19-Regression-III-More-Linear.ipynb

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   "source": [
    "# More on Linear Regression"
   ]
  },
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   "source": [
    "Today, we'll look at some additional aspects of Linear Regression.\n",
    "\n",
    "Let's look at a standard regression.\n",
    "\n",
    "Here are the pieces of a standard linear model."
   ]
  },
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   "source": [
    "from __future__ import print_function\n",
    "import numpy as np\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt\n",
    "from statsmodels.sandbox.regression.predstd import wls_prediction_std\n",
    "\n",
    "import statsmodels.formula.api as smf\n",
    "import pandas\n",
    "\n",
    "import seaborn as sns\n",
    "%matplotlib inline\n",
    "\n",
    "np.random.seed(9876789)"
   ]
  },
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      " [  1.00000000e+01   1.00000000e+02]]\n"
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   ],
   "source": [
    "nsample = 100\n",
    "x = np.linspace(0, 10, 100)\n",
    "#print(x)\n",
    "X = np.column_stack((x, x**2))\n",
    "print(X)\n",
    "beta = np.array([1, 0.1, 10])\n",
    "e = np.random.normal(size=nsample)"
   ]
  },
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   "source": [
    "We add one more column of ones (1) so that we can estimate the intercept.\n",
    "\n",
    "We then go on to create data that comes from a particular model."
   ]
  },
  {
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   "source": [
    "X = sm.add_constant(X)\n",
    "y = np.dot(X, beta) + e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    }
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   "source": [
    "Now we have the explanatory variable X (predictor, regressor, input variable) and the response variable y (predicted, regressand, output). \n",
    "\n",
    "We are ready to fit the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       1.000\n",
      "Model:                            OLS   Adj. R-squared:                  1.000\n",
      "Method:                 Least Squares   F-statistic:                 4.020e+06\n",
      "Date:                Tue, 14 Nov 2017   Prob (F-statistic):          2.83e-239\n",
      "Time:                        10:52:34   Log-Likelihood:                -146.51\n",
      "No. Observations:                 100   AIC:                             299.0\n",
      "Df Residuals:                      97   BIC:                             306.8\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
      "------------------------------------------------------------------------------\n",
      "const          1.3423      0.313      4.292      0.000         0.722     1.963\n",
      "x1            -0.0402      0.145     -0.278      0.781        -0.327     0.247\n",
      "x2            10.0103      0.014    715.745      0.000         9.982    10.038\n",
      "==============================================================================\n",
      "Omnibus:                        2.042   Durbin-Watson:                   2.274\n",
      "Prob(Omnibus):                  0.360   Jarque-Bera (JB):                1.875\n",
      "Skew:                           0.234   Prob(JB):                        0.392\n",
      "Kurtosis:                       2.519   Cond. No.                         144.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = sm.OLS(y, X)\n",
    "results = model.fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Let's look at the various aspects of the fitted model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
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    "slideshow": {
     "slide_type": "-"
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameters:  [  1.34233516  -0.04024948  10.01025357]\n",
      "R2:  0.999987936503\n",
      "Predicted values:  [    1.34233516     1.44040458     1.74274404     2.24935355     2.9602331\n",
      "     3.87538271     4.99480235     6.31849204     7.84645178     9.57868156\n",
      "    11.51518139    13.65595126    16.00099118    18.55030114    21.30388115\n",
      "    24.2617312     27.4238513     30.79024145    34.36090164    38.13583187\n",
      "    42.11503215    46.29850248    50.68624285    55.27825327    60.07453373\n",
      "    65.07508424    70.27990479    75.68899539    81.30235603    87.11998672\n",
      "    93.14188746    99.36805824   105.79849906   112.43320993   119.27219085\n",
      "   126.31544181   133.56296282   141.01475387   148.67081497   156.53114611\n",
      "   164.5957473    172.86461853   181.33775981   190.01517113   198.8968525\n",
      "   207.98280392   217.27302538   226.76751688   236.46627843   246.36931003\n",
      "   256.47661167   266.78818336   277.30402509   288.02413687   298.94851869\n",
      "   310.07717056   321.41009247   332.94728443   344.68874643   356.63447848\n",
      "   368.78448058   381.13875272   393.69729491   406.46010714   419.42718941\n",
      "   432.59854174   445.9741641    459.55405651   473.33821897   487.32665148\n",
