{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# HIDDEN\n",
    "from datascience import *\n",
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plots\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "plots.style.use('fivethirtyeight')\n",
    "import pylab as pl\n",
    "import math\n",
    "from scipy import stats\n",
    "from scipy import misc\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# HIDDEN\n",
    "\n",
    "# Functions from earlier in the chapter\n",
    "\n",
    "# Correlation coefficient\n",
    "\n",
    "def corr(table, column_A, column_B):\n",
    "    x = table[column_A]\n",
    "    y = table[column_B]\n",
    "    x_su = (x-np.mean(x))/np.std(x)\n",
    "    y_su = (y-np.mean(y))/np.std(y)\n",
    "    return np.mean(x_su*y_su)\n",
    "\n",
    "# Slope and intercept of regression line\n",
    "\n",
    "def regress(table, column_x, column_y):\n",
    "    r = corr(table, column_x, column_y)\n",
    "    reg_slope = r*np.std(table[column_y])/np.std(table[column_x])\n",
    "    reg_int = np.mean(table[column_y]) - reg_slope*np.mean(table[column_x])\n",
    "    return np.array([reg_slope, reg_int])\n",
    "\n",
    "# Fitted value at x\n",
    "\n",
    "def fit(table, column_x, column_y, x):\n",
    "    slope_int = regress(table, column_x, column_y)\n",
    "    return slope_int[0]*x + slope_int[1]\n",
    "\n",
    "# Fitted values for all points in the scatter\n",
    "\n",
    "def fitted_values(table, column_x, column_y):\n",
    "    slope_int = regress(table, column_x, column_y)\n",
    "    return slope_int[0]*table[column_x] + slope_int[1]\n",
    "\n",
    "# Scatter plot with fitted (regression) line\n",
    "\n",
    "def scatter_fit(table, column_x, column_y):\n",
    "    t = table\n",
    "    t['fit'] = fitted_values(table, column_x, column_y)\n",
    "    ts = t.sort(column_x)\n",
    "    plots.scatter(table[column_x], table[column_y], s=10)\n",
    "    plots.plot(ts[column_x], ts['fit'], lw=1, color='green')\n",
    "    plots.xlabel(column_x)\n",
    "    plots.ylabel(column_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Correlated Predictors\n",
    "\n",
    "Correlations between predictor variables are important factors in selecting the set of predictors to use in a regression model. Here is an example that demonstrates some of the considerations that are involved in variable selection.\n",
    "\n",
    "The data consist of measurements on the eggs of a species of small bird, as recorded by Abrahams and Rizzardi in the BLSS statistical system. The goal is to use dimensions of an egg to estimate the weight of the bird that hatches from the egg; as bigger hatchlings are more likely to survive, the estimates can be used to help predict the population size of the species.\n",
    "\n",
    "The variables are:\n",
    "\n",
    "- ``e_length``: the length of the egg, in millimeters\n",
    "- ``e_breadth``: the width of the egg at its widest part, in millimeters\n",
    "- ``e_weight``: the weight of the egg, in grams\n",
    "- ``b_weight``: the weight of the bird that hatched from the egg, in grams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>e_length</th> <th>e_breadth</th> <th>e_weight</th> <th>b_weight</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>28.8    </td> <td>21.84    </td> <td>7.4     </td> <td>5.2     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>29.04   </td> <td>22.45    </td> <td>7.7     </td> <td>5.4     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>29.36   </td> <td>22.48    </td> <td>7.9     </td> <td>5.6     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>30.1    </td> <td>21.71    </td> <td>7.5     </td> <td>5.3     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>30.17   </td> <td>22.75    </td> <td>8.3     </td> <td>5.9     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>30.34   </td> <td>22.84    </td> <td>8.5     </td> <td>5.8     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>30.36   </td> <td>22.5     </td> <td>8.2     </td> <td>5.8     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>30.46   </td> <td>22.72    </td> <td>8.3     </td> <td>6       </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>30.54   </td> <td>23.31    </td> <td>9       </td> <td>6.1     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>30.62   </td> <td>22.94    </td> <td>8.5     </td> <td>6.2     </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (34 rows omitted)</p"
      ],
      "text/plain": [
       "e_length | e_breadth | e_weight | b_weight\n",
       "28.8     | 21.84     | 7.4      | 5.2\n",
       "29.04    | 22.45     | 7.7      | 5.4\n",
       "29.36    | 22.48     | 7.9      | 5.6\n",
       "30.1     | 21.71     | 7.5      | 5.3\n",
       "30.17    | 22.75     | 8.3      | 5.9\n",
       "30.34    | 22.84     | 8.5      | 5.8\n",
       "30.36    | 22.5      | 8.2      | 5.8\n",
       "30.46    | 22.72     | 8.3      | 6\n",
       "30.54    | 23.31     | 9        | 6.1\n",
       "30.62    | 22.94     | 8.5      | 6.2\n",
       "... (34 rows omitted)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "birds = Table.read_table('birds.csv')\n",
    "birds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to estimate ``b_weight`` based on a combination of the other variables, we will start by examining the correlation matrix. Not surprisingly, the variable most highly correlated with the weight of the bird is the weight of the egg, ``e_weight``. But the linear dimensions ``e_length`` and ``e_breadth`` are also quite highly correlated with ``b_weight``; also, all the dimensions of the egg are correlated with each other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>e_length</th>\n",
