{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 6: Diagnostics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'%.5f'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy as sp\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "import seaborn as sns\n",
    "%matplotlib inline\n",
    "%precision 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check Error Assumptions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Read in the data for the example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>sr</th>\n",
       "      <th>pop15</th>\n",
       "      <th>pop75</th>\n",
       "      <th>dpi</th>\n",
       "      <th>ddpi</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Australia</th>\n",
       "      <td>11.43</td>\n",
       "      <td>29.35</td>\n",
       "      <td>2.87</td>\n",
       "      <td>2329.68</td>\n",
       "      <td>2.87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Austria</th>\n",
       "      <td>12.07</td>\n",
       "      <td>23.32</td>\n",
       "      <td>4.41</td>\n",
       "      <td>1507.99</td>\n",
       "      <td>3.93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Belgium</th>\n",
       "      <td>13.17</td>\n",
       "      <td>23.80</td>\n",
       "      <td>4.43</td>\n",
       "      <td>2108.47</td>\n",
       "      <td>3.82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bolivia</th>\n",
       "      <td>5.75</td>\n",
       "      <td>41.89</td>\n",
       "      <td>1.67</td>\n",
       "      <td>189.13</td>\n",
       "      <td>0.22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Brazil</th>\n",
       "      <td>12.88</td>\n",
       "      <td>42.19</td>\n",
       "      <td>0.83</td>\n",
       "      <td>728.47</td>\n",
       "      <td>4.56</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              sr  pop15  pop75      dpi  ddpi\n",
       "Australia  11.43  29.35   2.87  2329.68  2.87\n",
       "Austria    12.07  23.32   4.41  1507.99  3.93\n",
       "Belgium    13.17  23.80   4.43  2108.47  3.82\n",
       "Bolivia     5.75  41.89   1.67   189.13  0.22\n",
       "Brazil     12.88  42.19   0.83   728.47  4.56"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "savings = pd.read_csv(\"data/savings.csv\",index_col=0)\n",
    "savings.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>sr</td>        <th>  R-squared:         </th> <td>   0.338</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.280</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   5.756</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 25 Sep 2018</td> <th>  Prob (F-statistic):</th> <td>0.000790</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:52:59</td>     <th>  Log-Likelihood:    </th> <td> -135.10</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    50</td>      <th>  AIC:               </th> <td>   280.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    45</td>      <th>  BIC:               </th> <td>   289.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     4</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>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>   28.5661</td> <td>    7.355</td> <td>    3.884</td> <td> 0.000</td> <td>   13.753</td> <td>   43.379</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>pop15</th>     <td>   -0.4612</td> <td>    0.145</td> <td>   -3.189</td> <td> 0.003</td> <td>   -0.753</td> <td>   -0.170</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>pop75</th>     <td>   -1.6915</td> <td>    1.084</td> <td>   -1.561</td> <td> 0.126</td> <td>   -3.874</td> <td>    0.491</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>dpi</th>       <td>   -0.0003</td> <td>    0.001</td> <td>   -0.362</td> <td> 0.719</td> <td>   -0.002</td> <td>    0.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ddpi</th>      <td>    0.4097</td> <td>    0.196</td> <td>    2.088</td> <td> 0.042</td> <td>    0.015</td> <td>    0.805</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.866</td> <th>  Durbin-Watson:     </th> <td>   1.934</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.649</td> <th>  Jarque-Bera (JB):  </th> <td>   0.493</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.241</td> <th>  Prob(JB):          </th> <td>   0.782</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.064</td> <th>  Cond. No.          </th> <td>2.04e+04</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 2.04e+04. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                     sr   R-squared:                       0.338\n",
       "Model:                            OLS   Adj. R-squared:                  0.280\n",
       "Method:                 Least Squares   F-statistic:                     5.756\n",
       "Date:                Tue, 25 Sep 2018   Prob (F-statistic):           0.000790\n",
       "Time:                        15:52:59   Log-Likelihood:                -135.10\n",
       "No. Observations:                  50   AIC:                             280.2\n",
       "Df Residuals:                      45   BIC:                             289.8\n",
       "Df Model:                           4                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     28.5661      7.355      3.884      0.000      13.753      43.379\n",
       "pop15         -0.4612      0.145     -3.189      0.003      -0.753      -0.170\n",
       "pop75         -1.6915      1.084     -1.561      0.126      -3.874       0.491\n",
       "dpi           -0.0003      0.001     -0.362      0.719      -0.002       0.002\n",
       "ddpi           0.4097      0.196      2.088      0.042       0.015       0.805\n",
       "==============================================================================\n",
       "Omnibus:                        0.866   Durbin-Watson:                   1.934\n",
       "Prob(Omnibus):                  0.649   Jarque-Bera (JB):                0.493\n",
       "Skew:                           0.241   Prob(JB):                        0.782\n",
       "Kurtosis:                       3.064   Cond. No.                     2.04e+04\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+04. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lmod = smf.ols(formula='sr ~ pop15 + pop75 + dpi + ddpi', data=savings).fit()\n",
    "lmod.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The simple residual-fitted plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1c20ce2160>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(lmod.fittedvalues, lmod.resid)\n",
    "plt.ylabel(\"Residuals\")\n",
    "plt.xlabel(\"Fitted values\")\n",
    "plt.axhline(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot is slightly better for checking for constant variance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'Fitted values')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(lmod.fittedvalues, np.sqrt(abs(lmod.resid)))\n",