      "   501.51935402   515.91632662   530.51756926   545.32308194   560.33286467\n",
      "   575.54691745   590.96524027   606.58783314   622.41469605   638.445829\n",
      "   654.68123201   671.12090505   687.76484815   704.61306128   721.66554447\n",
      "   738.9222977    756.38332097   774.04861429   791.91817766   809.99201107\n",
      "   828.27011452   846.75248802   865.43913157   884.33004516   903.4252288\n",
      "   922.72468248   942.22840621   961.93639998   981.8486638   1001.96519767]\n"
     ]
    }
   ],
   "source": [
    "#dir(results)\n",
    "print('Parameters: ', results.params)\n",
    "print('R2: ', results.rsquared)\n",
    "print('Predicted values: ', results.predict())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now we'll load a standard dataset as an example.\n",
    "\n",
    "The Longley dataset contains various US macroeconomic variables that are known to be highly collinear. It has been used to appraise the accuracy of least squares routines."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
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     "slide_type": "fragment"
    }
   },
   "outputs": [
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       "<div>\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>const</th>\n",
       "      <th>GNPDEFL</th>\n",
       "      <th>GNP</th>\n",
       "      <th>UNEMP</th>\n",
       "      <th>ARMED</th>\n",
       "      <th>POP</th>\n",
       "      <th>YEAR</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>83.0</td>\n",
       "      <td>234289.0</td>\n",
       "      <td>2356.0</td>\n",
       "      <td>1590.0</td>\n",
       "      <td>107608.0</td>\n",
       "      <td>1947.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>88.5</td>\n",
       "      <td>259426.0</td>\n",
       "      <td>2325.0</td>\n",
       "      <td>1456.0</td>\n",
       "      <td>108632.0</td>\n",
       "      <td>1948.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>88.2</td>\n",
       "      <td>258054.0</td>\n",
       "      <td>3682.0</td>\n",
       "      <td>1616.0</td>\n",
       "      <td>109773.0</td>\n",
       "      <td>1949.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>89.5</td>\n",
       "      <td>284599.0</td>\n",
       "      <td>3351.0</td>\n",
       "      <td>1650.0</td>\n",
       "      <td>110929.0</td>\n",
       "      <td>1950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>96.2</td>\n",
       "      <td>328975.0</td>\n",
       "      <td>2099.0</td>\n",
       "      <td>3099.0</td>\n",
       "      <td>112075.0</td>\n",
       "      <td>1951.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>98.1</td>\n",
       "      <td>346999.0</td>\n",
       "      <td>1932.0</td>\n",
       "      <td>3594.0</td>\n",
       "      <td>113270.0</td>\n",
       "      <td>1952.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>99.0</td>\n",
       "      <td>365385.0</td>\n",
       "      <td>1870.0</td>\n",
       "      <td>3547.0</td>\n",
       "      <td>115094.0</td>\n",
       "      <td>1953.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1</td>\n",
       "      <td>100.0</td>\n",
       "      <td>363112.0</td>\n",
       "      <td>3578.0</td>\n",
       "      <td>3350.0</td>\n",
       "      <td>116219.0</td>\n",
       "      <td>1954.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>101.2</td>\n",
       "      <td>397469.0</td>\n",
       "      <td>2904.0</td>\n",
       "      <td>3048.0</td>\n",
       "      <td>117388.0</td>\n",
       "      <td>1955.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1</td>\n",
       "      <td>104.6</td>\n",
       "      <td>419180.0</td>\n",
       "      <td>2822.0</td>\n",
       "      <td>2857.0</td>\n",
       "      <td>118734.0</td>\n",
       "      <td>1956.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1</td>\n",
       "      <td>108.4</td>\n",
       "      <td>442769.0</td>\n",
       "      <td>2936.0</td>\n",
       "      <td>2798.0</td>\n",
       "      <td>120445.0</td>\n",
       "      <td>1957.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1</td>\n",
       "      <td>110.8</td>\n",
       "      <td>444546.0</td>\n",
       "      <td>4681.0</td>\n",
       "      <td>2637.0</td>\n",
       "      <td>121950.0</td>\n",
       "      <td>1958.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1</td>\n",
       "      <td>112.6</td>\n",
       "      <td>482704.0</td>\n",
       "      <td>3813.0</td>\n",
       "      <td>2552.0</td>\n",
       "      <td>123366.0</td>\n",
       "      <td>1959.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1</td>\n",
       "      <td>114.2</td>\n",
       "      <td>502601.0</td>\n",
       "      <td>3931.0</td>\n",
       "      <td>2514.0</td>\n",
       "      <td>125368.0</td>\n",
       "      <td>1960.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1</td>\n",
       "      <td>115.7</td>\n",
       "      <td>518173.0</td>\n",
       "      <td>4806.0</td>\n",
       "      <td>2572.0</td>\n",
       "      <td>127852.0</td>\n",
       "      <td>1961.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1</td>\n",
