{
 "metadata": {
  "name": "stats_linear_models"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "This notebook introduces the use of pandas and the formula framework in statsmodels in the context of linear modeling."
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "It is based heavily on Jonathan Taylor's class notes that use R\n",
      "http://www.stanford.edu/class/stats191/interactions.html"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Formula interface may change slightly before 0.5.0 release."
     ]
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Some general imports"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import statsmodels.api as sm\n",
      "import matplotlib.pyplot as plt\n",
      "import pandas\n",
      "from scipy import stats\n",
      "\n",
      "np.set_printoptions(precision=4, suppress=True)\n",
      "pandas.set_printoptions(notebook_repr_html=False,\n",
      "                        precision=4,\n",
      "                        max_columns=12)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from statsmodels.formula.api import ols\n",
      "from statsmodels.graphics.api import interaction_plot, abline_plot, qqplot\n",
      "from statsmodels.stats.api import anova_lm"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1: IT salary data"
     ]
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Outcome:    S, salaries for IT staff in a corporation\n",
      "Predictors: X, experience in years\n",
      "            M, managment, 2 levels, 0=non-management, 1=management\n",
      "            E, education, 3 levels, 1=Bachelor's, 2=Master's, 3=Ph.D"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "try:\n",
      "    salary_table = pandas.read_csv('salary.table')\n",
      "except:\n",
      "    url = 'http://stats191.stanford.edu/data/salary.table'\n",
      "    salary_table = pandas.read_table(url) # needs pandas 0.7.3\n",
      "    salary_table.to_csv('salary.table', index=False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print salary_table.head(10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "       S  X  E  M\n",
        "0  13876  1  1  1\n",
        "1  11608  1  3  0\n",
        "2  18701  1  3  1\n",
        "3  11283  1  2  0\n",
        "4  11767  1  3  0\n",
        "5  20872  2  2  1\n",
        "6  11772  2  2  0\n",
        "7  10535  2  1  0\n",
        "8  12195  2  3  0\n",
        "9  12313  3  2  0\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "E = salary_table.E # Education\n",
      "M = salary_table.M # Management\n",
      "X = salary_table.X # Experience\n",
      "S = salary_table.S # Salary"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "A context manager that mimics R's with() function can be found here: https://gist.github.com/2347382"
     ]
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Let's explore the data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(10,8))\n",
      "ax = fig.add_subplot(111, xlabel='Experience', ylabel='Salary',\n",
      "            xlim=(0, 27), ylim=(9600, 28800))\n",
      "symbols = ['D', '^']\n",
      "man_label = [\"Non-Mgmt\", \"Mgmt\"]\n",
      "educ_label = [\"Bachelors\", \"Masters\", \"PhD\"]\n",
      "colors = ['r', 'g', 'blue']\n",
      "factor_groups = salary_table.groupby(['E','M'])\n",
      "for values, group in factor_groups:\n",
      "    i,j = values\n",
      "    label = \"%s - %s\" % (man_label[j], educ_label[i-1])\n",
      "    ax.scatter(group['X'], group['S'], marker=symbols[j], color=colors[i-1],\n",
      "               s=350, label=label)\n",
      "ax.legend(scatterpoints=1, markerscale=.7, labelspacing=1);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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/+/btuHXrFgBAqVRCEATIZLJGa5w2bRqWL1+OCxcuAIB2nFpTfvjhB5w6dQrV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\ngP8PVi6KW3qaXDUAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xaebeaac>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Fit a linear model\n",
      "\n",
      "$$S_i = \\beta_0 + \\beta_1X_i + \\beta_2E_{i2} + \\beta_3E_{i3} + \\beta_4M_i + \\epsilon_i$$\n",
      "\n",
      "where\n",
      "\n",
      "$$ E_{i2}=\\cases{1,&if $E_i=2$;\\cr 0,&otherwise. \\cr}$$ \n",
      "$$ E_{i3}=\\cases{1,&if $E_i=3$;\\cr 0,&otherwise. \\cr}$$ \n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "formula = 'S ~ C(E) + C(M) + X'\n",
      "lm = ols(formula, salary_table).fit()\n",
      "print lm.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                            OLS Regression Results                            \n",
        "==============================================================================\n",
        "Dep. Variable:                      S   R-squared:                       0.957\n",
        "Model:                            OLS   Adj. R-squared:                  0.953\n",
        "Method:                 Least Squares   F-statistic:                     226.8\n",
        "Date:                Sat, 01 Dec 2012   Prob (F-statistic):           2.23e-27\n",
        "Time:                        12:28:58   Log-Likelihood:                -381.63\n",
        "No. Observations:                  46   AIC:                             773.3\n",
        "Df Residuals:                      41   BIC:                             782.4\n",
        "Df Model:                           4                                         \n",
        "==============================================================================\n",
        "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
        "------------------------------------------------------------------------------\n",
        "Intercept   8035.5976    386.689     20.781      0.000      7254.663  8816.532\n",
        "C(E)[T.2]   3144.0352    361.968      8.686      0.000      2413.025  3875.045\n",
        "C(E)[T.3]   2996.2103    411.753      7.277      0.000      2164.659  3827.762\n",
        "C(M)[T.1]   6883.5310    313.919     21.928      0.000      6249.559  7517.503\n",
        "X            546.1840     30.519     17.896      0.000       484.549   607.819\n",
        "==============================================================================\n",
        "Omnibus:                        2.293   Durbin-Watson:                   2.237\n",
        "Prob(Omnibus):                  0.318   Jarque-Bera (JB):                1.362\n",
        "Skew:                          -0.077   Prob(JB):                        0.506\n",
        "Kurtosis:                       2.171   Cond. No.                         33.5\n",
        "==============================================================================\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Aside: Contrasts (see contrasts notebook)"
     ]
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Look at the design matrix created for us. Every results instance has a reference to the model."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lm.model.exog"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "array([[  1.,   0.,   0.,   1.,   1.],\n",
        "       [  1.,   0.,   1.,   0.,   1.],\n",
        "       [  1.,   0.,   1.,   1.,   1.],\n",
        "       [  1.,   1.,   0.,   0.,   1.],\n",
        "       [  1.,   0.,   1.,   0.,   1.],\n",
        "       [  1.,   1.,   0.,   1.,   2.],\n",
        "       [  1.,   1.,   0.,   0.,   2.],\n",
        "       [  1.,   0.,   0.,   0.,   2.],\n",
        "       [  1.,   0.,   1.,   0.,   2.],\n",
        "       [  1.,   1.,   0.,   0.,   3.],\n",
        "       [  1.,   0.,   0.,   1.,   3.],\n",
        "       [  1.,   1.,   0.,   1.,   3.],\n",
        "       [  1.,   0.,   1.,   1.,   3.],\n",
        "       [  1.,   0.,   0.,   0.,   4.],\n",
        "       [  1.,   0.,   1.,   1.,   4.],\n",
        "       [  1.,   0.,   1.,   0.,   4.],\n",
        "       [  1.,   1.,   0.,   0.,   4.],\n",
        "       [  1.,   1.,   0.,   0.,   5.],\n",
        "       [  1.,   0.,   1.,   0.,   5.],\n",
        "       [  1.,   0.,   0.,   1.,   5.],\n",
        "       [  1.,   0.,   0.,   0.,   6.],\n",
        "       [  1.,   0.,   1.,   1.,   6.],\n",
        "       [  1.,   1.,   0.,   0.,   6.],\n",
        "       [  1.,   1.,   0.,   1.,   6.],\n",
        "       [  1.,   0.,   0.,   1.,   7.],\n",
        "       [  1.,   1.,   0.,   0.,   8.],\n",
        "       [  1.,   0.,   0.,   1.,   8.],\n",
        "       [  1.,   0.,   1.,   1.,   8.],\n",
        "       [  1.,   0.,   0.,   0.,   8.],\n",
        "       [  1.,   0.,   0.,   0.,  10.],\n",
        "       [  1.,   1.,   0.,   0.,  10.],\n",
        "       [  1.,   0.,   1.,   1.,  10.],\n",
        "       [  1.,   1.,   0.,   1.,  10.],\n",
        "       [  1.,   1.,   0.,   1.,  11.],\n",
        "       [  1.,   0.,   0.,   0.,  11.],\n",
        "       [  1.,   1.,   0.,   0.,  12.],\n",
        "       [  1.,   0.,   1.,   1.,  12.],\n",
        "       [  1.,   0.,   0.,   0.,  13.],\n",
        "       [  1.,   1.,   0.,   1.,  13.],\n",
        "       [  1.,   1.,   0.,   0.,  14.],\n",
        "       [  1.,   0.,   1.,   1.,  15.],\n",
        "       [  1.,   1.,   0.,   1.,  16.],\n",
        "       [  1.,   1.,   0.,   0.,  16.],\n",
        "       [  1.,   0.,   0.,   0.,  16.],\n",
        "       [  1.,   1.,   0.,   0.,  17.],\n",
        "       [  1.,   0.,   0.,   0.,  20.]])"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Since we initially passed in a DataFrame, we have a transformed DataFrame available."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "try: # interface changed in most recent statsmodels\n",
      "    print lm.model._data._orig_exog.head(10)\n",
      "except Exception:\n",
      "    print lm.model.data.orig_exog.head(10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   Intercept  C(E)[T.2]  C(E)[T.3]  C(M)[T.1]  X\n",
        "0          1          0          0          1  1\n",
        "1          1          0          1          0  1\n",
        "2          1          0          1          1  1\n",
        "3          1          1          0          0  1\n",
        "4          1          0          1          0  1\n",
        "5          1          1          0          1  2\n",
        "6          1          1          0          0  2\n",
        "7          1          0          0          0  2\n",
        "8          1          0          1          0  2\n",
        "9          1          1          0          0  3\n"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "There is a reference to the original untouched data in"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "try:\n",
      "    print lm.model._data.frame.head(10)\n",
      "except Exception:\n",
      "    print lm.model.data.frame.head(10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "       S  X  E  M\n",
        "0  13876  1  1  1\n",
        "1  11608  1  3  0\n",
        "2  18701  1  3  1\n",
        "3  11283  1  2  0\n",
        "4  11767  1  3  0\n",
        "5  20872  2  2  1\n",
        "6  11772  2  2  0\n",
        "7  10535  2  1  0\n",
        "8  12195  2  3  0\n",
        "9  12313  3  2  0\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "If you use the formula interface, statsmodels remembers this transformation. Say you want to know the predicted salary for someone with 12 years experience and a Master's degree who is in a management position"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lm.predict({'X' : [12], 'M' : [1], 'E' : [2]})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "array([ 24617.3721])"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "So far we've assumed that the effect of experience is the same for each level of education and professional role.\n",
      "Perhaps this assumption isn't merited. We can formally test this using some interactions."