    "plt.ylabel(\"sqrt |Residuals|\")\n",
    "plt.xlabel(\"Fitted values\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check that there is no significant relationship:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.061</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.041</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   3.117</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 25 Sep 2018</td> <th>  Prob (F-statistic):</th>  <td>0.0838</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:52:59</td>     <th>  Log-Likelihood:    </th> <td> -47.153</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    50</td>      <th>  AIC:               </th> <td>   98.31</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    48</td>      <th>  BIC:               </th> <td>   102.1</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>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>    2.1622</td> <td>    0.348</td> <td>    6.215</td> <td> 0.000</td> <td>    1.463</td> <td>    2.862</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x</th>         <td>   -0.0614</td> <td>    0.035</td> <td>   -1.766</td> <td> 0.084</td> <td>   -0.131</td> <td>    0.009</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 1.170</td> <th>  Durbin-Watson:     </th> <td>   2.050</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.557</td> <th>  Jarque-Bera (JB):  </th> <td>   1.184</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.273</td> <th>  Prob(JB):          </th> <td>   0.553</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.479</td> <th>  Cond. No.          </th> <td>    39.2</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.061\n",
       "Model:                            OLS   Adj. R-squared:                  0.041\n",
       "Method:                 Least Squares   F-statistic:                     3.117\n",
       "Date:                Tue, 25 Sep 2018   Prob (F-statistic):             0.0838\n",
       "Time:                        15:52:59   Log-Likelihood:                -47.153\n",
       "No. Observations:                  50   AIC:                             98.31\n",
       "Df Residuals:                      48   BIC:                             102.1\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      2.1622      0.348      6.215      0.000       1.463       2.862\n",
       "x             -0.0614      0.035     -1.766      0.084      -0.131       0.009\n",
       "==============================================================================\n",
       "Omnibus:                        1.170   Durbin-Watson:                   2.050\n",
       "Prob(Omnibus):                  0.557   Jarque-Bera (JB):                1.184\n",
       "Skew:                           0.273   Prob(JB):                        0.553\n",
       "Kurtosis:                       2.479   Cond. No.                         39.2\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": [
    "ddf = pd.DataFrame({'x':lmod.fittedvalues,'y':np.sqrt(abs(lmod.resid))})\n",
    "dmod = smf.ols('y ~ x',data=ddf).fit()\n",
    "dmod.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simulate some residual-fitted plots:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1c20ea8cf8>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 50\n",
    "x = np.random.sample(n)\n",
    "y = np.random.normal(size=n)\n",
    "plt.scatter(x,y)\n",
    "plt.title(\"No problem plot\")\n",
    "plt.axhline(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1c20f6bb70>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x,y*x)\n",
    "plt.title(\"Increasing variance\")\n",
    "plt.axhline(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1c2102ea90>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x,y*np.sqrt(x))\n",
    "plt.title(\"Mildly increasing variance\")\n",
    "plt.axhline(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1c210f7048>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y = np.cos(2*x*np.pi) + np.random.normal(size=n)\n",
    "plt.scatter(x,y)\n",
    "plt.title(\"Lack of fit plot\")\n",
    "sx = np.sort(x)\n",
    "plt.plot(sx,np.cos(2*sx*np.pi),c='red')\n",
    "plt.axhline(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plots of residuals against predictors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1c20e48940>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(savings.pop15, lmod.resid)\n",
    "plt.xlabel(\"%pop under 15\")\n",
    "plt.ylabel(\"Residuals\")\n",
    "plt.axhline(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1c21263d68>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(savings.pop75, lmod.resid)\n",
    "plt.xlabel(\"%pop over 75\")\n",
    "plt.ylabel(\"Residuals\")\n",
    "plt.axhline(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check for equality of the variances in the two groups seen in pop15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.013575950424159933"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numres = lmod.resid[savings.pop15 > 35]\n",
    "denres = lmod.resid[savings.pop15 < 35]\n",
    "fstat = np.var(numres,ddof=1)/np.var(denres,ddof=1)\n",
    "2*(1-sp.stats.f.cdf(fstat,len(numres)-1,len(denres)-1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Do the residual fitted plot for the Galapagos data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1c21321e10>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZEAAAEKCAYAAADTgGjXAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvIxREBQAAGY5JREFUeJzt3XGUnXV95/H3hyHgHLEOlIGSAUxks7GwLAmdQ7FxFdE6UXfNwErFY09pyzbtWTi6tic9yXa7sqe7S9xUWbWKpZaKLTVNLQ1ZoKaYsGWPK4WJSQmBpkQCJJNowmIE7BST8N0/nt9NbiZ3Zu48c5/73PvM53XOnLnP7z73zpefnueT53l+v9+jiMDMzCyPU8ouwMzMupdDxMzMcnOImJlZbg4RMzPLzSFiZma5OUTMzCw3h4iZmeXmEDEzs9wcImZmltupZRdQpLPPPjvmzZtXdhlmZl1ly5YtL0REfzP7VjpE5s2bx8jISNllmJl1FUnPNbuvL2eZmVluDhEzM8vNIWJmZrk5RMzMLDeHiJmZ5Vbp0Vlm1jnWbx1lzcad7Ds0xty+XlYMLWR48UDZZdkMOUTMrHDrt46y6p7tjB0+CsDooTFW3bMdwEHS5Xw5y8wKt2bjzmMBUjN2+ChrNu4sqSJrFYeImRVu36GxabVb93CImFnh5vb1TqvduodDxMwKt2JoIb1zek5o653Tw4qhhSVVZK3iG+tmVrjazXOPzqoeh4iZtcXw4gGHRgX5cpaZmeXmEDEzs9wcImZmlptDxMzMcnOImJlZbg4RMzPLzSFiZma5OUTMzCw3h4iZmeXmEDEzs9wcImZmlptDxMzMcnOImJlZbqWGiKQ7JR2Q9ERd2y2SRiVtSz/vq3tvlaRdknZKGiqnajMzqyn7TOTLwNIG7bdFxKL08wCApIuB64FL0me+IKmnwWfNzKxNSg2RiHgYeLHJ3ZcBayPi1YjYDewCriisODMzm1LZZyITuVnS4+ly15mpbQDYU7fP3tRmZmYl6cQQuR24CFgE7Ac+ldrVYN8Y3yBpuaQRSSMHDx4srkozM+u8EImI70XE0Yh4DfgDjl+y2gtcULfr+cC+Bp+/IyIGI2Kwv7+/+ILNzGaxjgsRSefVbV4D1EZubQCul3S6pPnAAuDRdtdnZmbHnVrmH5f0VeAq4GxJe4FPAFdJWkR2qepZ4FcBImKHpHXAk8AR4KaIOFpG3WZmllHESbcVKmNwcDBGRkbKLsPMrKtI2hIRg83s23GXs8zMrHs4RMzMLDeHiJmZ5eYQMTOz3BwiZmaWm0PEzMxyc4iYmVluDhEzM8vNIWJmZrk5RMzMLDeHiJmZ5eYQMTOz3BwiZmaWm0PEzMxyc4iYmVluDhEzM8vNIWJmZrk5RMzMLDeHiJmZ5eYQMTOz3BwiZmaWm0PEzMxyc4iYmVluDhEzM8vNIWJmZrmVGiKS7pR0QNITdW1nSXpQ0tPp95mpXZI+K2mXpMclXV5e5WZmBuWfiXwZWDqubSWwKSIWAJvSNsB7gQXpZzlwe5tqNDOzCZQaIhHxMPDiuOZlwF3p9V3AcF37VyLzCNAn6bz2VGpmZo2UfSbSyLkRsR8g/T4ntQ8Ae+r225vazMysJJ0YIhNRg7Y4aSdpuaQRSSMHDx5sQ1lmZrNXJ4bI92qXqdLvA6l9L3BB3X7nA/vGfzgi7oiIwYgY7O/vL7xYM7PZrBNDZANwQ3p9A3BvXfsvpFFaVwI/qF32MjOzcpxa5h+X9FXgKuBsSXuBTwCrgXWSbgSeB65Luz8AvA/YBfwj8EttL9jMzE5QaohExIcneOtdDfYN4KZiKzLrbOu3jrJm4072HRpjbl8vK4YWMrzY40usPKWGiJk1b/3WUVbds52xw0cBGD00xqp7tgM4SKw0nXhPxMwaWLNx57EAqRk7fJQ1G3eWVJGZQ8Ssa+w7NDatdrN2cIiYdYm5fb3TajdrB4eIWZdYMbSQ3jk9J7T1zulhxdDCkioy8411s65Ru3nu0VnWSRwiZl1kePGAQ8M6ii9nmZlZbg4RMzPLzSFiZma5+Z6IWYV4WRRrN4eIWUV4WRQrgy9nmVWEl0WxMjhEzCrCy6JYGRwiZhXhZVGsDA4Rs4rwsihWhqZCRNISSa9Pr39e0qclvanY0sxsOoYXD3DrtZcy0NeLgIG+Xm699lLfVLdCNTs663bgMkmXAb8J/CHwFeAdRRVWVR6CaUXysijWbs1ezjqSHk+7DPhMRHwGeENxZVVTbQjm6KExguNDMNdvHS27NDOzXJoNkZclrQJ+HrhfUg8wp7iyqslDMM2sapoNkQ8BrwI3RsR3gQFgTWFVVZSHYJpZ1TR1TyQFx6frtp8nuydi0zC3r5fRBoHhIZhm1q0mPROR9LKklxr8vCzppXYVWRUegmlmVTPpmUhE+OZ5C/nJdGZWNdNagFHSOcDratvpspZNg4dgmlmVNDvZ8AOSngZ2A38DPAv8VYF1IelZSdslbZM0ktrOkvSgpKfT7zOLrMHMzCbX7Ois3wGuBP4hIuYD7wK+WVhVx70zIhZFxGDaXglsiogFwKa0bTO0fusoS1ZvZv7K+1myerPnrZhZ05oNkcMR8f+AUySdEhEPAYsKrGsiy4C70uu7gOESaqgUT4A0s5loNkQOSToDeBi4W9JngCPFlQVAAH8taYuk5ant3IjYD5B+nzP+Q5KWSxqRNHLw4MGCS+x+ngBpZjPRbIgsA8aAjwNfB74D/JuiikqWRMTlwHuBmyS9vZkPRcQdETEYEYP9/f3FVlgBngBpZjPR7GTDH9Zt3jXhji0UEfvS7wOS/hK4AviepPMiYr+k84AD7ailyjwB0sxmotnRWfWTDv9J0tEiJxtKer2kN9ReA+8BngA2ADek3W4A7i2qhtnCEyDNbCaaPRM5YdKhpGGyM4OinAv8pSTIavzTiPi6pMeAdZJuBJ4HriuwhsJ1wrLwngBpZjOhbIX3HB+UHomIK1tcT0sNDg7GyMjItD9XxMF9/He+8y39/MWW0RNuavfO6fFDhMysdJK21E2tmFRTZyKSrq3bPAUYJBs9VTm1Ia+1g3ttyCuQ++De6DvvfuT5kzqwNirKIWJm3aLZZU/qR2IdIZuxvqzl1XSAyYa85j24N/rOiRLYo6LMrJs0e0/kl4oupFMUMeR1Op/1qCgz6yaThoikzzHJZauI+GjLKypZEUNeJ/pOcWLnelSUmXWbqYb4jgBbyFbuvRx4Ov0sAo5O8rmuVcSQ14m+8yNXXshAXy8CBvp6fVPdzLrOVM8TuQtA0i+SLYZ4OG1/EfjrwqsrQRFDXj2M1syqqqkhvpJ2Am+NiBfT9pnAIxHR0dde8g7xNTObzVo+xBdYDWyV9FDafgdwS47azMysQpodnfVHkv4K+OnUtDIivltcWWZm1g0mvbEu6S3p9+XAXGBP+pmb2szMbBab6kzk14HlwKcavBfA1S2vyMzMusZUo7OWp9/vbE85ZmbWTZpdCv66uqXZ/5OkeyQtLra0avDzy82sypp9suFvR8TLkt4GDJE9mOqLxZVVDX5+uZlVXbMhUpud/n7g9oi4FzitmJKqw88vN7Oqa3aeyKik3wfeDXxS0uk0H0Cz1kwWc+yEB1aZmU2l2SD4OWAjsDQiDgFnASsKq6oiJlq0carFHH0ZzMy6RVMhEhH/CBwA3paajpAtxGiTyLuYoy+DmVm3aPbJhp8ge5rhQuCPgDnAnwBLiiut++VdeLGIZ5qYmRWh2Xsi1wCLgW8DRMS+2pBfm9zw4oFp38so4pkmZmZFaPaeyI8iW+43ACS9vriSrIhnmpiZFaHZM5F1aXRWn6RfAX4Z+FJxZc1ufv6ImXWLpp4nAiDpZ4H3kD3VdWNEPFhkYa3g54mYmU1fEc8TIYXGg+kP9Ej6SETcnbNGMzOrgKmWgv8xSask/Z6k9yhzM/AM2dyRtpO0VNJOSbskrSyjBjMzy0x1JvLHwPeBbwH/jmyC4WnAsojYVnBtJ5HUA3we+FlgL/CYpA0R8WS7azEzs6lD5M0RcSmApC8BLwAXRsTLhVfW2BXAroh4JtW0FlgGdH2IeJkTM+tGU4XI4dqLiDgqaXeJAQIwQPZkxZq9HH9k70meOfhDPvT73yq8qJl64ZVX2f3CD3ktjXEYPTTGr6/bxuc2P83ZZ5xebnFmZpOYKkQuk/RSei2gN20LiIj4sUKrO5katJ0wvEzScrKnMXLGeRe1o6YZ2/Pi2LEAqXktsvbZGCIvvPIqe14c40dHX+O0nlO44KzeWdkPZt2g6SG+nUDSW4FbImIoba8CiIhbG+3fLUN856+8n0b/KwjYvfr9TX1HKy6HteqS2ky+p7b4ZP3aYb1zerj12kt9ec+sTaYzxLfblnN/DFggab6k04DrgQ0l1zRjeVf7rWnFqr+tWjl4pt/jxSfNuktXhUhEHAFuJluW/ilgXUTsKLeqmZvpMietOPC26uA90+/x4pNm3aXpyYadIiIeAB4ou45WmukyJxMdYEcPjbFk9eamvrNVB++Zfo8XnzTrLl0XIlWVZ7XfmokOvIJj7bXLSrW/1ex3TPfgPdPvWTG0sOE9ES8+adaZuupyljXW6HKY4KSb9ZNdVmrVysEz/Z7hxQPceu2lDPT1ImCgr9c31c06mM9EKqDR5bBGZwMw8WWlVq0c3IrvmclZmZm1V1cN8Z2ubhniW4Qlqzc3DJKBvl6+ufLqEioys25R5SG+1iQ/2MrM2sGXsyrKD7Yys3ZwiFRIo5nivnRlZkVyiFTE+OVCakN6R557kYf+/qDPRsysEA6Riphopvjdjzx/bKjvVHNF2sFL3ptVi0OkIiYaujvZXJF2H8wnOluC8kLNzGbGo7MqYjozy2sH75kutjhdXlzRrHocIhWxYmghc3oaPW7lZD1SKQdzL65oVj0OkYoYXjzA60+b+upk75wejk4wwbTog/lMl7w3s87jEKmQH4wdnvT92jpUAyUdzD0B0qx6fGO9QiZbM0twwpyRMlbK9QRIs+pxiFTIiqGFfPzPtjV81G79WUaZB3MvrmhWLQ6RChlePMDIcy+eMDcEGp9l+GBuZq3gEKmY/zp8KYNvOmtGZxntmhDoiYdm3c8hUkEzOcto14RATzw0K0a7/3Hm0Vl2gnZNCPTEQ5vK+q2jLFm9mfkr72fJ6s2FT4atgto/zto5kdhnInaCdk0I7MaJh7781j4+U81nsn+cFdVvPhOxE7RrQmC3TTws4194s5nPVPMp4x9nDhE7QbsmBHbbxEMf1NqrG89UO0EZ/zhziNgJhhcPHJvVLo7Pcm/1qXC7/k6r+KDWXt12ptopyvjHme+J2EnaNYekm+aqTLQagA9qxVgxtLCUVRW6XRkTiTsuRCTdAvwKcDA1/ceIeCC9twq4ETgKfDQiNpZSpM06Pqi1l5fIya/d/zjruBBJbouI361vkHQxcD1wCTAX+Iakfx4RRxt9gVkr+aDWft10pjqbdWqINLIMWBsRrwK7Je0CrgC+VW5ZNlv4oGZ2sk69sX6zpMcl3SnpzNQ2AOyp22dvajuBpOWSRiSNHDx4cPzbZmbWQqWEiKRvSHqiwc8y4HbgImARsB/4VO1jDb7qpAVrI+KOiBiMiMH+/v7C/hvMzKyky1kR8e5m9pP0B8B9aXMvcEHd2+cD+1pcmpmZTUPH3RORdF5E7E+b1wBPpNcbgD+V9GmyG+sLgEdLKNE6lJclMWu/jgsR4H9IWkR2qepZ4FcBImKHpHXAk8AR4CaPzCpHJx6svdaSWTkU0eg5eNUwODgYIyMjZZdRKeMP1pDNlyh7tvmS1ZsbTgYc6Os94bHAZjY1SVsiYrCZfTt1dJZ1qE5dQ8rLkpiVwyFi09KpB2uvtWRWDoeITUunHqy7bVVgs6pwiNi0dOrButtWBTarik4cnWUdrJPXkPKyJGbt5xCxafPB2sxqfDnLzMxyc4iYmVluDhEzM8vNIWJmZrk5RMzMLDeHiJmZ5eYQMTOz3BwiZmaWm0PEzMxyc4iYmVluDhEzM8vNIWJmZrk5RMzMLDeHiJmZ5eYQMTOz3BwiZmaWm0PEzMxyc4iYmVlupYSIpOsk7ZD0mqTBce+tkrRL0k5JQ3XtS1PbLkkr21+1mZmNV9aZyBPAtcDD9Y2SLgauBy4BlgJfkNQjqQf4PPBe4GLgw2lfMzMr0all/NGIeApA0vi3lgFrI+JVYLekXcAV6b1dEfFM+tzatO+T7anYzMwa6bR7IgPAnrrtvaltonYzMytRYWcikr4B/ESDt34rIu6d6GMN2oLGYRcT/N3lwHKACy+8sIlKzcwsr8JCJCLeneNje4EL6rbPB/al1xO1j/+7dwB3AAwODjYMGjMza41Ou5y1Abhe0umS5gMLgEeBx4AFkuZLOo3s5vuGEus0MzNKurEu6Rrgc0A/cL+kbRExFBE7JK0ju2F+BLgpIo6mz9wMbAR6gDsjYkcZtZuZ2XGKqO4Vn8HBwRgZGSm7DDOzriJpS0QMTr1nSWciZtZe67eOsmbjTvYdGmNuXy8rhhYyvNgDHG3mHCJmFbd+6yir7tnO2OGjAIweGmPVPdsBHCQ2Y512Y93MWmzNxp3HAqRm7PBR1mzcWVJFViUOEbOK23dobFrtZtPhEDGruLl9vdNqN5sOh4hZxa0YWkjvnJ4T2nrn9LBiaGFJFVmV+Ma6WcXVbp57dJYVwSFiNgsMLx5waFghfDnLzMxyc4iYmVluDhEzM8vNIWJmZrk5RMzMLLdKr+Ir6SDwXNl1NOFs4IWyi+hg7p/JuX8m5/6ZXKP+eVNE9Dfz4UqHSLeQNNLsssuzkftncu6fybl/JjfT/vHlLDMzy80hYmZmuTlEOsMdZRfQ4dw/k3P/TM79M7kZ9Y/viZiZWW4+EzEzs9wcIiWStFTSTkm7JK0su56ySLpT0gFJT9S1nSXpQUlPp99npnZJ+mzqs8clXV5e5cWTdIGkhyQ9JWmHpI+ldvcPIOl1kh6V9Hepf/5Lap8v6W9T//yZpNNS++lpe1d6f16Z9beLpB5JWyXdl7Zb1j8OkZJI6gE+D7wXuBj4sKSLy62qNF8Glo5rWwlsiogFwKa0DVl/LUg/y4Hb21RjWY4AvxERPwlcCdyU/n/i/sm8ClwdEZcBi4Clkq4EPgnclvrn+8CNaf8bge9HxD8Dbkv7zQYfA56q225Z/zhEynMFsCsinomIHwFrgWUl11SKiHgYeHFc8zLgrvT6LmC4rv0rkXkE6JN0Xnsqbb+I2B8R306vXyY7EAzg/gEg/Xe+kjbnpJ8Arga+ltrH90+t374GvEuS2lRuKSSdD7wf+FLaFi3sH4dIeQaAPXXbe1ObZc6NiP2QHUiBc1L7rO23dGlhMfC3uH+OSZdqtgEHgAeB7wCHIuJI2qW+D471T3r/B8CPt7fitvufwG8Cr6XtH6eF/eMQKU+jdPdQuanNyn6TdAbwF8B/iIiXJtu1QVul+ycijkbEIuB8sjP8n2y0W/o9q/pH0r8GDkTElvrmBrvm7h+HSHn2AhfUbZ8P7Cuplk70vdplmPT7QGqfdf0maQ5ZgNwdEfekZvfPOBFxCPjfZPeO+iTVntxa3wfH+ie9/0ZOvpRaJUuAD0h6luyS+dVkZyYt6x+HSHkeAxakURKnAdcDG0quqZNsAG5Ir28A7q1r/4U0CulK4Ae1yzpVlK5H/yHwVER8uu4t9w8gqV9SX3rdC7yb7L7RQ8AH027j+6fWbx8ENkeFJ8tFxKqIOD8i5pEdYzZHxEdoZf9EhH9K+gHeB/wD2TXc3yq7nhL74avAfuAw2b+EbiS7DrsJeDr9PivtK7JRbd8BtgODZddfcN+8jexywuPAtvTzPvfPsf75l8DW1D9PAP85tb8ZeBTYBfw5cHpqf13a3pXef3PZ/w1t7KurgPta3T+esW5mZrn5cpaZmeXmEDEzs9wcImZmlptDxMzMcnOImJlZbg4Rm9UkHZW0re5nnqRBSZ9N718l6Wfq9h/Os1CmpFem3qt932PWKqdOvYtZpY1FtmRGvWeBkfT6KuAV4P+m7WHgPuDJdhRn1ul8JmI2Tjr7uC8tePhrwMfTWco7gA8Aa9L2Renn65K2SPo/kt6SvmO+pG9JekzS70zwdz4p6d/Xbd8i6TcknSFpk6RvS9ou6aTVnWs11m3/nqRfTK9/StLfpJo21i2P8lFJTyp7zsjalnWYzWo+E7HZrjetAAuwOyKuqb0REc9K+iLwSkT8LoCkDWSzfr+WtjcBvxYRT0v6aeALZOsTfQa4PSK+IummCf72WrJ1jL6Qtn+O7Lkq/wRcExEvSTobeETShmhiZnBaZ+tzwLKIOCjpQ8B/A36Z7Jkj8yPi1dpSIWYz5RCx2a7R5aympJV1fwb487pHLpyefi8B/m16/cc0eLhPRGyVdI6kuUA/2cOAnk9B8N8lvZ1s+e4B4Fzgu02UtRD4F8CDqaYesiVlIFsa5G5J64H10/lvNZuIQ8Qsv1PInsswUQg1s6bQ18gWuvsJsjMTgI+QhcpPRcThtALr68Z97ggnXo6uvS9gR0S8tcHfej/wdrJLcr8t6ZI4/kwJs1x8T8Rsci8Db2i0HdlzPXZLug6OPd/8srTfN8lWTYUsFCayNu33QY4/ae6NZM+AOCzpncCbGnzuOeBiZc/EfiPwrtS+E+iX9NZU0xxJl0g6BbggIh4ie0BRH3BGUz1gNgmHiNnk/hdwTbqR/q/IDvorJG2VdBFZQNwo6e+AHRx/xPHHyJ6H/hhZKDQUETvIQmk0ji/ZfjcwKGkkff/fN/jcHmAd6RIV2Uq2RPao5Q8Cn0w1bSO75NYD/Imk7Wnf2yJ7/obZjHgVXzMzy81nImZmlptDxMzMcnOImJlZbg4RMzPLzSFiZma5OUTMzCw3h4iZmeXmEDEzs9z+P+dotGSzDHnyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gala = pd.read_csv(\"data/gala.csv\")\n",