       "      <td>116.9</td>\n",
       "      <td>554894.0</td>\n",
       "      <td>4007.0</td>\n",
       "      <td>2827.0</td>\n",
       "      <td>130081.0</td>\n",
       "      <td>1962.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    const  GNPDEFL       GNP   UNEMP   ARMED       POP    YEAR\n",
       "0       1     83.0  234289.0  2356.0  1590.0  107608.0  1947.0\n",
       "1       1     88.5  259426.0  2325.0  1456.0  108632.0  1948.0\n",
       "2       1     88.2  258054.0  3682.0  1616.0  109773.0  1949.0\n",
       "3       1     89.5  284599.0  3351.0  1650.0  110929.0  1950.0\n",
       "4       1     96.2  328975.0  2099.0  3099.0  112075.0  1951.0\n",
       "5       1     98.1  346999.0  1932.0  3594.0  113270.0  1952.0\n",
       "6       1     99.0  365385.0  1870.0  3547.0  115094.0  1953.0\n",
       "7       1    100.0  363112.0  3578.0  3350.0  116219.0  1954.0\n",
       "8       1    101.2  397469.0  2904.0  3048.0  117388.0  1955.0\n",
       "9       1    104.6  419180.0  2822.0  2857.0  118734.0  1956.0\n",
       "10      1    108.4  442769.0  2936.0  2798.0  120445.0  1957.0\n",
       "11      1    110.8  444546.0  4681.0  2637.0  121950.0  1958.0\n",
       "12      1    112.6  482704.0  3813.0  2552.0  123366.0  1959.0\n",
       "13      1    114.2  502601.0  3931.0  2514.0  125368.0  1960.0\n",
       "14      1    115.7  518173.0  4806.0  2572.0  127852.0  1961.0\n",
       "15      1    116.9  554894.0  4007.0  2827.0  130081.0  1962.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from statsmodels.datasets.longley import load_pandas\n",
    "y = load_pandas().endog\n",
    "X = load_pandas().exog\n",
    "X = sm.add_constant(X)\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 TOTEMP   R-squared:                       0.995\n",
      "Model:                            OLS   Adj. R-squared:                  0.992\n",
      "Method:                 Least Squares   F-statistic:                     330.3\n",
      "Date:                Tue, 14 Nov 2017   Prob (F-statistic):           4.98e-10\n",
      "Time:                        10:52:34   Log-Likelihood:                -109.62\n",
      "No. Observations:                  16   AIC:                             233.2\n",
      "Df Residuals:                       9   BIC:                             238.6\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
      "------------------------------------------------------------------------------\n",
      "const      -3.482e+06    8.9e+05     -3.911      0.004      -5.5e+06 -1.47e+06\n",
      "GNPDEFL       15.0619     84.915      0.177      0.863      -177.029   207.153\n",
      "GNP           -0.0358      0.033     -1.070      0.313        -0.112     0.040\n",
      "UNEMP         -2.0202      0.488     -4.136      0.003        -3.125    -0.915\n",
      "ARMED         -1.0332      0.214     -4.822      0.001        -1.518    -0.549\n",
      "POP           -0.0511      0.226     -0.226      0.826        -0.563     0.460\n",
      "YEAR        1829.1515    455.478      4.016      0.003       798.788  2859.515\n",
      "==============================================================================\n",
      "Omnibus:                        0.749   Durbin-Watson:                   2.559\n",
      "Prob(Omnibus):                  0.688   Jarque-Bera (JB):                0.684\n",
      "Skew:                           0.420   Prob(JB):                        0.710\n",
      "Kurtosis:                       2.434   Cond. No.                     4.86e+09\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, 4.86e+09. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "import warnings\n",
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter('ignore')\n",
    "    ols_model = sm.OLS(y, X)\n",
    "    ols_results = ols_model.fit()\n",
    "    print(ols_results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "What does this mean?\n",
    "\n",
    ">In statistics, multicollinearity (also collinearity) is a phenomenon in which two or more predictor variables in a multiple regression model are highly correlated, meaning that one can be linearly predicted from the others with a substantial degree of accuracy.\n",
    "\n",
    "(Wikipedia)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The condition number being referred to is the condition number of the design matrix.\n",
    "\n",
    "That is the $X$ in $X\\beta = y$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Remember that to solve a least-squares problem $X\\beta = y$, we solve the normal equations\n",
    "\n",
    "$$X^TX\\beta = X^Ty.$$\n",
    "\n",
    "These equations always have at least one solution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "However, the \"at least one\" part is problematic!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "If there are multiple solutions, they are in a sense all equivalent in that they yield the same value of $\\Vert X\\beta - y\\Vert$.\n",
    "\n",
    "However, the actual values of $\\beta$ can vary tremendously and so it is not clear how best to interpret the case when $X$ does not have full column rank."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "When does this problem occur?   Look at the normal equations:\n",