     ]
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "We can start by seeing if our model assumptions are met. Let's look at a residuals plot."
     ]
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "And some formal tests"
     ]
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Plot the residuals within the groups separately."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "resid = lm.resid"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(12,8))\n",
      "xticks = []\n",
      "ax = fig.add_subplot(111, xlabel='Group (E, M)', ylabel='Residuals')\n",
      "for values, group in factor_groups:\n",
      "    i,j = values\n",
      "    xticks.append(str((i, j)))\n",
      "    group_num = i*2 + j - 1 # for plotting purposes\n",
      "    x = [group_num] * len(group)\n",
      "    ax.scatter(x, resid[group.index], marker=symbols[j], color=colors[i-1],\n",
      "            s=144, edgecolors='black')\n",
      "ax.set_xticks([1,2,3,4,5,6])\n",
      "ax.set_xticklabels(xticks)\n",
      "ax.axis('tight');\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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S9dB92WWXsXjx4p2O3X///QwfPpz//Oc/DBs2jPvvvx+AVatWMWvWLFatWsXixYu55ppr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\nzNatW9l//4PYsmUpkE9OzlM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1qqHcaeiWpHoEg0Gu/3/XU1pWytTfTTVwS5IaZOhu3y9R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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb0584ec>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Add an interaction between salary and experience, allowing different intercepts for level of experience.\n",
      "\n",
      "$$S_i = \\beta_0+\\beta_1X_i+\\beta_2E_{i2}+\\beta_3E_{i3}+\\beta_4M_i+\\beta_5E_{i2}X_i+\\beta_6E_{i3}X_i+\\epsilon_i$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "interX_lm = ols('S ~ C(E)*X + C(M)', salary_table).fit()\n",
      "print interX_lm.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                            OLS Regression Results                            \n",
        "==============================================================================\n",
        "Dep. Variable:                      S   R-squared:                       0.961\n",
        "Model:                            OLS   Adj. R-squared:                  0.955\n",
        "Method:                 Least Squares   F-statistic:                     158.6\n",
        "Date:                Sat, 01 Dec 2012   Prob (F-statistic):           8.23e-26\n",
        "Time:                        12:28:59   Log-Likelihood:                -379.47\n",
        "No. Observations:                  46   AIC:                             772.9\n",
        "Df Residuals:                      39   BIC:                             785.7\n",
        "Df Model:                           6                                         \n",
        "===============================================================================\n",
        "                  coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
        "-------------------------------------------------------------------------------\n",
        "Intercept    7256.2800    549.494     13.205      0.000      6144.824  8367.736\n",
        "C(E)[T.2]    4172.5045    674.966      6.182      0.000      2807.256  5537.753\n",
        "C(E)[T.3]    3946.3649    686.693      5.747      0.000      2557.396  5335.333\n",
        "C(M)[T.1]    7102.4539    333.442     21.300      0.000      6428.005  7776.903\n",
        "X             632.2878     53.185     11.888      0.000       524.710   739.865\n",
        "C(E)[T.2]:X  -125.5147     69.863     -1.797      0.080      -266.826    15.796\n",
        "C(E)[T.3]:X  -141.2741     89.281     -1.582      0.122      -321.861    39.313\n",
        "==============================================================================\n",
        "Omnibus:                        0.432   Durbin-Watson:                   2.179\n",
        "Prob(Omnibus):                  0.806   Jarque-Bera (JB):                0.590\n",
        "Skew:                           0.144   Prob(JB):                        0.744\n",
        "Kurtosis:                       2.526   Cond. No.                         69.7\n",
        "==============================================================================\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Test that $B_5 = \\beta_6 = 0$. We can use anova_lm or we can use an F-test."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print anova_lm(lm, interX_lm)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   df_resid           ssr  df_diff      ss_diff      F  Pr(>F)\n",
        "0        41  43280719.493        0          NaN    NaN     NaN\n",
        "1        39  39410679.808        2  3870039.685  1.915   0.161\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print interX_lm.f_test('C(E)[T.2]:X = C(E)[T.3]:X = 0')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "<F test: F=array([[ 1.9149]]), p=[[ 0.161]], df_denom=39, df_num=2>\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "The contrasts are created here under the hood by patsy."
     ]