       "      <th>e_breadth</th>\n",
       "      <th>e_weight</th>\n",
       "      <th>b_weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>e_length</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.402764</td>\n",
       "      <td>0.792449</td>\n",
       "      <td>0.676142</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>e_breadth</th>\n",
       "      <td>0.402764</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.839077</td>\n",
       "      <td>0.733687</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>e_weight</th>\n",
       "      <td>0.792449</td>\n",
       "      <td>0.839077</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.847228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b_weight</th>\n",
       "      <td>0.676142</td>\n",
       "      <td>0.733687</td>\n",
       "      <td>0.847228</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           e_length  e_breadth  e_weight  b_weight\n",
       "e_length   1.000000   0.402764  0.792449  0.676142\n",
       "e_breadth  0.402764   1.000000  0.839077  0.733687\n",
       "e_weight   0.792449   0.839077  1.000000  0.847228\n",
       "b_weight   0.676142   0.733687  0.847228  1.000000"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# HIDDEN\n",
    "\n",
    "df_birds = pd.read_csv('birds.csv')\n",
    "df_birds.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The scatter plot of the weight of the bird and the weight of the egg is shown below, along with the regression line. Just based on the graph, it is reasonable to conclude that the fit is fairly good."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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3bx/Wrl2LwMBAIapAeiLlVgoGbhuIS3mXkDQpCdO7T9eZREhETwnWM+zVqxe2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\n2IVKJNEucX8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109e77e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter_fit(birds, 'e_weight', 'b_weight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The summary statistics confirm this assessment. For example $R^2$ is quite high: 0.718. The 95% confidence interval for the slope does not contain 0. All of this points to a genuine linear trend in the relation between the weight of the egg and the weight of the bird that hatches from the egg."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>b_weight</td>     <th>  R-squared:         </th> <td>   0.718</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.711</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   106.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 05 Dec 2015</td> <th>  Prob (F-statistic):</th> <td>4.15e-13</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:16:55</td>     <th>  Log-Likelihood:    </th> <td>  5.0722</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    44</td>      <th>  AIC:               </th> <td>  -6.144</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    42</td>      <th>  BIC:               </th> <td>  -2.576</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>        <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>    <td>   -0.0583</td> <td>    0.601</td> <td>   -0.097</td> <td> 0.923</td> <td>   -1.271     1.155</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>e_weight</th> <td>    0.7185</td> <td>    0.070</td> <td>   10.336</td> <td> 0.000</td> <td>    0.578     0.859</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 2.737</td> <th>  Durbin-Watson:     </th> <td>   1.797</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.254</td> <th>  Jarque-Bera (JB):  </th> <td>   1.986</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.033</td> <th>  Prob(JB):          </th> <td>   0.370</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.039</td> <th>  Cond. No.          </th> <td>    158.</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:               b_weight   R-squared:                       0.718\n",
       "Model:                            OLS   Adj. R-squared:                  0.711\n",
       "Method:                 Least Squares   F-statistic:                     106.8\n",
       "Date:                Sat, 05 Dec 2015   Prob (F-statistic):           4.15e-13\n",
       "Time:                        15:16:55   Log-Likelihood:                 5.0722\n",
       "No. Observations:                  44   AIC:                            -6.144\n",
       "Df Residuals:                      42   BIC:                            -2.576\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
       "------------------------------------------------------------------------------\n",
       "const         -0.0583      0.601     -0.097      0.923        -1.271     1.155\n",
       "e_weight       0.7185      0.070     10.336      0.000         0.578     0.859\n",
       "==============================================================================\n",
       "Omnibus:                        2.737   Durbin-Watson:                   1.797\n",
       "Prob(Omnibus):                  0.254   Jarque-Bera (JB):                1.986\n",
       "Skew:                          -0.033   Prob(JB):                        0.370\n",
       "Kurtosis:                       4.039   Cond. No.                         158.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# HIDDEN\n",
