882</td>\n",
       "      <td>4.805490</td>\n",
       "      <td>985</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>14.902598</td>\n",
       "      <td>17.68695</td>\n",
       "      <td>69.6087</td>\n",
       "      <td>16.652113</td>\n",
       "      <td>7.443949</td>\n",
       "      <td>801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>8.050924</td>\n",
       "      <td>9.47025</td>\n",
       "      <td>43.7273</td>\n",
       "      <td>16.636703</td>\n",
       "      <td>7.437060</td>\n",
       "      <td>1349</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>8.200000</td>\n",
       "      <td>10.60610</td>\n",
       "      <td>59.0435</td>\n",
       "      <td>10.739832</td>\n",
       "      <td>4.800998</td>\n",
       "      <td>1562</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>9.305237</td>\n",
       "      <td>11.46350</td>\n",
       "      <td>43.6957</td>\n",
       "      <td>12.522300</td>\n",
       "      <td>5.597810</td>\n",
       "      <td>1600</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   season  yr  mnth  holiday  weekday  workingday  weathersit       temp  \\\n",
       "0       1   0     1        0        6           0           2  14.110847   \n",
       "1       1   0     1        0        0           0           2  14.902598   \n",
       "2       1   0     1        0        1           1           1   8.050924   \n",
       "3       1   0     1        0        2           1           1   8.200000   \n",
       "4       1   0     1        0        3           1           1   9.305237   \n",
       "\n",
       "      atemp      hum  windspeed(mph)  windspeed(ms)   cnt  \n",
       "0  18.18125  80.5833       10.749882       4.805490   985  \n",
       "1  17.68695  69.6087       16.652113       7.443949   801  \n",
       "2   9.47025  43.7273       16.636703       7.437060  1349  \n",
       "3  10.60610  59.0435       10.739832       4.800998  1562  \n",
       "4  11.46350  43.6957       12.522300       5.597810  1600  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Explore the dataset and look at the different features and their distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Correlations\n",
    "Let's explore the\n",
    "[correlation coefficients](https://en.wikipedia.org/wiki/Pearson_correlation_coefficient)\n",
    "between different features. The `df.corr()` function computes correlation coefficients between all paris of columns in the dataframe. `df.corrwith(other_df)` works similarly, but pairs up columns from one df with columns from the other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "weathersit       -0.297391\n",
       "windspeed(ms)    -0.234545\n",
       "windspeed(mph)   -0.234545\n",
       "hum              -0.100659\n",
       "holiday          -0.068348\n",
       "workingday        0.061156\n",
       "weekday           0.067443\n",
       "mnth              0.279977\n",
       "season            0.406100\n",
       "yr                0.566710\n",
       "temp              0.627494\n",
       "atemp             0.631066\n",
       "cnt               1.000000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Look at correlation coefficients between the target column cnt and all other columns\n",
    "df.corrwith(df.cnt).sort_values()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>season</th>\n",
       "      <th>yr</th>\n",
       "      <th>mnth</th>\n",
       "      <th>holiday</th>\n",
       "      <th>weekday</th>\n",
       "      <th>workingday</th>\n",
       "      <th>weathersit</th>\n",
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       "      <th>atemp</th>\n",
       "      <th>hum</th>\n",
       "      <th>windspeed(mph)</th>\n",
       "      <th>windspeed(ms)</th>\n",
       "      <th>cnt</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>season</th>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.00</td>\n",
       "      <td>0.83</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.00</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.33</td>\n",
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       "      <td>-0.23</td>\n",
       "      <td>0.41</td>\n",
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       "    <tr>\n",
       "      <th>yr</th>\n",
       "      <td>-0.00</td>\n",
       "      <td>1.00</td>\n",
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       "      <td>-0.01</td>\n",
       "      <td>-0.01</td>\n",
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       "    <tr>\n",
       "      <th>mnth</th>\n",
       "      <td>0.83</td>\n",
       "      <td>-0.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.01</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.23</td>\n",
       "      <td>0.22</td>\n",
       "      <td>-0.21</td>\n",