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Interact education with management"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "interM_lm = ols('S ~ X + C(E)*C(M)', salary_table).fit()\n",
      "print interM_lm.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                            OLS Regression Results                            \n",
        "==============================================================================\n",
        "Dep. Variable:                      S   R-squared:                       0.999\n",
        "Model:                            OLS   Adj. R-squared:                  0.999\n",
        "Method:                 Least Squares   F-statistic:                     5517.\n",
        "Date:                Sat, 01 Dec 2012   Prob (F-statistic):           1.67e-55\n",
        "Time:                        12:29:00   Log-Likelihood:                -298.74\n",
        "No. Observations:                  46   AIC:                             611.5\n",
        "Df Residuals:                      39   BIC:                             624.3\n",
        "Df Model:                           6                                         \n",
        "=======================================================================================\n",
        "                          coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
        "---------------------------------------------------------------------------------------\n",
        "Intercept            9472.6854     80.344    117.902      0.000      9310.175  9635.196\n",
        "C(E)[T.2]            1381.6706     77.319     17.870      0.000      1225.279  1538.063\n",
        "C(E)[T.3]            1730.7483    105.334     16.431      0.000      1517.690  1943.806\n",
        "C(M)[T.1]            3981.3769    101.175     39.351      0.000      3776.732  4186.022\n",
        "C(E)[T.2]:C(M)[T.1]  4902.5231    131.359     37.322      0.000      4636.825  5168.222\n",
        "C(E)[T.3]:C(M)[T.1]  3066.0351    149.330     20.532      0.000      2763.986  3368.084\n",
        "X                     496.9870      5.566     89.283      0.000       485.728   508.246\n",
        "==============================================================================\n",
        "Omnibus:                       74.761   Durbin-Watson:                   2.244\n",
        "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1037.873\n",
        "Skew:                          -4.103   Prob(JB):                    4.25e-226\n",
        "Kurtosis:                      24.776   Cond. No.                         79.0\n",
        "==============================================================================\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print anova_lm(lm, interM_lm)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   df_resid           ssr  df_diff       ss_diff        F     Pr(>F)\n",
        "0        41  43280719.493        0           NaN      NaN        NaN\n",
        "1        39   1178167.865        2  42102551.628  696.844  3.026e-31\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "infl = interM_lm.get_influence()\n",
      "resid = infl.resid_studentized_internal"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(12,8))\n",
      "ax = fig.add_subplot(111, xlabel='X', ylabel='standardized resids')\n",
      "\n",
      "for values, group in factor_groups:\n",
      "    i,j = values\n",
      "    idx = group.index\n",
      "    ax.scatter(X[idx], resid[idx], marker=symbols[j], color=colors[i-1],\n",
      "            s=144, edgecolors='black')\n",
      "ax.axis('tight');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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c4A1HjpowYaLmzFlViUiWjmyWZ+vpp5/WnDlzKnX9D6dOlW/nTj0UYiRLRzbL4/LytGjp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\nG/8BPOfaxXGqOXQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xaed538c>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "There looks to be an outlier."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "outl = interM_lm.outlier_test('fdr_bh')\n",
      "outl.sort('unadj_p', inplace=True)\n",
      "print outl"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "    student_resid    unadj_p  fdr_bh(p)\n",
        "32        -14.951  1.677e-17  7.714e-16\n",
        "33          1.288  2.055e-01  9.599e-01\n",
        "23          1.023  3.127e-01  9.599e-01\n",
        "41          0.942  3.520e-01  9.599e-01\n",
        "11          0.897  3.756e-01  9.599e-01\n",
        "5           0.891  3.787e-01  9.599e-01\n",
        "39          0.835  4.089e-01  9.599e-01\n",
        "38          0.819  4.178e-01  9.599e-01\n",
        "21          0.730  4.700e-01  9.599e-01\n",
        "20         -0.726  4.722e-01  9.599e-01\n",
        "30          0.704  4.854e-01  9.599e-01\n",
        "28          0.603  5.500e-01  9.599e-01\n",
        "44         -0.600  5.523e-01  9.599e-01\n",
        "1          -0.590  5.584e-01  9.599e-01\n",
        "17         -0.565  5.755e-01  9.599e-01\n",
        "0          -0.482  6.322e-01  9.599e-01\n",
        "34         -0.475  6.377e-01  9.599e-01\n",
        "6          -0.464  6.453e-01  9.599e-01\n",
        "7           0.429  6.705e-01  9.599e-01\n",