    "\n",
    "bird_x = df_birds[['e_weight']]\n",
    "bird_x = sm.add_constant(bird_x)\n",
    "bird_y = df_birds['b_weight']\n",
    "est = sm.OLS(bird_y, bird_x).fit()\n",
    "est.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is interesting to see what happens when we use all of the dimensions of the egg – length, breadth, and weight – as predictors. Compared to the simple regression based on egg weight alone, there is only a tiny increase in $R^2$: 0.724 compared to 0.718. Also, the adjusted $R^2$ goes down slightly, from 0.711 to 0.703. There is no substantial gain in throwing in the linear dimensions of the egg as predictors, compared to using just egg weight alone."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>b_weight</td>     <th>  R-squared:         </th> <td>   0.724</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.703</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   34.98</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 05 Dec 2015</td> <th>  Prob (F-statistic):</th> <td>2.90e-11</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:17:03</td>     <th>  Log-Likelihood:    </th> <td>  5.5617</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    44</td>      <th>  AIC:               </th> <td>  -3.123</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    40</td>      <th>  BIC:               </th> <td>   4.013</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     3</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>     <td>   -4.6057</td> <td>    4.843</td> <td>   -0.951</td> <td> 0.347</td> <td>  -14.394     5.183</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>e_weight</th>  <td>    0.4312</td> <td>    0.317</td> <td>    1.360</td> <td> 0.181</td> <td>   -0.209     1.072</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>e_breadth</th> <td>    0.2159</td> <td>    0.229</td> <td>    0.944</td> <td> 0.351</td> <td>   -0.246     0.678</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>e_length</th>  <td>    0.0666</td> <td>    0.083</td> <td>    0.803</td> <td> 0.426</td> <td>   -0.101     0.234</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 3.670</td> <th>  Durbin-Watson:     </th> <td>   1.716</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.160</td> <th>  Jarque-Bera (JB):  </th> <td>   3.399</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.029</td> <th>  Prob(JB):          </th> <td>   0.183</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.360</td> <th>  Cond. No.          </th> <td>5.74e+03</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:               b_weight   R-squared:                       0.724\n",
       "Model:                            OLS   Adj. R-squared:                  0.703\n",
       "Method:                 Least Squares   F-statistic:                     34.98\n",
       "Date:                Sat, 05 Dec 2015   Prob (F-statistic):           2.90e-11\n",
       "Time:                        15:17:03   Log-Likelihood:                 5.5617\n",
       "No. Observations:                  44   AIC:                            -3.123\n",
       "Df Residuals:                      40   BIC:                             4.013\n",
       "Df Model:                           3                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
       "------------------------------------------------------------------------------\n",
       "const         -4.6057      4.843     -0.951      0.347       -14.394     5.183\n",
       "e_weight       0.4312      0.317      1.360      0.181        -0.209     1.072\n",
       "e_breadth      0.2159      0.229      0.944      0.351        -0.246     0.678\n",
       "e_length       0.0666      0.083      0.803      0.426        -0.101     0.234\n",
       "==============================================================================\n",
       "Omnibus:                        3.670   Durbin-Watson:                   1.716\n",
       "Prob(Omnibus):                  0.160   Jarque-Bera (JB):                3.399\n",
       "Skew:                          -0.029   Prob(JB):                        0.183\n",
       "Kurtosis:                       4.360   Cond. No.                     5.74e+03\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 5.74e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# HIDDEN\n",
    "\n",
    "bird_x = df_birds[['e_weight', 'e_breadth', 'e_length']]\n",
    "bird_x = sm.add_constant(bird_x)\n",
    "bird_y = df_birds['b_weight']\n",
    "est = sm.OLS(bird_y, bird_x).fit()\n",
    "est.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###Collinearity\n",
    "\n",
    "That too many predictor variables have been used in this regression is most apparent when you look at the confidence intervals for the slopes. All of the intervals contain 0, so it appears that there could be no linear trend in the relation between the response variable and the predictors. Yet $R^2$ is high. How can we reconcile these two apparently contradictory observations?\n",
    "\n",
    "The answer lies in the correlation matrix. It shows that the three predictor variables are all correlated with each other. This is called *collinearity*. Because of collinearity, none of the slopes has a clear practical interpretation: it is not possible to increase one of the predictor variables while holding the others constant.\n",
    "\n",