    "\n",
    "$$X^TX\\beta = X^Ty.$$\n",
    "\n",
    "It occurs when $X^TX$ is __not invertible.__\n",
    "\n",
    "In that case, we cannot simply solve the normal equations by computing $\\hat{\\beta} = (X^TX)^{-1}X^Ty.$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "When is $(X^TX)$ not invertible?\n",
    "\n",
    "A matrix is not invertible iff at least one of its eigenvalues is zero.\n",
    "\n",
    "This happens when the columns of $X$ are not linearly independent, ie, one column can be expressed as a linear combination of the other columns."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "One obvious case is if $X$ has more columns than rows.   That is, if there are more _variables_ than _equations_.\n",
    "\n",
    "This case is easy to recognize. \n",
    "\n",
    "However, a more insidious case occurs when the columns of $X$ happen to be linearly dependent because of the nature of the data itself."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This happens when one column is a linear function of the other columns.   Ie, one independent variable is a linear function of one or more of the others."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Unfortunately, in practice we will run into trouble even if variables are __almost__ linearly dependent. \n",
    "\n",
    "This presents problems because machine arithmetic is not exact, so small errors are magnified when computing $(X^TX)^{-1}$. \n",
    "\n",
    "So, more simply, when two or more columns are __strongly correlated__, we will have problems with linear regression.\n",
    "\n",
    "This is called __multicollinearity__ in the terminology of statistics."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Condition number is a measure of whether $X$ is __nearly__ lacking full column rank.\n",
    "\n",
    "In other words, whether some column is __close to__ being a linear combination of the other columns.\n",
    "\n",
    "Even in this case, the actual values of $\\beta$ can vary a lot due to the limitations of numerical precision in the computer."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Recall that $X^TX$ will not be invertible if it has at least one zero eigenvalue.   \n",
    "\n",
    "Condition number relaxes this -- it asks if $X^TX$ has a __very small__ eigenvalue (compared to its largest eigenvalue)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "An easy way to assess this is using the SVD of $X$.\n",
    "\n",
    "(Thank you, \"swiss army knife\"!)\n",
    "\n",
    "The eigenvalues of $X^TX$ are the squares of the singular values of $X$.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "So the condition number of $X$ is defined as:\n",
    "\n",
    "$$\\kappa(X) = \\frac{\\sigma_{\\mbox{max}}}{\\sigma_{\\mbox{min}}}$$\n",
    "\n",
    "where $\\sigma_{\\mbox{max}}$ and $\\sigma_{\\mbox{min}}$ are the largest and smallest singular values of $X$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "A large condition number -- is a problem.   Generally I would be concerned by condition numbers bigger than about $10^6$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This does not happen too often in practice, but there are some things that can be done if it does happen:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "(1) We can __regularize__ the regression.   This consists of adding a penalty term to the regression:\n",
    "\n",
    "$$ \\hat{\\beta} = \\arg \\min \\Vert X\\beta - y \\Vert + \\lambda \\Vert\\beta\\Vert.$$\n",
    "\n",
    "This goes by the term __ridge regression__ (or __Tikhanov regularization__)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The idea here is (basically): there may be many solutions that are (approximately) consistent with the equations.   However erroneous solutions tend to have large values (which are used to create cancellations among the columns).   We want to avoid those solutions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "(2) We can try to find one of the offending predictor variables, and leave it out of the regression.\n",
    "\n",
    "This goes by the term __variable elimination__ or __feature selection__ (which you can investigate as needed)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Influence"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Also, it can happen that dropping a single observation can have a dramatic effect on the coefficient estimates."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Restricting ourselves to the first 14 observations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "ols_results2 = sm.OLS(y.ix[:14], X.ix[:14]).fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Let us see how much each parameter changes if we compare to all 16 observations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Percentage change -13.35%\n",
      "Percentage change -236.18%\n",
      "Percentage change -23.69%\n",
      "Percentage change -3.36%\n",
      "Percentage change -7.26%\n",
      "Percentage change -200.46%\n",