       "      <td>-0.21</td>\n",
       "      <td>0.28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>holiday</th>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.02</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.10</td>\n",
       "      <td>-0.25</td>\n",
       "      <td>-0.03</td>\n",
       "      <td>-0.03</td>\n",
       "      <td>-0.03</td>\n",
       "      <td>-0.02</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.01</td>\n",
       "      <td>-0.07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>weekday</th>\n",
       "      <td>-0.00</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.01</td>\n",
       "      <td>-0.10</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.00</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>workingday</th>\n",
       "      <td>0.01</td>\n",
       "      <td>-0.00</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.25</td>\n",
       "      <td>0.04</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.02</td>\n",
       "      <td>-0.02</td>\n",
       "      <td>-0.02</td>\n",
       "      <td>0.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>weathersit</th>\n",
       "      <td>0.02</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>0.04</td>\n",
       "      <td>-0.03</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.06</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>0.59</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.04</td>\n",
       "      <td>-0.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>temp</th>\n",
       "      <td>0.33</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.22</td>\n",
       "      <td>-0.03</td>\n",
       "      <td>-0.00</td>\n",
       "      <td>0.05</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.13</td>\n",
       "      <td>-0.16</td>\n",
       "      <td>-0.16</td>\n",
       "      <td>0.63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>atemp</th>\n",
       "      <td>0.34</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.23</td>\n",
       "      <td>-0.03</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.05</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>0.99</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.14</td>\n",
       "      <td>-0.18</td>\n",
       "      <td>-0.18</td>\n",
       "      <td>0.63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hum</th>\n",
       "      <td>0.21</td>\n",
       "      <td>-0.11</td>\n",
       "      <td>0.22</td>\n",
       "      <td>-0.02</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.59</td>\n",
       "      <td>0.13</td>\n",
       "      <td>0.14</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.25</td>\n",
       "      <td>-0.25</td>\n",
       "      <td>-0.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>windspeed(mph)</th>\n",
       "      <td>-0.23</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.21</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.01</td>\n",
       "      <td>-0.02</td>\n",
       "      <td>0.04</td>\n",
       "      <td>-0.16</td>\n",
       "      <td>-0.18</td>\n",
       "      <td>-0.25</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>windspeed(ms)</th>\n",
       "      <td>-0.23</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.21</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.01</td>\n",
       "      <td>-0.02</td>\n",
       "      <td>0.04</td>\n",
       "      <td>-0.16</td>\n",
       "      <td>-0.18</td>\n",
       "      <td>-0.25</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cnt</th>\n",
       "      <td>0.41</td>\n",
       "      <td>0.57</td>\n",
       "      <td>0.28</td>\n",
       "      <td>-0.07</td>\n",
       "      <td>0.07</td>\n",
       "      <td>0.06</td>\n",
       "      <td>-0.30</td>\n",
       "      <td>0.63</td>\n",
       "      <td>0.63</td>\n",
       "      <td>-0.10</td>\n",
       "      <td>-0.23</td>\n",
       "      <td>-0.23</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                season    yr  mnth  holiday  weekday  workingday  weathersit  \\\n",
       "season            1.00 -0.00  0.83    -0.01    -0.00        0.01        0.02   \n",
       "yr               -0.00  1.00 -0.00     0.01    -0.01       -0.00       -0.05   \n",
       "mnth              0.83 -0.00  1.00     0.02     0.01       -0.01        0.04   \n",
       "holiday          -0.01  0.01  0.02     1.00    -0.10       -0.25       -0.03   \n",
       "weekday          -0.00 -0.01  0.01    -0.10     1.00        0.04        0.03   \n",
       "workingday        0.01 -0.00 -0.01    -0.25     0.04        1.00        0.06   \n",
       "weathersit        0.02 -0.05  0.04    -0.03     0.03        0.06        1.00   \n",
       "temp              0.33  0.05  0.22    -0.03    -0.00        0.05       -0.12   \n",