    "Therefore this regression gives little indication of how each individual predictor variable affects the estimate of the response. The small increase in $R^2$ has been obtained at a steep price: the interpretability of the model. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The problem of collinearity can be mitigated by choosing the predictors more carefully. The correlation matrix shows that egg weight is highly correlated with both egg length and egg breadth. However, the correlation between egg length and egg breadth is much smaller. So it is a reasonable to regress bird weight on just the two linear dimensions of the egg."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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vLDC+GE/PXuerNoXAo4507lUJXH+fW8Y1FwMgAcBgS6O91q8Nt9/gaNpk+zW6racv5zWi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IBJkyZhwIABqKqqQn5+fsg+tGZuMwHIYMSBX/KjsbkRqqYnccjQO3t4OS8UXjFLsiiCAlVVIfMy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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c088780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# HIDDEN\n",
    "\n",
    "fig = plots.figure(figsize=(10,10))\n",
    "ax = plots.axes(projection='3d')\n",
    "ax.scatter(birds['e_breadth'], birds['e_length'], birds['b_weight'], zdir='z')\n",
    "x = np.arange(22,24,0.01)\n",
    "y = np.arange(28,34,0.01)\n",
    "x,y = np.meshgrid(x,y)\n",
    "z = 0.5057*x + 0.1695*y - 10.7386\n",
    "ax.plot_surface(x,y,z,alpha=0.15,color='g')\n",
    "ax.view_init(elev=18,azim=350)\n",
    "ax.set_xlabel('e_breadth')\n",
    "ax.set_ylabel('e_length')\n",
    "ax.set_zlabel('b_weight')\n",
    "None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>b_weight</td>     <th>  R-squared:         </th> <td>   0.711</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.697</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   50.49</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 05 Dec 2015</td> <th>  Prob (F-statistic):</th> <td>8.73e-12</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:17:34</td>     <th>  Log-Likelihood:    </th> <td>  4.5668</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    44</td>      <th>  AIC:               </th> <td>  -3.134</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    41</td>      <th>  BIC:               </th> <td>   2.219</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>     <td>  -10.7386</td> <td>    1.788</td> <td>   -6.007</td> <td> 0.000</td> <td>  -14.349    -7.128</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>e_breadth</th> <td>    0.5057</td> <td>    0.084</td> <td>    6.006</td> <td> 0.000</td> <td>    0.336     0.676</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>e_length</th>  <td>    0.1695</td> <td>    0.034</td> <td>    4.955</td> <td> 0.000</td> <td>    0.100     0.239</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 4.685</td> <th>  Durbin-Watson:     </th> <td>   1.648</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.096</td> <th>  Jarque-Bera (JB):  </th> <td>   5.379</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.016</td> <th>  Prob(JB):          </th> <td>  0.0679</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.713</td> <th>  Cond. No.          </th> <td>2.04e+03</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:               b_weight   R-squared:                       0.711\n",
       "Model:                            OLS   Adj. R-squared:                  0.697\n",
       "Method:                 Least Squares   F-statistic:                     50.49\n",
       "Date:                Sat, 05 Dec 2015   Prob (F-statistic):           8.73e-12\n",
       "Time:                        15:17:34   Log-Likelihood:                 4.5668\n",
       "No. Observations:                  44   AIC:                            -3.134\n",
       "Df Residuals:                      41   BIC:                             2.219\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
       "------------------------------------------------------------------------------\n",
       "const        -10.7386      1.788     -6.007      0.000       -14.349    -7.128\n",
       "e_breadth      0.5057      0.084      6.006      0.000         0.336     0.676\n",
       "e_length       0.1695      0.034      4.955      0.000         0.100     0.239\n",
       "==============================================================================\n",
       "Omnibus:                        4.685   Durbin-Watson:                   1.648\n",
       "Prob(Omnibus):                  0.096   Jarque-Bera (JB):                5.379\n",
       "Skew:                           0.016   Prob(JB):                       0.0679\n",
       "Kurtosis:                       4.713   Cond. No.                     2.04e+03\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 2.04e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# HIDDEN\n",
    "\n",
    "bird_x = df_birds[['e_breadth', 'e_length']]\n",
    "bird_x = sm.add_constant(bird_x)\n",
    "bird_y = df_birds['b_weight']\n",
    "est = sm.OLS(bird_y, bird_x).fit()\n",
    "est.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This regression can be much more clearly interpreted than the regression based on all three predictors. The value of $R^2$ is just over 0.7, and the confidence intervals for the two slopes don't contain 0. Because of the relative lack of collinearity between the two predictors, each slope has meaning.\n",
    "\n",