      "Percentage change -13.34%\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(\"Percentage change %4.2f%%\\n\"*7 % tuple([i for i in (ols_results2.params - ols_results.params)/ols_results.params*100]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Formal statistics for this such as the DFBETAS -- a standardized measure of how much each coefficient changes when that observation is left out.\n",
    "\n",
    "An observation is considered troublesome if its DFBETA is greater than $2/\\sqrt{\\text{number of observations}}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "infl = ols_results.get_influence()\n",
    "## significant influence\n",
    "2./len(X)**.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    dfb_const  dfb_GNPDEFL   dfb_GNP  dfb_UNEMP  dfb_ARMED   dfb_POP  dfb_YEAR\n",
      "0   -0.016406    -0.234566 -0.045095  -0.121513  -0.149026  0.211057  0.013388\n",
      "1   -0.020608    -0.289091  0.124453   0.156964   0.287700 -0.161890  0.025958\n",
      "2   -0.008382     0.007161 -0.016799   0.009575   0.002227  0.014871  0.008103\n",
      "3    0.018093     0.907968 -0.500022  -0.495996   0.089996  0.711142 -0.040056\n",
      "4    1.871260    -0.219351  1.611418   1.561520   1.169337 -1.081513 -1.864186\n",
      "5   -0.321373    -0.077045 -0.198129  -0.192961  -0.430626  0.079916  0.323275\n",
      "6    0.315945    -0.241983  0.438146   0.471797  -0.019546 -0.448515 -0.307517\n",
      "7    0.015816    -0.002742  0.018591   0.005064  -0.031320 -0.015823 -0.015583\n",
      "8   -0.004019    -0.045687  0.023708   0.018125   0.013683 -0.034770  0.005116\n",
      "9   -1.018242    -0.282131 -0.412621  -0.663904  -0.715020 -0.229501  1.035723\n",
      "10   0.030947    -0.024781  0.029480   0.035361   0.034508 -0.014194 -0.030805\n",
      "11   0.005987    -0.079727  0.030276  -0.008883  -0.006854 -0.010693 -0.005323\n",
      "12  -0.135883     0.092325 -0.253027  -0.211465   0.094720  0.331351  0.129120\n",
      "13   0.032736    -0.024249  0.017510   0.033242   0.090655  0.007634 -0.033114\n",
      "14   0.305868     0.148070  0.001428   0.169314   0.253431  0.342982 -0.318031\n",
      "15  -0.538323     0.432004 -0.261262  -0.143444  -0.360890 -0.467296  0.552421\n"
     ]
    }
   ],
   "source": [
    "print(infl.summary_frame().filter(regex=\"dfb\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x115e17198>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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BkXru5CnAj2y/vaG4bqda3jxT67WxWgSw5pfPy6iS685U/f3/XuJa/5mMu9iQ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\neDSvjF8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115dc87b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(infl.summary_frame().filter(regex=\"dfb\") > 0.5 )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Flexible Modeling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The Guerry dataset is a collection of historical data used in support of Andre-Michel Guerry’s 1833 \"Essay on the Moral Statistics of France.\"\n",
    "\n",
    ">Andre-Michel Guerry’s (1833) Essai sur la Statistique Morale\n",
    "de la France was one of the foundation studies of modern social science.\n",
    "Guerry assembled data on crimes, suicides, literacy and other “moral\n",
    "statistics,” and used tables and maps to analyze a variety of social issues\n",
    "in perhaps the first comprehensive study relating such variables.\n",
    "\n",
    "Wikipedia\n",
    "\n",
    ">Guerry’s results were startling for two reasons.\n",
    "First he showed that rates of crime and suicide remained\n",
    "remarkably stable over time, when broken\n",
    "down by age, sex, region of France and even season\n",
    "of the year; yet these numbers varied systematically\n",
    "across departements of France. This regularity\n",
    "of social numbers created the possibility to\n",
    "conceive, for the first time, that human actions in\n",
    "the social world were governed by social laws, just\n",
    "as inanimate objects were governed by laws of the\n",
    "physical world.\n",
    "\n",
    "Source: \"A.-M. Guerry’s Moral Statistics of France: Challenges for Multivariable\n",
    "Spatial Analysis\", Michael Friendly.  Statistical Science 2007, Vol. 22, No. 3, 368–399."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Lottery</th>\n",
       "      <th>Literacy</th>\n",
       "      <th>Wealth</th>\n",
       "      <th>Region</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>41</td>\n",
       "      <td>37</td>\n",
       "      <td>73</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>38</td>\n",
       "      <td>51</td>\n",
       "      <td>22</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>66</td>\n",
       "      <td>13</td>\n",
       "      <td>61</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>80</td>\n",
       "      <td>46</td>\n",
       "      <td>76</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>79</td>\n",
       "      <td>69</td>\n",
       "      <td>83</td>\n",
       "      <td>E</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Lottery  Literacy  Wealth Region\n",
       "0       41        37      73      E\n",