    "gmod = smf.ols(formula='Species ~ Area + Elevation + Nearest + Scruz  + Adjacent', data=gala).fit()\n",
    "plt.scatter(gmod.fittedvalues, gmod.resid)\n",
    "plt.ylabel(\"Residuals\")\n",
    "plt.xlabel(\"Fitted values\")\n",
    "plt.axhline(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See how transformation improves the plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1c212599e8>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmod = smf.ols(formula='np.sqrt(Species) ~ Area + Elevation + Nearest + Scruz  + Adjacent', data=gala).fit()\n",
    "plt.scatter(gmod.fittedvalues, gmod.resid)\n",
    "plt.ylabel(\"Residuals\")\n",
    "plt.xlabel(\"Fitted values\")\n",
    "plt.axhline(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check the QQ plot of the residuals. Plot is assigned to foo so it doesn't print twice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda/lib/python3.7/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "foo = sm.qqplot(lmod.resid, line=\"q\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Histogram is not a good way to check:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'Residuals')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(lmod.resid)\n",
    "plt.xlabel(\"Residuals\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate some random QQ plots from known distributions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda/lib/python3.7/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "foo = sm.qqplot(np.random.normal(size=50),line=\"q\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda/lib/python3.7/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "foo = sm.qqplot(np.exp(np.random.normal(size=50)),line=\"q\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda/lib/python3.7/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "foo = sm.qqplot(np.random.standard_t(1,size=50),line=\"q\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda/lib/python3.7/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "foo = sm.qqplot(np.random.sample(size=50),line=\"q\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Do the Shapiro test - second value is the p-value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.98698, 0.85240)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.stats.shapiro(lmod.resid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Correlated Errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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>nhtemp</th>\n",
       "      <th>wusa</th>\n",
       "      <th>jasper</th>\n",
       "      <th>westgreen</th>\n",
       "      <th>chesapeake</th>\n",
       "      <th>tornetrask</th>\n",
       "      <th>urals</th>\n",
       "      <th>mongolia</th>\n",
       "      <th>tasman</th>\n",
       "      <th>year</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.66</td>\n",
       "      <td>-0.03</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.66</td>\n",
       "      <td>0.33</td>\n",
       "      <td>-1.49</td>\n",
       "      <td>0.83</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.63</td>\n",
       "      <td>-0.07</td>\n",
       "      <td>0.09</td>\n",
       "      <td>-0.67</td>\n",
       "      <td>0.21</td>\n",
       "      <td>-1.44</td>\n",
       "      <td>0.96</td>\n",
       "      <td>-0.17</td>\n",
       "      <td>1001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.60</td>\n",
       "      <td>-0.11</td>\n",
       "      <td>0.18</td>\n",
       "      <td>-0.67</td>\n",
       "      <td>0.13</td>\n",
       "      <td>-1.39</td>\n",
       "      <td>0.99</td>\n",
       "      <td>-0.22</td>\n",
       "      <td>1002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.55</td>\n",
       "      <td>-0.14</td>\n",
       "      <td>0.30</td>\n",
       "      <td>-0.68</td>\n",
       "      <td>0.08</td>\n",
       "      <td>-1.34</td>\n",
       "      <td>0.95</td>\n",
       "      <td>-0.26</td>\n",
       "      <td>1003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.51</td>\n",
       "      <td>-0.15</td>\n",
       "      <td>0.41</td>\n",
       "      <td>-0.68</td>\n",
       "      <td>0.06</td>\n",
       "      <td>-1.30</td>\n",
       "      <td>0.87</td>\n",
       "      <td>-0.31</td>\n",
       "      <td>1004</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   nhtemp  wusa  jasper  westgreen  chesapeake  tornetrask  urals  mongolia  \\\n",
       "0     NaN -0.66   -0.03       0.03       -0.66        0.33  -1.49      0.83   \n",
       "1     NaN -0.63   -0.07       0.09       -0.67        0.21  -1.44      0.96   \n",
       "2     NaN -0.60   -0.11       0.18       -0.67        0.13  -1.39      0.99   \n",
       "3     NaN -0.55   -0.14       0.30       -0.68        0.08  -1.34      0.95   \n",
       "4     NaN -0.51   -0.15       0.41       -0.68        0.06  -1.30      0.87   \n",
       "\n",
       "   tasman  year  \n",
       "0   -0.12  1000  \n",
       "1   -0.17  1001  \n",
       "2   -0.22  1002  \n",
       "3   -0.26  1003  \n",
       "4   -0.31  1004  "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "globwarm = pd.read_csv(\"data/globwarm.csv\")\n",
    "globwarm.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>nhtemp</td>      <th>  R-squared:         </th> <td>   0.476</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.446</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   15.47</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 25 Sep 2018</td> <th>  Prob (F-statistic):</th> <td>5.03e-16</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:53:00</td>     <th>  Log-Likelihood:    </th> <td>  50.995</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   145</td>      <th>  AIC:               </th> <td>  -83.99</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   136</td>      <th>  BIC:               </th> <td>  -57.20</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     8</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>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>  <td>   -0.2426</td> <td>    0.027</td> <td>   -8.980</td> <td> 0.000</td> <td>   -0.296</td> <td>   -0.189</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>wusa</th>       <td>    