    "Indeed, the regression based on the two linear dimensions of the egg is quite comparable to the simple regression based on egg weight. To see why, let us examine the relation between egg weight and the two linear dimensions. How can we do this?\n",
    "\n",
    "A good way is to use the technique that we have been using all through this section: multiple regression. Let's see what happens when we try to estimate egg weight based on egg length and egg breadth."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>e_weight</td>     <th>  R-squared:         </th> <td>   0.951</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.948</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   394.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 05 Dec 2015</td> <th>  Prob (F-statistic):</th> <td>1.65e-27</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:17:41</td>     <th>  Log-Likelihood:    </th> <td>  36.169</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    44</td>      <th>  AIC:               </th> <td>  -66.34</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    41</td>      <th>  BIC:               </th> <td>  -60.98</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>     <td>  -14.2220</td> <td>    0.872</td> <td>  -16.314</td> <td> 0.000</td> <td>  -15.983   -12.461</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>e_breadth</th> <td>    0.6719</td> <td>    0.041</td> <td>   16.367</td> <td> 0.000</td> <td>    0.589     0.755</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>e_length</th>  <td>    0.2386</td> <td>    0.017</td> <td>   14.308</td> <td> 0.000</td> <td>    0.205     0.272</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 1.287</td> <th>  Durbin-Watson:     </th> <td>   2.036</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.526</td> <th>  Jarque-Bera (JB):  </th> <td>   0.605</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.250</td> <th>  Prob(JB):          </th> <td>   0.739</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.281</td> <th>  Cond. No.          </th> <td>2.04e+03</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:               e_weight   R-squared:                       0.951\n",
       "Model:                            OLS   Adj. R-squared:                  0.948\n",
       "Method:                 Least Squares   F-statistic:                     394.6\n",
       "Date:                Sat, 05 Dec 2015   Prob (F-statistic):           1.65e-27\n",
       "Time:                        15:17:41   Log-Likelihood:                 36.169\n",
       "No. Observations:                  44   AIC:                            -66.34\n",
       "Df Residuals:                      41   BIC:                            -60.98\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
       "------------------------------------------------------------------------------\n",
       "const        -14.2220      0.872    -16.314      0.000       -15.983   -12.461\n",
       "e_breadth      0.6719      0.041     16.367      0.000         0.589     0.755\n",
       "e_length       0.2386      0.017     14.308      0.000         0.205     0.272\n",
       "==============================================================================\n",
       "Omnibus:                        1.287   Durbin-Watson:                   2.036\n",
       "Prob(Omnibus):                  0.526   Jarque-Bera (JB):                0.605\n",
       "Skew:                           0.250   Prob(JB):                        0.739\n",
       "Kurtosis:                       3.281   Cond. No.                     2.04e+03\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 2.04e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# HIDDEN\n",
    "\n",
    "bird_x = df_birds[['e_breadth', 'e_length']]\n",
    "bird_x = sm.add_constant(bird_x)\n",
    "bird_y = df_birds['e_weight']\n",
    "est = sm.OLS(bird_y, bird_x).fit()\n",
    "est.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice the extremely high value of $R^2$. This indicates that egg weight is very close to a linear function of egg length and egg breadth. Therefore, the information in egg weight as a predictor of bird weight is essentially the same as the information in a linear function of egg length and breadth. For confirmation, here is the scatter plot of the three variables. As you can see, the points are closely clustered about a plane."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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ORgFQDkwvdBFZJ4s+542W31rmOXfSKNDwPsEKgatNcwBlIg0Bi4g8Y79z4izOmcMrb+dx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\nhRBCWDbJAFYRKSkp9OvXjwsXLrBw4UIGDx5scPvmzZt5+eWX2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45BxiQpKYk5c+YQFxdH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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c0606a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# HIDDEN \n",
    "\n",
    "fig = plots.figure(figsize=(10,10))\n",
    "ax = plots.axes(projection='3d')\n",
    "ax.scatter(birds['e_breadth'], birds['e_length'], birds['e_weight'], zdir='z', color='r')\n",
    "x = np.arange(22,24,0.01)\n",
    "y = np.arange(28,34,0.01)\n",
    "x,y = np.meshgrid(x,y)\n",
    "z = 0.6719*x + 0.2386*y - 14.222\n",
    "ax.plot_surface(x,y,z,alpha=0.15,color='gold')\n",
    "ax.view_init(elev=18,azim=350)\n",
    "ax.set_xlabel('e_breadth')\n",
    "ax.set_ylabel('e_length')\n",
    "ax.set_zlabel('e_weight')\n",
    "None"
   ]
  }
 ],
 "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": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}