       "1       38        51      22      N\n",
       "2       66        13      61      C\n",
       "3       80        46      76      E\n",
       "4       79        69      83      E"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Lottery is per-capital wager on Royal Lottery\n",
    "df = sm.datasets.get_rdataset(\"Guerry\", \"HistData\").data\n",
    "df = df[['Lottery', 'Literacy', 'Wealth', 'Region']].dropna()\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We can use another version of the module that can directly type formulas and expressions in the functions of the models.\n",
    "\n",
    "\n",
    "We can specify the name of the columns to be used to predict another column, remove columns, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Lottery   R-squared:                       0.338\n",
      "Model:                            OLS   Adj. R-squared:                  0.287\n",
      "Method:                 Least Squares   F-statistic:                     6.636\n",
      "Date:                Tue, 14 Nov 2017   Prob (F-statistic):           1.07e-05\n",
      "Time:                        10:52:35   Log-Likelihood:                -375.30\n",
      "No. Observations:                  85   AIC:                             764.6\n",
      "Df Residuals:                      78   BIC:                             781.7\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===============================================================================\n",
      "                  coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
      "-------------------------------------------------------------------------------\n",
      "Intercept      38.6517      9.456      4.087      0.000        19.826    57.478\n",
      "Region[T.E]   -15.4278      9.727     -1.586      0.117       -34.793     3.938\n",
      "Region[T.N]   -10.0170      9.260     -1.082      0.283       -28.453     8.419\n",
      "Region[T.S]    -4.5483      7.279     -0.625      0.534       -19.039     9.943\n",
      "Region[T.W]   -10.0913      7.196     -1.402      0.165       -24.418     4.235\n",
      "Literacy       -0.1858      0.210     -0.886      0.378        -0.603     0.232\n",
      "Wealth          0.4515      0.103      4.390      0.000         0.247     0.656\n",
      "==============================================================================\n",
      "Omnibus:                        3.049   Durbin-Watson:                   1.785\n",
      "Prob(Omnibus):                  0.218   Jarque-Bera (JB):                2.694\n",
      "Skew:                          -0.340   Prob(JB):                        0.260\n",
      "Kurtosis:                       2.454   Cond. No.                         371.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "mod = smf.ols(formula='Lottery ~ Literacy + Wealth + Region', data=df)\n",
    "res = mod.fit()\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Categorical variables__\n",
    "\n",
    "Patsy is the name of the interpreter that parses the formulas.\n",
    "\n",
    "Looking at the summary printed above, notice that patsy determined that elements of Region were text strings, so it treated Region as a categorical variable. \n",
    "\n",
    "Patsy‘s default is also to include an intercept, so we automatically dropped one of the Region categories."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Removing variables__\n",
    "\n",
    "The “-” sign can be used to remove columns/variables. For instance, we can remove the intercept from a model by:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Lottery   R-squared:                       0.338\n",
      "Model:                            OLS   Adj. R-squared:                  0.287\n",
      "Method:                 Least Squares   F-statistic:                     6.636\n",
      "Date:                Tue, 14 Nov 2017   Prob (F-statistic):           1.07e-05\n",
      "Time:                        10:52:35   Log-Likelihood:                -375.30\n",
      "No. Observations:                  85   AIC:                             764.6\n",
      "Df Residuals:                      78   BIC:                             781.7\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "================================================================================\n",
      "                   coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
      "--------------------------------------------------------------------------------\n",
      "C(Region)[C]    38.6517      9.456      4.087      0.000        19.826    57.478\n",
      "C(Region)[E]    23.2239     14.931      1.555      0.124        -6.501    52.949\n",
      "C(Region)[N]    28.6347     13.127      2.181      0.032         2.501    54.769\n",
      "C(Region)[S]    34.1034     10.370      3.289      0.002        13.459    54.748\n",
      "C(Region)[W]    28.5604     10.018      2.851      0.006         8.616    48.505\n",
      "Literacy        -0.1858      0.210     -0.886      0.378        -0.603     0.232\n",
      "Wealth           0.4515      0.103      4.390      0.000         0.247     0.656\n",
      "==============================================================================\n",