0.0774</td> <td>    0.043</td> <td>    1.803</td> <td> 0.074</td> <td>   -0.008</td> <td>    0.162</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>jasper</th>     <td>   -0.2288</td> <td>    0.078</td> <td>   -2.929</td> <td> 0.004</td> <td>   -0.383</td> <td>   -0.074</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>westgreen</th>  <td>    0.0096</td> <td>    0.042</td> <td>    0.229</td> <td> 0.819</td> <td>   -0.073</td> <td>    0.092</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>chesapeake</th> <td>   -0.0321</td> <td>    0.034</td> <td>   -0.943</td> <td> 0.347</td> <td>   -0.099</td> <td>    0.035</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>tornetrask</th> <td>    0.0927</td> <td>    0.045</td> <td>    2.057</td> <td> 0.042</td> <td>    0.004</td> <td>    0.182</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>urals</th>      <td>    0.1854</td> <td>    0.091</td> <td>    2.027</td> <td> 0.045</td> <td>    0.005</td> <td>    0.366</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>mongolia</th>   <td>    0.0420</td> <td>    0.046</td> <td>    0.917</td> <td> 0.361</td> <td>   -0.049</td> <td>    0.133</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>tasman</th>     <td>    0.1155</td> <td>    0.030</td> <td>    3.834</td> <td> 0.000</td> <td>    0.056</td> <td>    0.175</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>12.501</td> <th>  Durbin-Watson:     </th> <td>   0.817</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.002</td> <th>  Jarque-Bera (JB):  </th> <td>  17.388</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.490</td> <th>  Prob(JB):          </th> <td>0.000168</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.384</td> <th>  Cond. No.          </th> <td>    12.9</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                 nhtemp   R-squared:                       0.476\n",
       "Model:                            OLS   Adj. R-squared:                  0.446\n",
       "Method:                 Least Squares   F-statistic:                     15.47\n",
       "Date:                Tue, 25 Sep 2018   Prob (F-statistic):           5.03e-16\n",
       "Time:                        15:53:00   Log-Likelihood:                 50.995\n",
       "No. Observations:                 145   AIC:                            -83.99\n",
       "Df Residuals:                     136   BIC:                            -57.20\n",
       "Df Model:                           8                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     -0.2426      0.027     -8.980      0.000      -0.296      -0.189\n",
       "wusa           0.0774      0.043      1.803      0.074      -0.008       0.162\n",
       "jasper        -0.2288      0.078     -2.929      0.004      -0.383      -0.074\n",
       "westgreen      0.0096      0.042      0.229      0.819      -0.073       0.092\n",
       "chesapeake    -0.0321      0.034     -0.943      0.347      -0.099       0.035\n",
       "tornetrask     0.0927      0.045      2.057      0.042       0.004       0.182\n",
       "urals          0.1854      0.091      2.027      0.045       0.005       0.366\n",
       "mongolia       0.0420      0.046      0.917      0.361      -0.049       0.133\n",
       "tasman         0.1155      0.030      3.834      0.000       0.056       0.175\n",
       "==============================================================================\n",
       "Omnibus:                       12.501   Durbin-Watson:                   0.817\n",
       "Prob(Omnibus):                  0.002   Jarque-Bera (JB):               17.388\n",
       "Skew:                           0.490   Prob(JB):                     0.000168\n",
       "Kurtosis:                       4.384   Cond. No.                         12.9\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lmod = smf.ols(formula='nhtemp ~ wusa + jasper + westgreen + chesapeake + tornetrask + urals + mongolia + tasman',\n",
    "               data=globwarm).fit()\n",
    "lmod.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1c21a24c50>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(globwarm.year[lmod.resid.keys()], lmod.resid)\n",
    "plt.axhline(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x10d15d908>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(lmod.resid.iloc[:-1],lmod.resid.iloc[1:])\n",
    "plt.axhline(0,alpha=0.5)\n",
    "plt.axvline(0,alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the statistic. P-values do not seem to be available. 2 is considered null but less than 1 is a sign of a problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8166063726402724"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm.stats.stattools.durbin_watson(lmod.resid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finding Unusual Observations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Australia    0.067713\n",
       "Austria      0.120384\n",
       "Belgium      0.087482\n",
       "Bolivia      0.089471\n",
       "Brazil       0.069559\n",
       "dtype: float64"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lmod = smf.ols(formula='sr ~ pop15 + pop75 + dpi + ddpi', data=savings).fit()\n",
    "diagv = lmod.get_influence()\n",
    "hatv = pd.Series(diagv.hat_matrix_diag, savings.index)\n",
    "hatv.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make the half-normal plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x10df3b470>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=50\n",
    "ix = np.arange(1,n+1)\n",
    "halfq = sp.stats.norm.ppf((n+ix)/(2*n+1)),\n",
    "plt.scatter(halfq, np.sort(hatv))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Should tag these on the plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "South Rhodesia    0.160809\n",
       "Ireland           0.212236\n",
       "Japan             0.223310\n",
       "United States     0.333688\n",
       "Libya             0.531457\n",
       "dtype: float64"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hatv.sort_values().iloc[-5:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the built-in plots. Not sure about residuals^2 as a diagnostic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "foo = sm.graphics.plot_leverage_resid2(lmod)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Would prefer R style plot here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "foo = sm.graphics.influence_plot(lmod)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make a QQ plot of the Pearson residuals. These are not the same as the standardised residuals in R."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "foo = sm.qqplot(lmod.resid_pearson)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make the example plots with outliers. (Seems like this could be done more neatly)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(123)\n",