        "45         -0.426  6.722e-01  9.599e-01\n",
        "4           0.424  6.736e-01  9.599e-01\n",
        "3          -0.419  6.779e-01  9.599e-01\n",
        "35          0.382  7.043e-01  9.599e-01\n",
        "43          0.361  7.203e-01  9.599e-01\n",
        "12          0.358  7.224e-01  9.599e-01\n",
        "37          0.343  7.338e-01  9.599e-01\n",
        "2          -0.292  7.721e-01  9.599e-01\n",
        "24          0.287  7.756e-01  9.599e-01\n",
        "31         -0.285  7.771e-01  9.599e-01\n",
        "36         -0.275  7.848e-01  9.599e-01\n",
        "13         -0.269  7.896e-01  9.599e-01\n",
        "27         -0.260  7.964e-01  9.599e-01\n",
        "15          0.252  8.023e-01  9.599e-01\n",
        "16          0.250  8.040e-01  9.599e-01\n",
        "42          0.196  8.458e-01  9.599e-01\n",
        "9          -0.195  8.466e-01  9.599e-01\n",
        "10          0.191  8.497e-01  9.599e-01\n",
        "26         -0.166  8.691e-01  9.599e-01\n",
        "19          0.165  8.697e-01  9.599e-01\n",
        "25         -0.162  8.724e-01  9.599e-01\n",
        "14          0.148  8.831e-01  9.599e-01\n",
        "29          0.147  8.837e-01  9.599e-01\n",
        "40         -0.130  8.973e-01  9.599e-01\n",
        "18         -0.072  9.426e-01  9.855e-01\n",
        "22          0.016  9.872e-01  9.879e-01\n",
        "8          -0.015  9.879e-01  9.879e-01\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "salary_table_clean = salary_table.drop(32)\n",
      "print salary_table_clean"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "        S   X  E  M\n",
        "0   13876   1  1  1\n",
        "1   11608   1  3  0\n",
        "2   18701   1  3  1\n",
        "3   11283   1  2  0\n",
        "4   11767   1  3  0\n",
        "5   20872   2  2  1\n",
        "6   11772   2  2  0\n",
        "7   10535   2  1  0\n",
        "8   12195   2  3  0\n",
        "9   12313   3  2  0\n",
        "10  14975   3  1  1\n",
        "11  21371   3  2  1\n",
        "12  19800   3  3  1\n",
        "13  11417   4  1  0\n",
        "14  20263   4  3  1\n",
        "15  13231   4  3  0\n",
        "16  12884   4  2  0\n",
        "17  13245   5  2  0\n",
        "18  13677   5  3  0\n",
        "19  15965   5  1  1\n",
        "20  12336   6  1  0\n",
        "21  21352   6  3  1\n",
        "22  13839   6  2  0\n",
        "23  22884   6  2  1\n",
        "24  16978   7  1  1\n",
        "25  14803   8  2  0\n",
        "26  17404   8  1  1\n",
        "27  22184   8  3  1\n",
        "28  13548   8  1  0\n",
        "29  14467  10  1  0\n",
        "30  15942  10  2  0\n",
        "31  23174  10  3  1\n",
        "33  25410  11  2  1\n",
        "34  14861  11  1  0\n",
        "35  16882  12  2  0\n",
        "36  24170  12  3  1\n",
        "37  15990  13  1  0\n",
        "38  26330  13  2  1\n",
        "39  17949  14  2  0\n",
        "40  25685  15  3  1\n",
        "41  27837  16  2  1\n",
        "42  18838  16  2  0\n",
        "43  17483  16  1  0\n",
        "44  19207  17  2  0\n",
        "45  19346  20  1  0\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Exercise\n",
      "--------"
     ]
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "1. Fit the same linear model as above (i.e. without interaction terms) but with the cleaned data (=salary_table_clean). Remember to call the .fit() method on your model.\n",
      "\n",
      "Print the model summary.\n",
      "\n",
      "Compare the R-squared between this and the previous model."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "2. Fit the same linear model above but with an interaction term between education and experience. Again, use the cleaned data set. \n",
      "Print the model summary."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "3. Run an ANOVA (or F-test) to test whether the interaction (education*experience) is significant (there are two valid ways to do this)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "4. Run an ANOVA to test whether there exists an interaction between *education* and *management* on salary. Is there?\n",
      "Note: so that the code will continue to run below, create an interaction model and call it \"interM_lm32\"."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Re-plotting the residuals"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "idx = salary_table.index.drop(32)\n",
      "interM_lm32 = ols('S ~ X + C(E) * C(M)', salary_table, subset=idx).fit()\n",
      "resid = interM_lm32.get_influence().summary_frame()['standard_resid']\n",
      "fig = plt.figure(figsize=(12,8))\n",
      "ax = fig.add_subplot(111, xlabel='X[~[32]]', ylabel='standardized resids')\n",
      "\n",
      "for values, group in factor_groups:\n",
      "    i,j = values\n",
      "    idx = group.index\n",
      "    ax.scatter(X[idx], resid[idx], marker=symbols[j], color=colors[i-1],\n",
      "            s=144, edgecolors='black')\n",