      "Omnibus:                        3.049   Durbin-Watson:                   1.785\n",
      "Prob(Omnibus):                  0.218   Jarque-Bera (JB):                2.694\n",
      "Skew:                          -0.340   Prob(JB):                        0.260\n",
      "Kurtosis:                       2.454   Cond. No.                         653.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "res = smf.ols(formula='Lottery ~ Literacy + Wealth + C(Region) -1 ', data=df).fit()\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Functions__\n",
    "\n",
    "We can also apply vectorized functions to the variables in our model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Lottery   R-squared:                       0.161\n",
      "Model:                            OLS   Adj. R-squared:                  0.151\n",
      "Method:                 Least Squares   F-statistic:                     15.89\n",
      "Date:                Tue, 14 Nov 2017   Prob (F-statistic):           0.000144\n",
      "Time:                        10:52:35   Log-Likelihood:                -385.38\n",
      "No. Observations:                  85   AIC:                             774.8\n",
      "Df Residuals:                      83   BIC:                             779.7\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "====================================================================================\n",
      "                       coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
      "------------------------------------------------------------------------------------\n",
      "Intercept          115.6091     18.374      6.292      0.000        79.064   152.155\n",
      "np.log(Literacy)   -20.3940      5.116     -3.986      0.000       -30.570   -10.218\n",
      "==============================================================================\n",
      "Omnibus:                        8.907   Durbin-Watson:                   2.019\n",
      "Prob(Omnibus):                  0.012   Jarque-Bera (JB):                3.299\n",
      "Skew:                           0.108   Prob(JB):                        0.192\n",
      "Kurtosis:                       2.059   Cond. No.                         28.7\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "res = smf.ols(formula='Lottery ~ np.log(Literacy)', data=df).fit()\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Understanding Problematic Observations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from statsmodels.formula.api import ols\n",
    "from statsmodels.compat import lzip\n",
    "prestige = sm.datasets.get_rdataset(\"Duncan\", \"car\", cache=True).data\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "This is data on the\n",
    "\"prestige\" and other characteristics of 45 U. S. occupations in 1950.\n",
    "\n",
    "* type: Type of occupation. A factor with the following levels: ``prof``,\n",
    "    professional and managerial; ``wc``, white-collar; ``bc``,\n",
    "    blue-collar.\n",
    "* income: Percent of males in occupation earning USD 3500 or more in 1950.\n",
    "* education: Percent of males in occupation in 1950 who were high-school graduates.\n",
    "* prestige: Percent of raters in NORC study rating occupation as excellent or good in prestige."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>type</th>\n",
       "      <th>income</th>\n",
       "      <th>education</th>\n",
       "      <th>prestige</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>accountant</th>\n",
       "      <td>prof</td>\n",
       "      <td>62</td>\n",
       "      <td>86</td>\n",
       "      <td>82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pilot</th>\n",
       "      <td>prof</td>\n",
       "      <td>72</td>\n",
       "      <td>76</td>\n",
       "      <td>83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>architect</th>\n",
       "      <td>prof</td>\n",
       "      <td>75</td>\n",
       "      <td>92</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>author</th>\n",
       "      <td>prof</td>\n",
       "      <td>55</td>\n",
       "      <td>90</td>\n",
       "      <td>76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>chemist</th>\n",
       "      <td>prof</td>\n",
       "      <td>64</td>\n",
       "      <td>86</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            type  income  education  prestige\n",
       "accountant  prof      62         86        82\n",
       "pilot       prof      72         76        83\n",
       "architect   prof      75         92        90\n",
       "author      prof      55         90        76\n",
       "chemist     prof      64         86        90"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prestige.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               prestige   R-squared:                       0.828\n",
      "Model:                            OLS   Adj. R-squared:                  0.820\n",
      "Method:                 Least Squares   F-statistic:                     101.2\n",
      "Date:                Tue, 14 Nov 2017   Prob (F-statistic):           8.65e-17\n",