    "testdata = pd.DataFrame({'x' : np.arange(1,11), 'y' : np.arange(1,11) + np.random.normal(size=10)})\n",
    "p1 = pd.DataFrame({'x': [5.5], 'y':[12]})\n",
    "alldata = testdata.append(p1,ignore_index=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10deb5e80>]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "marksize = np.ones(11)\n",
    "marksize[10] = 3\n",
    "plt.scatter(alldata.x, alldata.y, s= marksize*5)\n",
    "slope, intercept = np.polyfit(testdata.x, testdata.y,1)\n",
    "plt.plot(testdata.x, intercept + slope * testdata.x)\n",
    "slope, intercept = np.polyfit(alldata.x, alldata.y,1)\n",
    "plt.plot(alldata.x, intercept + slope * alldata.x, color='red')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c2193f4a8>]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = pd.DataFrame({'x': [15], 'y':[15.1]})\n",
    "alldata = testdata.append(p1,ignore_index=True)\n",
    "plt.scatter(alldata.x, alldata.y, s= marksize*5)\n",
    "slope, intercept = np.polyfit(testdata.x, testdata.y,1)\n",
    "plt.plot(testdata.x, intercept + slope * testdata.x)\n",
    "slope, intercept = np.polyfit(alldata.x, alldata.y,1)\n",
    "plt.plot(alldata.x, intercept + slope * alldata.x, color='red')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c2171eb70>]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = pd.DataFrame({'x': [15], 'y':[5.1]})\n",
    "alldata = testdata.append(p1,ignore_index=True)\n",
    "plt.scatter(alldata.x, alldata.y, s= marksize*5)\n",
    "slope, intercept = np.polyfit(testdata.x, testdata.y,1)\n",
    "plt.plot(testdata.x, intercept + slope * testdata.x)\n",
    "slope, intercept = np.polyfit(alldata.x, alldata.y,1)\n",
    "plt.plot(alldata.x, intercept + slope * alldata.x, color='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the studentized residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('Zambia', 2.8535583382284377)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stud = pd.Series(diagv.resid_studentized_external, savings.index)\n",
    "(pd.Series.idxmax(abs(stud)), np.max(abs(stud)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find the Bonferroni-adjusted critical value:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3.525801306486005"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.stats.t.ppf(0.05/(2*50),44)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Star example that has multiple outliers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "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>temp</th>\n",
       "      <th>light</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4.37</td>\n",
       "      <td>5.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.56</td>\n",
       "      <td>5.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.26</td>\n",
       "      <td>4.93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.56</td>\n",
       "      <td>5.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.30</td>\n",
       "      <td>5.19</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   temp  light\n",
       "0  4.37   5.23\n",
       "1  4.56   5.74\n",
       "2  4.26   4.93\n",
       "3  4.56   5.74\n",
       "4  4.30   5.19"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "star = pd.read_csv(\"data/star.csv\")\n",
    "star.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Put the line on the plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c216cac50>]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lmod = smf.ols(formula='light ~ temp',data=star).fit()\n",
    "plt.scatter(star.temp, star.light)\n",
    "plt.plot([3.4, 4.7], [lmod.params[0] + lmod.params[1]*3.4, lmod.params[0] + lmod.params[1]*4.7])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Look for outliers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2.049392729378057, 1.905847201766315)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stud = lmod.get_influence().resid_studentized_external\n",
    "np.min(stud), np.max(stud)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the line without the four points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c225b73c8>]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lmodr = smf.ols(formula='light ~ temp',data=star[star.temp > 3.6]).fit()\n",
    "plt.scatter(star.temp, star.light)\n",
    "plt.plot([3.4, 4.7], [lmod.params[0] + lmod.params[1]*3.4, lmod.params[0] + lmod.params[1]*4.7])\n",
    "plt.plot([3.4, 4.7], [lmodr.params[0] + lmodr.params[1]*3.4, lmodr.params[0] + lmodr.params[1]*4.7],color='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Influential observations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1c2188e9b0>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lmod = smf.ols(formula='sr ~ pop15 + pop75 + dpi + ddpi', data=savings).fit()\n",
    "diagv = lmod.get_influence()\n",
    "cooks = pd.Series(diagv.cooks_distance[0], savings.index)\n",
    "n=50\n",
    "ix = np.arange(1,n+1)\n",
    "halfq = sp.stats.norm.ppf((n+ix)/(2*n+1)),\n",
    "plt.scatter(halfq, np.sort(cooks))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Would be best placed on the plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Philippines    0.045221\n",
       "Ireland        0.054396\n",
       "Zambia         0.096633\n",
       "Japan          0.142816\n",
       "Libya          0.268070\n",
       "dtype: float64"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cooks.sort_values().iloc[-5:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First column is the all data estimates and second is one without largest cook stat."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "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>with</th>\n",
       "      <th>without</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>28.566087</td>\n",
       "      <td>24.524046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pop15</th>\n",
       "      <td>-0.461193</td>\n",
       "      <td>-0.391440</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pop75</th>\n",
       "      <td>-1.691498</td>\n",
       "      <td>-1.280867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dpi</th>\n",
       "      <td>-0.000337</td>\n",
       "      <td>-0.000319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ddpi</th>\n",
       "      <td>0.409695</td>\n",
       "      <td>0.610279</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                with    without\n",
       "Intercept  28.566087  24.524046\n",
       "pop15      -0.461193  -0.391440\n",
       "pop75      -1.691498  -1.280867\n",
       "dpi        -0.000337  -0.000319\n",
       "ddpi        0.409695   0.610279"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lmodi = smf.ols(formula='sr ~ pop15 + pop75 + dpi + ddpi', data=savings[cooks < 0.2]).fit()\n",