      "ax.axis('tight');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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8hx9+kCR99913+u677zR37lzNnTs392vAKvnPSp8rxpI7e7jdbo1+7DE9n5Ki\nEEm1JP0jJ0evvPiiqe8LSPlD+lZJkzIy1GHHDnVv317Hjx+3ezwACGqWP7SlNLGZDnyet9IG87fT\nebfSIX9+76DYTsN854a0wS3pETbUAGCJYm2mDW+++aZOnTolt9utwYMHq2XLlvrf//5X6kMCBfG8\nlTaYu50+dyttYDsNsxUW0pLkEBtqAPAHRcb0v//9b1WuXFkLFy5UcnKypk2bpieffNKK2RDkzj7t\ncKOktpJ+9/hXevoNeuedd3TkyJFSn2PRokU6sXOnbi7gZ6MyMvTZtGnnPXgIKClPIW0gqBFs3nn3\nHa1YscLuMYB8irzPtLHSnjdvnu68805deeWVpg8FSNKWLb+qevVqkgZ6dX1ISC1t27atVI96FLaV\nNuTdTnNnD5QWb0LaYAT1I38GNUc+EKheGPOCXnvnNTkyHJr3zTwe0ga/UeSZ6XvuuUf79+/Xzp07\ntWnTJmVlZalz5875nopoF85Mw2wFnZU+F2enUZp8Cem8OEONQPbCmBc08f2Jcv3dJR2TIv8bSVDD\nUiW6z3R2drY2btyo+vXrq2rVqjp27JiSkpLUtGlTU4b1BTENM+W9r/SgIq59lPtOoxSkp6erTo0a\nGnvqlIYU4/VuSXeFhSm5QwfNW7KktMcDbJEvpI1nFe0mqGGtEn0A0eFwaMuWLZo8ebIkKSUlRWlp\naaU7IeCHFi1apD+2bVMdSauL+KtDRoY++vhjzk6jRCpUqKD77rtP71asqKPFeH2CpEWhobr/4YdL\nezTAFgWGtCTVlVwDXOozsI+cTqdN0wFnFXlmetiwYQoJCdHixYv1/PPPKyoqSsOGDdNPP/1kxXyA\nbQ4eOKAGDRpolJf/60ezkBAlJSVx1AMlMn7iRElS1/ff1/cpKfqbl6/bIKl3RITe+/xzDRgwwLT5\nAKsUGtKGun8FNRtq2KnIYx4tWrRQQkJC7v8rSc2aNdPGjRstGdATjnkACERut1tPP/aYFngZ1IQ0\nAk2RIZ3Xbo58wHwlOuZRvnx5ZWdn53595MgRlStX5MsAAMXkcDg0fuJE9RoyRF2LOPJBSCPQ+BTS\nEkc+YLsiq/ihhx7SwIEDdfjwYT399NNq3769nnrqKStmA4Cg5U1QE9IIND6HtKEuQQ37eDzmkZOT\no9WrV6t69epavHixJKlLly5q1KiRZQN6wjEPAIGusCMfhDQCjcvl0gUXXqC0nmlScW4Y5pZCvw1V\nxws7asmG2EjFAAAgAElEQVRC7maD0lWiW+M1b95cP//8symDlRQxDSAYnBvUe0VIIzCtWLFCPfv1\nVEq/FKmBDy90S2HLwhRzIEZrlq8p1Yd3AVIJz0x37dpVs2bNIloBwCZ5j3zERUYS0ghYHTp0UPx3\n8ar4XUVph5cvIqRhsyI301FRUXK5XAoJCVF4ePjZFzkcOnXqlCUDesJmGkAwcbvdmvjyy2rUtKn6\n9u1r9ziAabzeUBPSsEiJjnn4M2IaAIDAVGRQE9KwUImOeQAAAFjN45EPQhp+hJgGAAB+qcCgJqTh\nZ4hpoIwZdOcgTX5rst1jAIAlzg1qQhr+ptAz08nJyR5fWL16dVMG8gVnphFsNm/erNbtWqtChQra\nv2e/KlasaPdIAGCJFStWqHvv7rqo9kWENCxXrA8g1q1bN/eFe/fuVbVq1SRJx48f1yWXXKJdu3aZ\nN7GXiGkEmz4D+yg+NV7hh8L1/G3P64nHn7B7JACwzNatW1WjRg2/WOghuBTrA4i7d+/Wrl271K1b\nN82dO1fHjh3TsWPHNG/ePHXr1s20YQEUbPPmzVrqXKqcVjlyXePS+FfHKyUlxe6xAMAysbGxhDT8\nTpFnplevXq3evXvnft2rVy+tWrXK1KEAnO+J555Qept0qbykGlJWTJbenvK23WMBABDUiozp2rVr\na+zYsbmb6nHjxik6OtqK2QD8Ke9W2sB2GgAA+xUZ0zNmzNDhw4c1cOBA3XDDDTp8+LBmzJhhxWwA\n/pRvK21gOw0AgO28fgJiSkqK3905gA8gIhhs3rxZV3e8WqnDUvPHtCQdlip/WZk7ewAAYKISPQFx\n1apVuuKKKxQbGytJ2rhxo4YNG1a6EwIoVIFbaQPbaQAAbFXkZvrqq6/WrFmzdP311yshIUGS1Lhx\nY23ZssWSAT1hM41A53ErbWA7DQCAqUq0mZakiy++ON/XoaGhJZ8KQJE8bqUNbKcBALBNkTF98cUX\na+XKlZKkjIwMTZw4UY0aNTJ9MCDYFXQHj8JwZw8AAOxR5Ir53Xff1T//+U8lJSUpOjpa3bt315Qp\nU6yYDQhqc+bMUeqJVGm8d9ef0imtXr1aXbt2NXcwAACQq8gz04mJiYqJicn3vYMHD6pWrVqmDuYN\nzkwjGBw+fFhtO7XVvtr7lNkpU3L8+YMsKfKbSHWq10nfzv5W5ct7OgsCAACKq0RnpuvVq6dBgwbJ\n5XLlfq9Xr16lNx2AQhUa0pIUKrkGuvTDrh90/Y3XKyMjw7Y5AQAIVkXGdJMmTdSxY0e1b99ef/zx\nhxUzAVARIW0gqAEAsJVXd/MYPny43n77bfXr10/fffed2TMBQc+rkDYQ1AAA2KbIM9MtWrTIvb/0\ngQMHdPPNN2v9+vVKTU21ZEBPODONQORTSOfFGWoAAEzhqTmLjOkDBw7ooosuyv06KytLq1atUqdO\nnUp3ymIgphFoMjMzFdskVom1EpUZ50NIG7KkiK8j1Ltpb82aMcuUGQEACDaemrPQW+P95z//0Z13\n3qnPP/+8wF/oDzENBJrQ0FA1im2kg38cVGZ2phc3rzxHquQ47lCLpi1MmQ8AAORX6Jlp4+4dp0+f\n1pkzZ3L/On36tE6fPm3ZgEAwcTgc+uarbxTXIE6R30RKWT68+LQU+XmkRj04Ss889YxpMwIAgL8U\neczDn3HMA4EqMzNTA24aIOcOp1wDXUVvqPOE9OjnR1sxIgAAQaNYZ6YfeuihAn+Bw3H2EOfkyZNL\ne06fBWNMu91uPfLI04qNbaAhQ+6zexyYyOugJqQBADBVsR7a0qpVK7Vq1Urp6enasGGDLrvsMjVs\n2FAJCQncessmbrdb9903XB98sET/+tdLmjLlXbtHgonCwsL031n/9Xzkg5AGAMBWRR7zaNOmjVas\nWKGwsDBJZ7dlHTp00Nq1ay0Z0JNg2kwbIf3FFwlyuf4n6agiIjrrtdee1PDhQ+0eDyYqdENNSAMA\nYIkSPU78xIkTOnXqVO7Xp0+f1okTJ0o0UHx8vGJjY9WwYUO98sorBV7z8MMPq2HDhmrWrFnufa6D\n1fkhXVlSfaWmLtWoURPYUAe4AjfUhDQAAH6hyBtvPfnkk2rZsqU6d+4st9utZcuWafTo0cV+w+zs\nbI0YMULff/+9oqOjddVVV6l///5q1KhR7jXz58/XH3/8oe3bt2vt2rUaOnSo1qxZU+z3LMsKDmmD\nEdSdJYkNdQAzgnrATQO0dPZSOU44CGkAAPyAx5jOycnRZZddpjVr1mjt2rVyOByaMGFCvoe4+Grd\nunW69NJLVbduXUnSoEGD9O233+aL6Tlz5ujuu++WdPaYyYkTJ3To0CHVrFmz2O9bFnkOaQNBHSyM\noL79ntvV7Mpm3P4OAAA/4DGmy5Urp+HDh+vnn3/WgAEDSuUNk5KSFBMTk/t1nTp1zjt/XdA1+/bt\nKzCm827J4+LiFBcXVypz2s27kDYQ1MEiLCxMM6fPtHsMAAACmtPplNPp9OraIo95dO3aVbNmzdKN\nN96Ye1u8kvD2d5x7yLuw15XkyIm/8i2kDQQ1AABAaTh3QTtmzJhCry0ypt977z1NmjRJISEhCg8P\nl3Q2bPN+KNEX0dHRSkxMzP06MTFRderU8XjNvn37FB0dXaz3K4vuv3+EjyFt+Cuoy5Urp6FDh5gy\n35kzZxQeHq7QUF+fdQ0AABBYirybx5kzZ5STk6PMzMzcR4kXN6QlqXXr1tq+fbt2796tjIwMffnl\nl+rfv3++a/r3769p06ZJktasWaOqVasGzXnprKwszZ8fr/T0/vItpA11lZPTXrNnzyvt0XJd1/M6\n/fORf5r2+wEAAMoKr1aLx48f1/bt25WWlpb7vU6dOhXvDUND9fbbb6tHjx7Kzs7W4MGD1ahRI73/\n/vuSpCFDhqh3796aP3++Lr30UlWsWFFTp04t1nuVRaGhoVqzZqnatOmsI0cilZ3tS7TmKDz8ATVu\nnKT//tecmHY6ndq8bbN+2fSLnn3q2RJ9GBUAAKCsK/KhLR9++KEmT56sxMREtWjRQmvWrFG7du20\nZMkSq2YsVCA/tGXv3r1/BvXDXga1EdLb5XTOU1RUlClztb6mtdbXXK/yR8prcMvBemfyO6a8DwAA\ngL8o0UNb3nzzTa1bt05169bV0qVLlZCQoCpVqpT6kMjv4osv1tq1S3XhhZMVEvJmEVdbE9JOp1Nb\nd26VmkoZbTM09ZOpOnDggCnvBQAAUBYUGdPh4eGKiIiQJKWlpSk2Nlbbtm0zfTB4G9TWhLQkPfb0\nY0ppl3L2T00lKadpjl56+SXT3g8AAMDfFRnTMTExOn78uAYMGKBu3bqpf//+uQ9cgfnyBrU06Zyf\n5igk5B+WhHTerbSB7TQAAAh2RZ6ZzsvpdOrUqVPq2bOnypcvb+ZcXgnkM9Pnmjdvnvr2u1XSGMn9\nqKQcKeQuOdxztHvXZl188cWmvr9xVlrN83+//CLOTgMAgMDmqTkLjenk5GSPv7R69eoln6yEgimm\nu/TsoiUZS6QfI6WUF6SQTdKF36hC7WyN7DFSE8ZNMO29nU6n+g7qq5QhKef/bxmnpfAPwrVz207u\n7AEAAAJSsWK6bt26uS/cu3evqlWrJunsbfIuueQS7dq1y7yJvRQsMb1+/Xp16tFJrqEuKUXShxFS\nJYf0j7NfR06NVOKuRNP+BaewrbSB7TQAAAhkxbqbx+7du7Vr1y5169ZNc+fO1bFjx3Ts2DHNmzdP\n3bp1M21YnO/xZx5XapvUs3cFryLpoVRpsEsqL6malBObo1f/71VT3rugs9Ln4uw0AAAIVkWemb7y\nyiu1efPmIr9nh2DYTOfbShf2iJ3j5m2ni9pKG9hOAwCAQFWi+0zXrl1bY8eOzd1Ujxs3TtHR0aU+\nJAqWbytdGJO2006nU79s/kWqIemg578y6mboow8/YjsNAACCSpGPE58xY4bGjBmjgQMHSjr7GPEZ\nM2aYPhjObqVXrl4p971u6Yzna9OapmnyW5P1+KOPl9p