       "atemp             0.34  0.05  0.23    -0.03    -0.01        0.05       -0.12   \n",
       "hum               0.21 -0.11  0.22    -0.02    -0.05        0.02        0.59   \n",
       "windspeed(mph)   -0.23 -0.01 -0.21     0.01     0.01       -0.02        0.04   \n",
       "windspeed(ms)    -0.23 -0.01 -0.21     0.01     0.01       -0.02        0.04   \n",
       "cnt               0.41  0.57  0.28    -0.07     0.07        0.06       -0.30   \n",
       "\n",
       "                temp  atemp   hum  windspeed(mph)  windspeed(ms)   cnt  \n",
       "season          0.33   0.34  0.21           -0.23          -0.23  0.41  \n",
       "yr              0.05   0.05 -0.11           -0.01          -0.01  0.57  \n",
       "mnth            0.22   0.23  0.22           -0.21          -0.21  0.28  \n",
       "holiday        -0.03  -0.03 -0.02            0.01           0.01 -0.07  \n",
       "weekday        -0.00  -0.01 -0.05            0.01           0.01  0.07  \n",
       "workingday      0.05   0.05  0.02           -0.02          -0.02  0.06  \n",
       "weathersit     -0.12  -0.12  0.59            0.04           0.04 -0.30  \n",
       "temp            1.00   0.99  0.13           -0.16          -0.16  0.63  \n",
       "atemp           0.99   1.00  0.14           -0.18          -0.18  0.63  \n",
       "hum             0.13   0.14  1.00           -0.25          -0.25 -0.10  \n",
       "windspeed(mph) -0.16  -0.18 -0.25            1.00           1.00 -0.23  \n",
       "windspeed(ms)  -0.16  -0.18 -0.25            1.00           1.00 -0.23  \n",
       "cnt             0.63   0.63 -0.10           -0.23          -0.23  1.00  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# All column pairs, rounding all numbers to 2 decimal places\n",
    "df.corr().round(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2edac72fa58>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The table above is a bit difficult to look at, so let's display it as a heatmap\n",
    "sns.heatmap(df.corr())\n",
    "# Alternatively use\n",
    "# plt.imshow(df.corr())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### We obviously have values of 1 on the diagonal, but note the twho bright squares with values of (nearly) 1 off the diagonal. Waht are the parameters that are so closely related to each other?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot scatter plots for `cnt` as a function of each of the columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Use LinearRegression model from sklearn to build a linear regression model based on all the features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df.drop('cnt', 1)\n",
    "y = df.cnt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Find RMSE for the training data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Look at coefficients. Note how some of the are several oreders of magnitude larger than the others. Which features do they correspond to?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Try to come up with an intuitive explanation why the regression algorithm finds it difficult to deal with two higly correlated features.\n",
    "- The mathematical name for this problem is \"multicollinearity\"\n",
    "- One of the solutions is to remove one of the features\n",
    "- Another solution is to use regularization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### In order to use regularization effectively, we need to rescale the data so that all feature have roughly the same range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import scale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "scale?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = _"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### For each value of alpha train a Lasso and Ridge regressor and save the coefficients in the corresponding coefs_* array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "alphas = np.arange(1, 500, 50)\n",
    "coefs_lasso = np.zeros((alphas.shape[0], X.shape[1]))\n",
    "coefs_ridge = np.zeros((alphas.shape[0], X.shape[1]))\n",
    "# Your loop here\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot each coefficient as a function of alpha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Based on the plots above, select several informative features to use. Train the Lasso model using those features and select the best alpha using cross validation.\n",
    " - Use cross_val_score(..., scorer='neg_mean_squared_error') to compute the MSE score (np.sqrt() can convert it to RMSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot the cross validation score as a function of alpha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
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 },
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