    "pd.DataFrame({'with':lmod.params,'without':lmodi.params})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Would be better to autodetect extreme cases and label them. Note that dfbetas is the change in standard errors and not the change in coefficient as in R."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(48,-0.483244,'Libya')"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p15d = diagv.dfbetas[:,1]\n",
    "plt.scatter(np.arange(1,51),p15d)\n",
    "plt.axhline(0)\n",
    "ix = 22\n",
    "plt.annotate(savings.index[ix],(ix, p15d[ix]))\n",
    "ix = 48\n",
    "plt.annotate(savings.index[ix],(ix, p15d[ix]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Checking the structure of the model\n",
    "Partial regression plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c225839b0>]"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = smf.ols(formula='sr ~ pop75 + dpi + ddpi', data=savings).fit().resid\n",
    "m = smf.ols(formula='pop15 ~ pop75 + dpi + ddpi', data=savings).fit().resid\n",
    "plt.scatter(m,d)\n",
    "plt.xlabel(\"pop15 residuals\")\n",
    "plt.ylabel(\"sr residuals\")\n",
    "plt.plot([-10,8], [-10*lmod.params[1], 8*lmod.params[1]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Partial residual plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c2281f3c8>]"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pr = lmod.resid + savings.pop15*lmod.params[1]\n",
    "plt.scatter(savings.pop15, pr)\n",
    "plt.xlabel(\"pop15\")\n",
    "plt.ylabel(\"partial residuals\")\n",
    "plt.plot([20,50], [20*lmod.params[1], 50*lmod.params[1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>sr</td>        <th>  R-squared:         </th> <td>   0.156</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>  -0.032</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>  0.8302</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 25 Sep 2018</td> <th>  Prob (F-statistic):</th>  <td> 0.523</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:53:02</td>     <th>  Log-Likelihood:    </th> <td> -64.176</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    23</td>      <th>  AIC:               </th> <td>   138.4</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    18</td>      <th>  BIC:               </th> <td>   144.0</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     4</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>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>   -2.4340</td> <td>   21.155</td> <td>   -0.115</td> <td> 0.910</td> <td>  -46.879</td> <td>   42.011</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>pop15</th>     <td>    0.2739</td> <td>    0.439</td> <td>    0.624</td> <td> 0.541</td> <td>   -0.649</td> <td>    1.197</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>pop75</th>     <td>   -3.5485</td> <td>    3.033</td> <td>   -1.170</td> <td> 0.257</td> <td>   -9.921</td> <td>    2.824</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>dpi</th>       <td>    0.0004</td> <td>    0.005</td> <td>    0.084</td> <td> 0.934</td> <td>   -0.010</td> <td>    0.011</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ddpi</th>      <td>    0.3955</td> <td>    0.290</td> <td>    1.363</td> <td> 0.190</td> <td>   -0.214</td> <td>    1.005</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 1.851</td> <th>  Durbin-Watson:     </th> <td>   1.904</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.396</td> <th>  Jarque-Bera (JB):  </th> <td>   1.540</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.497</td> <th>  Prob(JB):          </th> <td>   0.463</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.213</td> <th>  Cond. No.          </th> <td>8.87e+03</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 8.87e+03. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                     sr   R-squared:                       0.156\n",
       "Model:                            OLS   Adj. R-squared:                 -0.032\n",
       "Method:                 Least Squares   F-statistic:                    0.8302\n",
       "Date:                Tue, 25 Sep 2018   Prob (F-statistic):              0.523\n",
       "Time:                        15:53:02   Log-Likelihood:                -64.176\n",
       "No. Observations:                  23   AIC:                             138.4\n",
       "Df Residuals:                      18   BIC:                             144.0\n",
       "Df Model:                           4                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     -2.4340     21.155     -0.115      0.910     -46.879      42.011\n",
       "pop15          0.2739      0.439      0.624      0.541      -0.649       1.197\n",
       "pop75         -3.5485      3.033     -1.170      0.257      -9.921       2.824\n",
       "dpi            0.0004      0.005      0.084      0.934      -0.010       0.011\n",
       "ddpi           0.3955      0.290      1.363      0.190      -0.214       1.005\n",
       "==============================================================================\n",
       "Omnibus:                        1.851   Durbin-Watson:                   1.904\n",
       "Prob(Omnibus):                  0.396   Jarque-Bera (JB):                1.540\n",
       "Skew:                           0.497   Prob(JB):                        0.463\n",
       "Kurtosis:                       2.213   Cond. No.                     8.87e+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, 8.87e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "smf.ols(formula='sr ~ pop15 + pop75 + dpi + ddpi', data=savings[savings.pop15 > 35]).fit().summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>sr</td>        <th>  R-squared:         </th> <td>   0.507</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.418</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   5.663</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 25 Sep 2018</td> <th>  Prob (F-statistic):</th>  <td>0.00273</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:53:02</td>     <th>  Log-Likelihood:    </th> <td> -63.072</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    27</td>      <th>  AIC:               </th> <td>   136.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    22</td>      <th>  BIC:               </th> <td>   142.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     4</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>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>   23.9618</td> <td>    8.084</td> <td>    2.964</td> <td> 0.007</td> <td>    7.197</td> <td>   40.726</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>pop15</th>     <td>   -0.3859</td> <td>    0.195</td> <td>   -1.975</td> <td> 0.061</td> <td>   -0.791</td> <td>    0.019</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>pop75</th>     <td>   -1.3277</td> <td>    0.926</td> <td>   -1.434</td> <td> 0.166</td> <td>   -3.248</td> <td>    0.593</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>dpi</th>       <td>   -0.0005</td> <td>    0.001</td> <td>   -0.634</td> <td> 0.533</td> <td>   -0.002</td> <td>    0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ddpi</th>      <td>    0.8844</td> <td>    0.295</td> <td>    2.994</td> <td> 0.007</td> <td>    0.272</td> <td>    1.497</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.363</td> <th>  Durbin-Watson:     </th> <td>   2.189</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.834</td> <th>  Jarque-Bera (JB):  </th> <td>   0.396</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.241</td> <th>  Prob(JB):          </th> <td>   0.820</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.654</td> <th>  Cond. No.          </th> <td>3.01e+04</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 3.01e+04. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                     sr   R-squared:                       0.507\n",