2eufOnYqOjpb7B++2/yH1QrRr1y4+iAgA\nAIKGT7fG8zeBfszjrbfe0jOjn/H6+nKOcvp65te67rrrTJwKAAAguBTrbh6Gbdu2aeLEidq9e7ey\nsrJyf+GSJUtKf1IfBXpMwz/9/PPPuuCCCxQTE2P3KAAAwAIliummTZtq6NChatmypUJCQnJ/YatW\nrUp/Uh8R07Ca0+lU7943KiqqktauXap69erZPRIAADBZiWK6VatWWr9+vSmDlRQxDSs5nU716XOz\nXK6vVK7cFl1wwWsENQAAQaBEMT169GhdeOGFuuGGG1ShQoXc7/MERASTvCEtxUmSypWbQlADABAE\nShTTxpMQz8UTEBEsCgppA0ENAEDgK1FM+zNiGmbzFNIGghoAgMBW4pjevHmzfv31V6WlpeV+7667\n7iq9CYuJmIaZvAlpA0ENAEDgKvGZ6WXLlmnLli3q06ePFixYoA4dOmjWrFmmDOsLYhpm8SWkDQQ1\nAACBqUSPE581a5a+//57XXTRRZo6dao2btyoEydOlPqQgL8oTkhLUk7OcB07Nkpt2nT2i88UAAAA\n8xUZ0xEREQoJCVFoaKhOnjypGjVqKDEx0YrZAMtlZmaqd+/+crlelS8hbTgb1H108832H4MCgECT\nk5Nj9wjAeYqM6datW+v48eO6//771bp1a7Vo0ULXXHONFbMBlgsLC9Mbb0xSRMTzkrYX4zcsVETE\nTL3xxsulPRoABL2uvbrqjTffsHsMIB+f7uaxa9cunTp1Ss2aNTNzJq9xZhpm+eCDjzRy5Bilpi6R\n1NDLVy1UxYq3Kz7+G3Xo0MHM8QAg6KxYsUJd+3ZVeGi4kvYkqWLFinaPhCBSojPTXbp0yf37evXq\nqVmzZvm+BwSiBx64T2+88YIiIq6TdxtqQhoAzDTqmVFKvzZdmTGZmvLOFLvHAXIVGtOpqak6duyY\njhw5ouTk5Ny/du/eraSkJCtnBGzhfVAT0gBgphUrVmjTb5ukZpLrGpfGvzJeKSkpdo8FSJJCC/vB\n+++/rzfffFP79+9Xq1atcr9fqVIljRgxwpLhALs98MB9kqSRI68r5MgHIQ0AZhv1zCi52rmkEEk1\nlLudfnzU43aPBhR9Zvqtt97SQw89ZNU8PuHMNKxS8BlqQhoAzLZixQr1uKGHXA/+GdOSdFiq8mUV\nzk7DMiU6M12zZk2dPn1akvTSSy/phhtu0IYNG0p3QpQZLpdLnXt01rCHhgXVv8icf+SDkAYAK+Tb\nShvybKcBuxUZ0y+99JIqVaqkFStWaPHixbr33nv14IMPWjEb/IzL5VK33t205vAafTr3Uw0ZNiQo\ngzo8/FpCGgAskPes9Lk4Ow1/UWRMh4Sc/VfBuXPn6v7771ffvn2VmZlp+mDwL0ZIbzi1QWn90+Qa\n5NL0+OlBGdT/+c9bWrx4LiFtkzNnzvDPICBIFLiVNrCdhp8o8sx0nz59FB0drUWLFikhIUHh4eFq\n06aNNm7caNWMheLMtDXyhXS/tL/+FSxNivwiUrf3vF3vv/O+HA6HrXMi8O3du1dtO7RVg0sbaOG8\nhYqIiLB7JAAmKfCs9Lk4Ow2LlOjM9MyZM9WjRw8tXLhQVatW1fHjx/Xaa6+V+pDwT4WGtCSFK2g3\n1LDe3r171aZDGx2+4rDWn1iv7n26KzU11e6xAJjE41bawHYafsCnJyD6GzbT5vIY0nmxoYbJjJA+\ncuURZbfJlnKkiO8i1KpqKzbUQABasWKFuvXvprT70jzHtCQdlir9t5IO7D3Adhqm8dSchd5nGsHN\n65CW/tpQfzFdGiaCGqXqvJCWpHJSar9Urf/u7IaaoAYCi3OZU45Mh8LfDffq+pxyOdq0aZPatWtn\n8mTA+dhM4zw+hXRebKhRygoM6bzYUAMALFCiM9MILjk5OcULaSnfGeqH/uWfD/pB2VFkSEt/bag5\nQw0AsAkxjXzcbrdS01LlDnNLxVksl5MUena7DRSXVyFtIKgBADYippFPSEiIli1apkZqpAoLKki+\nnKLJkCJnRur6dtfro/c+Mm1GBDafQtpAUAMAbMKZaRTo9OnT6tS1k37Tb0rvlV70ljpPSH/2yWcq\nV45/T4PvMjIyVLdhXR2+/LCy23sZ0nnlSOHfhKtLgy6a+83c0h8QABCUODMNn1WqVEk/fP+Ddxtq\nQhqlJCwsTJ06dVKFPRWkjGL8gpNSuYPl1Lt771KfDQCAglA9KJRXQU1IoxQ5HA5N/2S6+l3dT5Gz\nIn0L6uNS5OeRmvD8BA0bOsy0GRHcdu3apVOnTtk9BgA/QvnAI49BTUjDBCEhIb4HdZ6QfmgEd5KB\nObKzs9WpSyeNGDnC7lEA+BHqB0UqMKgJaZjIp6AmpGGRL774Qsk5yfpq1lfavXu33ePYIju7GJ9l\nAAKcpR9ATE5O1q233qo9e/aobt26mjlzpqpWrXredXXr1lXlypUVEhKisLAwrVu3rsDfxwcQrZX7\noUT3bwo5HkJIw3TZ2dm6/Z7b9d267+S6ySWVP+cCQhoWyc7O1iUNL1FSxySF7QnToPqDNO3jaXaP\nZblrr+2lvn27adSoR+weBbCU33wAccKECerWrZt+//13denSRRMmTCjwOofDIafTqYSEhEJDGtYz\nNtRNwproxo43EtIwnccNNSENC33xxRc6GXJSqidltskMyu308uXLtXZtgl566RWdOXPG7nEAv2Hp\nZjo2NlbLli1TzZo1dfDgQcXFxWnr1q3nXVevXj399NNPuuCCCzz+PjbT9nC73bY9KjwnJ0ePDBum\ny664QsMeftiWGWC97Oxs9RnQR/9L+J90t6QUSR9JE1+cqEcfedTu8RDg8m6lVf/s98KWBt92um3b\nrlq79jZFRi7SM8+00NNPP2H3SIBl/GYzfejQIdWsWVOSVLNmTR06dKjA6xwOh7p27arWrVvrww8/\ntHJEeMHOkL7vjju04T//0cSnntLk11+3ZQ5YLyQkRBUzpeaHpMipUuSHUrOsMCmL85swX96ttCHY\nttPLly/XL7/skHSXXK7nNGHCJLbTwJ9CS/sXduvWTQcPHjzv++PGjcv3tcPhKDTKVq5cqYsuukhH\njhxRt27dFBsbq44dOxZ47ejRo3P/Pi4uTnFxccWeHf7LCOmd336rBS6Xjkrq/OyzkqSH//Uve4eD\n6TZt2qSVP/yg37Okxw9LzXOka9yZ6j5unB4cPlwVK1a0e0QEqOzsbD3x3BM60/FM/odXRUrZLbP1\n/IvPB8V2etSoMXK5npUUJqmxsrM7a/LkKWynEbCcTqecTqdX11p+zMPpdKpWrVo6cOCAOnfuXOAx\nj7zGjBmjqKgoPfro+f9TLsc8gkPekJ7ncsnIpj2SOkdGauTYsQR1gLupVy+1W7hQj+bk5P9+ZKTa\nvfCCHn38cZsmQ6CbPn26Hhz9oM7cfub8J8G6pPB3w/Xbpt9Ut25dO8azxPLly9Wz511yuX7X2ZiW\npC2qVOk67d+/Q1FRUXaOB1jCb4559O/fX59++qkk6dNPP9WAAQPOu8blcun06dOSpJSUFC1cuFBN\nmjSxckz4kcJCWpIukbTU5dIbzz7LkY8AtmnTJq1YtkwPnhPSkvS8y6XXxo1TSkqKDZMh0OVupa8p\nIKSlfNvpQJZ/K234azsNBDtLY/rJJ5/UokWLdNlll2nJkiV68sknJUn79+9Xnz59JEkHDx5Ux44d\n1bx5c7Vp00Z9+/ZV9+7drRwTfsJTSBsI6sD34hNPaFR6eoH//TeV1CErS+9N4f9DR+kr6Kz0uQL9\n7HTes9Ln4uw0cJalxzxKG8c8Apc3IZ0XRz4C06ZNm9S9bVvtSE0t9M/AJkndK1fWjv37OTuNUlPQ\nHTwKE8h39jDu4CENLvDnkZGDuLMHgoLfHPMIFNnZ2US8iXwNaYkNdaDytJU2sJ2GGb744gsdTj4s\nuSRt8fxXZlSmpv9nesBtpz1tpQ1spwET7uYRDPr1u1WtWjXVSy8F9jk5O7jdbp9D2mAEdednn1U5\nh0MjRo40a0xYwDgr/WkBZ6XP9bzLxZ09UKrKly+v6669zvOj7A0hUmjfUKWlpZk+l5UKPit9Lu7s\nAXDMw0cbNmxQ+/a9VK5clhITt6t69eqWvn+gy8zMVOP69XXngQN6Ltv3ewhnS7o1PFzq3Fmz5s8v\n/QFhmXEvvaRnn/ftX1i///57denSxaSJgOCxfPlyde9+q9LS1stzTEvSFkVF3aQDB3ZxZw8ELE/N\nSUz7qGvX67VkSRdVqPCL/vnPWpow4SVL3z8YJCUlKe7qq3X/oUN63IegzpZ0V3i4jrRqpW8XLVJE\nRIR5QwJAABs/foLGj5/o9fUhIQ7Fx89Ru3btTJwKsA8xXUo2bNigDh36KTX1D0kHFRnZmu20SXwN\nakIaAACYhQ8glpLHHx+jtLQnJEVIqqecnBv06qt82M0M0dHRcq5bpw9r1tSrISEeryWkAQCAXdhM\neyn/VtqItV1sp01W1IaakAYAAGZjM10K8m+lDfWUkzOQ7bSJPG2oCWkAAGA3NtNeKHgrbdipyMir\n2E6b7NwNNSENAACswma6hAreShvqs522QN4N9YSQEEI6iE2bNl3r1q2zewwAACSxmS6S5620ge20\nVYwNdb169QjpIJScnKzo6HqqXz9WmzevkcPhsHskAEAQYDNdAp630ga201aJjo7Wz7//rvlOJyEd\nhM7+39iN2rMnRfHx8XaPAwAAm2lPNmzYoGuu6a709A3yHNOStEsRET20b98OttOACZKTkxUT01Au\n14+S1uuKKyaynQYAWMJTc4ZaPEuZsnLlKoWFORQW1sqr6x2OUCUkJPA4Y8AEr776unJyBkqqL6mu\n9uwZo/j4ePXq1cvu0QAAQYzNNAC/l38rXf/P737FdhoAYAnOTAMo0/JvpQ2cnQYA2I/NNAC/VvBW\n2sB2GgBgPjbTAMqsgrfSBrbTAAB7sZkG4Lc8b6UNbKcBAOZiMw2gTPK8lTawnQYA2IfNNAC/5N1W\n2sB2GgBgHu4zDaDMee+9D5SR4Vblyo95cXWOfv11nZYvX65OnTqZPpudHn/8ObVr10oDBw6wexQA\ngNhMA/BTe/bs0fr16316TdeuXVW5cmWTJrLfzp07FRvbVBdcUEuJiVsVGso+BACs4Kk5iWkAKCNu\nv/0+zZxZW+Hhy/XWW/fonnvutnsky3344cdq0uQKtW3b1u5RAAQRYhoAyridO3eqceOrlZb2u6RN\nqlXrvqDbTh85ckR16tTTpZc25nw8AEtxNw8AKOOee268srKGSaouKU5nzsTos8+m2z2WpcaPnyiH\n407t2XOGu7cA8BtspgHAz+XfSlf/87vOoNpOHzlyRJdcEqvU1J8lrdYVV/wf22kAlmEzDQBlWP6t\ntCG4ttPjx09UTs4gSTGSbmI7DcBvsJkGAD9W8FbaEBzb6fxb6Zg/vzuT7TQAy7CZBoAyquCttCE4\nttP5t9IGttMA/AObaQDwU5630obA3k4XvJU2sJ0GYA0206XswIEDOnXqlN1jAAhwnrfShsDeThe8\nlTawnQZgPzbTPvrtt990Tadr9Lcaf9PqZav1t7/9zdL3BxAcvNtKGwJzO+15K21gOw3AfGymS8lv\nv/2m9te218lOJ7X3wr1qd207HT161O6xAASgqVM/UWZmiqKirlJUVIMi/hqsgwd3aOnSpXaPXao8\nb6UNbKcB2IvNtJeMkD7R8YTcTd2SWyrvLK+Lj1zMhhpAqUtNTdX+/ft9ek29evVUrlxg7Ei820ob\n2E4DMBePEy+h80LaQFADgCnGjHlJY8e+rooV2xd5rdudo1On5uuHH35Qx44dLZgOQLAhpkug0JA2\nENQAUOr27t2rjRs3en29w+FQXFycoqKiTJwKQLAipoupyJA2ENQAAAABiw8gFoPXIS1JDikjLoMP\nJQIAAAQZYroAPoW0gaAGAAAIOhzzOEdWVpZqRtfU8VbH5W5TjN/tlsLmhalVRCut/mF1qc4GAAAA\n63HMwwehoaF6cMiDitgYIaUU4xcclkJ3hGrk8JGlPhsAAAD8CzFdgHEvjtPIwSMVOT3St6A+JEV8\nEaGP3/lYt956q2nzAQAAwD8Q04XwOajzhPSgQYNMnw8AAAD2szSmv/rqKzVu3FghISHasGFDodfF\nx8crNjZWDRs21CuvvGLhhPl5HdSENAAAQFCyNKabNGmib775Rp06dSr0muzsbI0YMULx8fH69ddf\nNWPGDP32228WTplfkUFNSAMAAAQtS2M6NjZWl112mcdr1q1bp0svvVR169ZVWFiYBg0apG+//dai\nCQtWaFDbFNJHjhxRSkpxPh0JAACA0uR3Z6aTkpIUExOT+3WdOnWUlJRk40RnnRfUNoX09u3bFdsk\nVld3uFonTpyw7H0BAABwvtDS/oXdunXTwYMHz/v++PHj1a9fvyJf73A4fHq/0aNH5/59XFyc4uLi\nfHq9L8a9OE6S9MZHb8id5rYlpNt1aqfjbY4r5ViK2ndur5VLV6pq1aqWzQAAABDonE6nnE6nV9eW\nekwvWrSoRK+Pjo5WYmJi7teJiYmqU6dOodfnjWkrjHtxnKpUqaIGdRvoxhtvtOx9jZBObpMsdwu3\n0t3p2vH9DoIaAACglJ27oB0zZkyh19p2zKOwp8i0bt1a27dv1+7du5WRkaEvv/xS/fv3t3g6zx5/\n9HFbQ1qS5JDSu6ZrR8WzQc2RDwAAAOtZGtPffPONYmJitGbNGvXp00e9evWSJO3fv199+vSRdPYJ\nhG+//bZ69OihK664QrfeeqsaNWpk5Zh+pcCQNhDUAAAAtnK4C1sRlwGenpMeCDyGdF5uqcL3FdQg\npQFHPgAAAEqZp+b0u7t54CyvQ1piQw0AAGATYtoP+RTSBoIaAADAchzz8DNZWVm6KOYiHWt+TO62\nxfjP5pbKzy2vNlXa6IfFP5T+gAAAAEGGYx5lSGhoqO64/Q5FbImQXMX4BUelkF0huv+e+0t9NgAA\nAJ5+7AgAABI2SURBVORHTPuhSa9N0gO3PKDIGZG+BfURKWJGhN57/T3deeedps0HAACAs4hpP+Rw\nOHwP6jwhfdddd5k+IwAAAIjpYlm+fLl+//13U9/Dp6AmpAEAAGzBBxB9lJ6erga1ayu2YUN9v2aN\n6e/ndrv1yKhH9MHMD+S6zSVFnnMBIQ0AAGAqPoBYiv790UdqnJ6unb/8ouXLl5v+fh431IQ0AACA\nrdhM+yA9PV2X1q6t2cnJ2izp8zZtLNlOSwVsqFMIaQAAACuwmS4l//7oIzVNT9fVku6ULNtOS+ds\nqD+PJKQBAAD8AJtpL+XdSl/95/c+lrXbaenshnrM2DG6/NLLddttt1n2vgAAAMHKU3MS0156Z8oU\nzXviCc1LScn9XqakyyMj9Wl8vDp27GjJHAAAALAWMV1CBW2lDXZspwHALpmZmQoNDZXD4bB7FACw\nDGemSyjvWelzWX12GgDscvDgQTVr2FC39OunzMxMu8cBAL/AZroInrbSBrbTAALdwYMHdV3btrop\nKUnry5dXxeuu0/Svv1ZYWJjdowGA6dhMl4CnrbSB7TSAQGaE9K379+vFrCzNdrmUsmSJbr/hBjbU\nAIIem2kPvNlKG9hOAwhEeUP6hTzhnCbpxshINtQAggIfQCymD95/X08NH677vbg2U9Lr2dlatXq1\n2rZta9pMAGCVwkLaQFADCBbEdDElJCTof//7n0+vuf322xUTE2PSRABgjaJC2kBQAwgGxDQAwGve\nhrSBoAYQ6PgAIgDAK76GtCSFS3woEUDQYjMNAJAkZWRkqPlll+mmpCS9mJXl8+vTJF0fEaE611+v\nf8+YUfoDAoBN2EwDAIoUGhqqyy6/XBvDwpRRjNcfk7TL4dAVzZuX9mgAoJ9//llHjhyxe4zzENMA\nAElSuXLlNPO77+To2FE3R0T4FNRJkjpHRurep57So088YdaIAILUwoULFde2rTq1bq2DBw/aPU4+\nxDQAIFf58uV9Duq8If3ks8+aPSKAILNw4ULdMXCg5qan6+/796tzmzZ+FdTENAAgH1+CmpAGYCYj\npL92udRB0nNZWX4X1MQ0AOA83gQ1IQ3ATOeGtMHfgpqYBny0e/duHT9+3O4xANN5CmpCGoCZCgtp\ngz8FNTEN+CAhIUFNWjRRq7atdPjwYbvHAUxXUFAT0gDMVFRIG/wlqLnPNOClhIQExXWN06mupxR2\nJEx1kupozfI1qlGjht2jAabLyMjQLf36KXP5cm13OAhpAKbwNqTzeik0VJ/Xrq2la9eqVq1apszF\n48SBEsob0rpCklsK+4GgRnDJyMjQ4NtuU/Orr+b2dwBKXXFC2mB2UBPTQAmcF9IGghoAgFJx5swZ\nXVi9uj7NzNQtxfwdd4aEKPnaa/X/7d19cBR1nsfxz+xklOQSJaxkIAYM1BWFhIeEDYQrDZVIQqLh\nKRXwYFFTBt2IXG0pEN0sexqoJXDgA8hyJUv5kBWu1LgXFLIgF3UCAgE8Ek8tPcsTBPJAaQlVMcPD\nkM394U4WDJNkmsl0Z+b9+ovK9DTfqWrbN53fdFe/915AZ5N4AiJgmM+QliSb5Jnq0elbT2tK+hTW\nUAMAYFB0dLRWrVypFVFROm3g/bskvRsZqafKywM9Wo+IacCHbkPai6AGACAgSkpL9avf/U6Zfgb1\nLklF0dHaWVOjtLS0vhrPJ2IauIZehbQXQQ0AQED4G9Rmh7RETANd+BXSXgQ1AAAB0dugtkJIS3wB\nEbiKx+PRz+N+rtY7W6VUAzvokCJ2RWjSP0zSwdqDAZ8PAIBwsX7NGv3x97/XB263En7yWrBDmi8g\nAr3kcDi0bOkyRf13lNRqYAdNkuP/HCpdXhrw2QAACCe+rlBb5Yq0FzHtp/b2dhUVLdG6dc+ZPQr6\nyNP/+rRKHilR1H/4GdSNUmRlpN740xuaOXNmn80HAEC4+GlQWy2kJSnC7AH6k/b2ds2f/6D+8pdT\nkmrk8Xi0YgUPLghFZU+VSZLWv7he7l+6pZge3kBIAwDQJ0pKf/xt7x2rVul8RISlQlpizXSv/T2k\nG+V275R0TlFRmfrtb4sI6hBWtqqs56AmpAEA6HMVr76qpLFjlZpq5EtN14cnIF6nriEd9bdXmgjq\nMNBtUBPSAACEvO6ak2UePfAd0pIUL7f7A5WXZ0oSQR2ifC75IKQBAAh7Qf0CYmVlpZKSkmS323Xs\n2DGf2yUmJmr8+PFKSUnR5MmTgzjh1boPaS9vUL+s1av/LdgjIkjKniq7+kuJhDQAAFCQr0yPGzdO\nVVVVKi4u7nY7m80ml8ulQYMGBWmyrnoX0l5coQ4H3ivU6/59nXRRhDQAAAhuTI8ePbrX25q5lNu/\nkPYiqMNB2VNlGjRokEb94yjl5uaaPQ4AADCZJddM22w2ZWVlyW63q7i4WA8//HDQ/u6Ojg4tWFDk\nZ0h7/T2oIyIi9OSTy/pqTJjo1//ya7NHAAAAFhHwmM7OzlZLS0uXn5eXl/f6V+IHDhzQ0KFD9e23\n3yo7O1ujR49Wenr6NbctKyvr/HNGRoYyMjKMjN2pvb1dR49+pEuX8uVfSHvF6a9/Hat9++r0JBen\nAQAA+h2XyyWXy9WrbU25NV5mZqaeffZZTZw4scdtV65cqejoaC1b1vUqb1/dGu/MmTNKS8tUU9M/\ny+N52o93XlZk5H1KTT2nvXt3aMCAAQGfDQAAAMHVXXOa9jhxXwO53W61tv74DOe2tjbt3btX48aN\nC+ZocjqdOnz4A8XHvyGHY2Uv30VIAwAAhJugxnRVVZWGDRumuro65eXl6e6775YkNTU1KS8vT5LU\n0tKi9PR0JScnKy0tTTNmzND06dODOaYkf4OakAYAAAhHPAGxBz0v+SCkAQAAQpkll3n0F91foSak\nAQAAwhkx3QvXDmpCGgAAINyxzMMP3iUfjY3z5HD8LyENAAAQBrprTmLaT96gHj58OCENAAAQBojp\nALtw4YIcDofsdnvQ/24AAAAEFzENAAAAGMTdPAAAAIA+QEwDAAAABhHTAAAAgEHENAAAAGAQMQ0A\nAAAYREwDAAAABhHTAAAAgEHENAAAAGAQMQ0AANALlZWV+vjjj80eAxZDTAMAAPRg0x826YHiB5R+\nV7qOHTtm9jiwEGIaAACgG5v+sEm/WfUbXXjgglqzW5WRnUFQoxMxDfQz1dXVamhoMHsMAAgL3pB2\n/9ItxUq6XQQ1rkJMA/3IttdeU9HcucqZOlUfffSR2eMAQEjrEtJeBDWuQEwD/cS2117TE8XF+uDC\nBf2xtVV5d91FUANAH/EZ0l4ENf6GmAb6AW9I15w/rzGSZksENQD0kR5D2oughohpwPJ+GtJeBDUA\nBF6vQ9qLoA57xDRgYb5C2ougBoDA8TukvQjqsGbr6OjoMHsIo2w2m/rx+EC3egrpK70t6VcxMap+\n/32lpqYGYzwACClut1sDYwfKM8sjjTW2j5+9/TPdMfAO7Xt/X2CHg+m6a06uTAMW5E9IS1yhBoDr\nFRUVpar/rFLkf0VKp/1/v/2wXXHfxWnbq9sCPxwsjZgGLMbfkPYiqAHg+uTl5alye6UiK/0Lavth\nuwZ/OliHPzys4cOH992AsCSWeQAW4vF4FBsTo80XL6rQ4D6W2Gz6n1/8QvuPHg3obAAQLqqrqzVv\n4Tydn3deSuh+W0I6PLDMA+gnHA6H3tqxQyVRUTpk4P0v22x6JzZWL23fHvDZACBc9PYKNSENiZgG\nLCc3N1d/+vOfNdvPoH7ZZtPTsbF679AhjRo1qs/mA4Bw0FNQE9LwIqYBC/I3qAlpAAg8X0FNSONK\nrJkGLGzPnj16oKBAb7vd+icf2xDSANC3rlxDbW8kpMNRd81JTAMW111QE9IAEBzV1dUqmF+g2NhY\nQjoMEdNAP3etoCakASC4jhw5ooSEBMXHx5s9CoKMmAZCwJVB/TkhDQBA0BDTQIjYs2ePFubnKyoq\nipAGACBIiGkghNTV1cnpdGrEiBFmjwIAQFggpgEAAACDeAIiAAAA0AeIaQAAAMAgYhoAAAAwiJgG\nAAAADCKmAQAAAIOIaQAAAMAgYhowwOVymT0CwhjHH8zE8QczWfH4I6YBA6z4HzPCB8cfzMTxBzNZ\n8fgjpgEAAACDiGkAAADAoH7/OHEAAACgr/lK5oggzxFQ/fjfAQAAAAgBLPMAAAAADCKmAQAAAIOI\nacAPiYmJGj9+vFJSUjR58mSzx0GIKyoqktPp1Lhx4zp/9v333ys7O1ujRo3S9OnTde7cORMnRCi7\n1vFXVlamhIQEpaSkKCUlRXv27DFxQoSyU6dOKTMzU0lJSRo7dqxeeOEFSdY8BxLTgB9sNptcLpfq\n6+t15MgRs8dBiHvwwQe7xMratWuVnZ2tL7/8UtOmTdPatWtNmg6h7lrHn81m09KlS1VfX6/6+nrl\n5uaaNB1CncPh0PPPP6/PPvtMdXV12rx5sz7//HNLngOJacBPfPEVwZKenq7Y2NirfvbOO++osLBQ\nklRYWKgdO3aYMRrCwLWOP4lzIIJjyJAhSk5OliRFR0fr9ttvV2NjoyXPgcQ04AebzaasrCylpqZq\n69atZo+DMHTmzBk5nU5JktPp1JkzZ0yeCOFm06ZNmjBhghYtWmSJX7Ej9J04cUL19fVKS0uz5DmQ\nmAb8cODAAdXX12v37t3avHmz9u/fb/ZICGM2m4377SOoFi9erOPHj6uhoUFDhw7VsmXLzB4JIe6H\nH35QQUGBNm7cqJiYmKtes8o5kJgG/DB06FBJ0uDBg5Wfn8+6aQSd0+lUS0uLJKm5uVlxcXEmT4Rw\nEhcX1xkwDz30EOdA9CmPx6OCggLdf//9mjNnjiRrngOJaaCX3G63WltbJUltbW3au3fvVd9yB4Jh\n1qxZqqiokCRVVFR0/g8GCIbm5ubOP1dVVXEORJ/p6OjQokWLNGbMGD322GOdP7fiObBfP04cCKbj\nx48rPz9fknT58mUtXLhQpaWlJk+FULZgwQLV1tbqu+++k9Pp1KpVqzR79mzde++9OnnypBITE/Xm\nm29q4MCBZo+KEPTT42/lypVyuVxqaGiQzWbTiBEjtGXLls71q0Agffjhh5o6darGjx/fuZRjzZo1\nmjx5suXOgcQ0AAAAYBDLPAAAAACDiGkAAADAIGIaAAAAMIiYBgAAAAwipgEAAACDiGkAsKhTp05p\n5MiROnv2rCTp7NmzGjlypCoqKnTzzTdrxowZvd6X3W7XxIkTOx92kJubq+TkZCUlJWnRokXyeDyS\npOeee05JSUmaMGGCsrKydPLkSUnS119/reTk5M4nkO3fv19jxozhPsMAwh63xgMAC1u/fr2++uor\nbdmyRcXFxRo5cqSmTJmiZ555Rjt37uz1fmJiYjofOiT9+Ije6OhoSdLcuXM1Z84c3XfffXK5XJoy\nZYoGDBigF198US6XS6+//vo19/PNN99oxowZ+uSTTwL0aQGg/+HKNABY2OOPP666ujpt2LBBBw8e\n1PLlyxWIayDekPZ4PLp06ZJuueUWSVJGRoYGDBggSUpLS9Pp06d97oNrMQBATAOApUVERGjdunVa\nunSpNmzYILvd3mWb9vZ2rVixQpMmTVJOTo7eeustffHFFyotLVVjY6PPfefk5MjpdCoyMlK5ubld\nXn/ppZd0zz33BPTzAECoIaYBwOJ2796t+Ph4n8spmpqaFB8fr6NHj2r16tXavn275s2bp4SEBN16\n660+9/vuu++qublZFy9eVEVFxVWvbdu2TceOHVNJSUlAPwsAhJoIswcAAPjW0NCgmpoaHTp0SHfe\neafmz5/fZZthw4ZpyZIlkqTU1FRVVVX1ev833nijCgoKdPjwYRUWFkqSampqVF5ern379snhcATm\ngwBAiOLKNABYVEdHhxYvXqyNGzdq2LBhKikp0fLly2Wz2a5rv21tbWpubpYkXb58Wbt27VJKSook\nqb6+Xo888oh27tzZuY4aAOAbV6YBwKK2bt2qxMRETZs2TZL06KOP6pVXXlFtbe117betrU2zZ8/W\nxYsX1dHRoZycHBUVFUmSnnjiCbW1tWnu3LmSpNtuu007duy4vg8CACGMW+MBQD9TW1t73bfGM+rK\n/Zw4cUIzZ87k1ngAwhrLPACgn7nhhhv06aef+vXQlptuukkTJ07sXN7hL+9DW4YMGSLpx4e2zJo1\nS4MHDza0PwAIFVyZBgAAAAziyjQAAABgEDENAAAAGERMAwAAAAYR0wAAAIBBxDQAAABg0P8DRl7U\nRV+IlvgAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb07fe8c>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "r final plot of the fitted values"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lm_final = ols('S ~ X + C(E)*C(M)', salary_table.drop([32])).fit()\n",
      "try:\n",
      "    mf = lm_final.model._data._orig_exog\n",
      "except Exception:\n",
      "    mf = lm_final.model.data.orig_exog\n",
      "lstyle = ['-','--']\n",
      "\n",
      "fig = plt.figure(figsize=(12,8))\n",
      "ax = fig.add_subplot(111, xlabel='Experience', ylabel='Salary')\n",
      "\n",
      "for values, group in factor_groups:\n",
      "    i,j = values\n",
      "    idx = group.index\n",
      "    ax.scatter(X[idx], S[idx], marker=symbols[j], color=colors[i-1],\n",
      "            s=144, edgecolors='black')\n",
      "    # drop NA because there is no idx 32 in the final model\n",
      "    ax.plot(mf.X[idx].dropna(), lm_final.fittedvalues[idx].dropna(),\n",
      "            ls=lstyle[j], color=colors[i-1])\n",
      "ax.axis('tight');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "From our first look at the data, the difference between Master's and PhD in the management group is different than in the non-management group. This is an interaction between the two qualitative variables management, M and education, E. We can visualize this by first removing the effect of experience, then plotting the means within each of the 6 groups using interaction.plot."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "U = S - X * interM_lm32.params['X']\n",
      "U.name = 'Salary|X'\n",
      "\n",
      "fig = plt.figure(figsize=(12,8))\n",
      "ax = fig.add_subplot(111)\n",
      "ax = interaction_plot(E, M, U, colors=['red','blue'], markers=['^','D'],\n",
      "        markersize=10, ax=ax)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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eMnRLklQdGLylODNjBmRkwG23wQMPQF1/riVJUrXg/5KlOBGJwD33wF/+Esx0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\nlEDwBgCAEgjeAABQAsEbAABK8B9vWj5t+qxZtgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb05cdac>"
       ]
      }
     ],
     "prompt_number": 27
    }
   ],
   "metadata": {}
  }
 ]
}