       "Model:                            OLS   Adj. R-squared:                  0.418\n",
       "Method:                 Least Squares   F-statistic:                     5.663\n",
       "Date:                Tue, 25 Sep 2018   Prob (F-statistic):            0.00273\n",
       "Time:                        15:53:02   Log-Likelihood:                -63.072\n",
       "No. Observations:                  27   AIC:                             136.1\n",
       "Df Residuals:                      22   BIC:                             142.6\n",
       "Df Model:                           4                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     23.9618      8.084      2.964      0.007       7.197      40.726\n",
       "pop15         -0.3859      0.195     -1.975      0.061      -0.791       0.019\n",
       "pop75         -1.3277      0.926     -1.434      0.166      -3.248       0.593\n",
       "dpi           -0.0005      0.001     -0.634      0.533      -0.002       0.001\n",
       "ddpi           0.8844      0.295      2.994      0.007       0.272       1.497\n",
       "==============================================================================\n",
       "Omnibus:                        0.363   Durbin-Watson:                   2.189\n",
       "Prob(Omnibus):                  0.834   Jarque-Bera (JB):                0.396\n",
       "Skew:                          -0.241   Prob(JB):                        0.820\n",
       "Kurtosis:                       2.654   Cond. No.                     3.01e+04\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, 3.01e+04. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "smf.ols(formula='sr ~ pop15 + pop75 + dpi + ddpi', data=savings[savings.pop15 < 35]).fit().summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the young and old groups with different colors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'sr')"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "savings['age'] = np.where(savings.pop15 > 35, 'red', 'blue')\n",
    "plt.scatter(savings.ddpi, savings.sr, color=savings.age)\n",
    "plt.xlabel(\"ddpi\")\n",
    "plt.ylabel(\"sr\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Would be nice to have a legend but `matplotlib` does not make this easy. Fortunately, `seaborn` makes this more convenient:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda/lib/python3.7/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x1c219cf9b0>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 427x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "savings['age'] = np.where(savings.pop15 > 35, 'young', 'old')\n",
    "sns.lmplot('ddpi','sr',data=savings, hue='age')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Can facet this also:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda/lib/python3.7/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x1c22b21278>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot('ddpi','sr',data=savings, col='age')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": {
       "Software versions": [
        {
         "module": "Python",
         "version": "3.7.0 64bit [Clang 4.0.1 (tags/RELEASE_401/final)]"
        },
        {
         "module": "IPython",
         "version": "6.5.0"
        },
        {
         "module": "OS",
         "version": "Darwin 17.7.0 x86_64 i386 64bit"
        },
        {
         "module": "pandas",
         "version": "0.23.4"
        },
        {
         "module": "numpy",
         "version": "1.15.1"
        },
        {
         "module": "matplotlib",
         "version": "2.2.3"
        },
        {
         "module": "seaborn",
         "version": "0.9.0"
        },
        {
         "module": "scipy",
         "version": "1.1.0"
        },
        {
         "module": "patsy",
         "version": "0.5.0"
        },
        {
         "module": "statsmodels",
         "version": "0.9.0"
        }
       ]
      },
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>3.7.0 64bit [Clang 4.0.1 (tags/RELEASE_401/final)]</td></tr><tr><td>IPython</td><td>6.5.0</td></tr><tr><td>OS</td><td>Darwin 17.7.0 x86_64 i386 64bit</td></tr><tr><td>pandas</td><td>0.23.4</td></tr><tr><td>numpy</td><td>1.15.1</td></tr><tr><td>matplotlib</td><td>2.2.3</td></tr><tr><td>seaborn</td><td>0.9.0</td></tr><tr><td>scipy</td><td>1.1.0</td></tr><tr><td>patsy</td><td>0.5.0</td></tr><tr><td>statsmodels</td><td>0.9.0</td></tr><tr><td colspan='2'>Tue Sep 25 15:53:03 2018 BST</td></tr></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{|l|l|}\\hline\n",
       "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
       "Python & 3.7.0 64bit [Clang 4.0.1 (tags/RELEASE\\_401/final)] \\\\ \\hline\n",
       "IPython & 6.5.0 \\\\ \\hline\n",
       "OS & Darwin 17.7.0 x86\\_64 i386 64bit \\\\ \\hline\n",
       "pandas & 0.23.4 \\\\ \\hline\n",
       "numpy & 1.15.1 \\\\ \\hline\n",
       "matplotlib & 2.2.3 \\\\ \\hline\n",
       "seaborn & 0.9.0 \\\\ \\hline\n",
       "scipy & 1.1.0 \\\\ \\hline\n",
       "patsy & 0.5.0 \\\\ \\hline\n",
       "statsmodels & 0.9.0 \\\\ \\hline\n",
       "\\hline \\multicolumn{2}{|l|}{Tue Sep 25 15:53:03 2018 BST} \\\\ \\hline\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "Software versions\n",
       "Python 3.7.0 64bit [Clang 4.0.1 (tags/RELEASE_401/final)]\n",
       "IPython 6.5.0\n",
       "OS Darwin 17.7.0 x86_64 i386 64bit\n",
       "pandas 0.23.4\n",
       "numpy 1.15.1\n",
       "matplotlib 2.2.3\n",
       "seaborn 0.9.0\n",
       "scipy 1.1.0\n",
       "patsy 0.5.0\n",
       "statsmodels 0.9.0\n",
       "Tue Sep 25 15:53:03 2018 BST"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%load_ext version_information\n",
    "%version_information pandas, numpy, matplotlib, seaborn, scipy, patsy, statsmodels"
   ]
  }
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