      "Time:                        10:52:36   Log-Likelihood:                -178.98\n",
      "No. Observations:                  45   AIC:                             364.0\n",
      "Df Residuals:                      42   BIC:                             369.4\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -6.0647      4.272     -1.420      0.163       -14.686     2.556\n",
      "income         0.5987      0.120      5.003      0.000         0.357     0.840\n",
      "education      0.5458      0.098      5.555      0.000         0.348     0.744\n",
      "==============================================================================\n",
      "Omnibus:                        1.279   Durbin-Watson:                   1.458\n",
      "Prob(Omnibus):                  0.528   Jarque-Bera (JB):                0.520\n",
      "Skew:                           0.155   Prob(JB):                        0.771\n",
      "Kurtosis:                       3.426   Cond. No.                         163.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "prestige_model = ols(\"prestige ~ income + education\", data=prestige).fit()\n",
    "print(prestige_model.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Influence plots__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "To ask about the impact of individual observations on the overall model, we can calculate the `influence` of each observation.\n",
    "\n",
    "`leverage` is a measure of how far away the independent variable values of an observation are from those of the other observations.\n",
    "\n",
    "The `residual` is the error obtained when predicting the observation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Influence plots show the studentized residuals vs. the leverage of each observation as measured by the projection matrix.\n",
    "\n",
    "Externally studentized residuals are residuals that are scaled by their standard deviation where\n",
    "$$\\text{var}(\\hat{\\epsilon}_i)=\\hat{\\sigma}^2(1-h_{ii}).$$\n",
    " $h_{ii}$ is the $i$-th diagonal element of the projection matrix\n",
    "$$H=X(X^TX)^{-1}X^T$$\n",
    "where $X$ is the design matrix.\n",
    "\n",
    "It can be shown that $$h_{ii} = \\frac{\\partial\\hat{y}_i}{\\partial y_i}.$$\n",
    "\n",
    "The influence of each point can be visualized by the criterion keyword argument. Options are Cook's distance and DFFITS, two measures of influence.   Basically these methods combine leverage and residual."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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J4OAJWK2lH4kaY0GkKkMq3azWU3E6r2T37hlVuk7Egd3uWe+eUkopVZ94lLgZ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\nIiIiIklCiZuIiIhIkvj/pXnNdgw4klgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116886c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10,6))\n",
    "fig = sm.graphics.influence_plot(prestige_model, ax=ax, criterion=\"cooks\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "As you can see there are a few worrisome observations. Both contractor and reporter have low leverage but a large residual. \n",
    "RR.engineer has small residual and large leverage. Conductor and minister have both high leverage and large residuals, and, \n",
    "therefore, large influence."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Partial Regression Plots__ are a principled way of looking at individual independent variables versus the dependent variable, for visualization.   \n",
    "\n",
    "In a partial regression plot, to discern the relationship between the response variable and the $k$-th variable, we compute \n",
    "the residuals by regressing the response variable versus the independent variables excluding $X_k$. We can denote this by \n",
    "$X_{\\sim k}$. We then compute the residuals by regressing $X_k$ on $X_{\\sim k}$.     The partial regression plot is the plot \n",
    "of the former versus the latter residuals. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AAHDckiVL1KFDB7377rtq2bKl0+VcN8xsAwAAwFEffPCBOnXqpHnz5uWooC0x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lAAAg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90bp1a5iZmeHChQuGNm3btsXFixeRlpZmWHflyhWcOnXKKDagYKDn3ccufEf8QZiZmSEvL69U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\nZVfG+AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10556e2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "fix, ax = plt.subplots(figsize=(12,14))\n",
    "fig = sm.graphics.plot_partregress(\"prestige\", \"income\", [\"education\"], data=prestige, ax=ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "As you can see the partial regression plot confirms the influence of conductor, minister, and RR.engineer on the partial relationship between income and prestige. The cases greatly decrease the effect of income on prestige. Dropping these cases confirms this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               prestige   R-squared:                       0.876\n",
      "Model:                            OLS   Adj. R-squared:                  0.870\n",
      "Method:                 Least Squares   F-statistic:                     138.1\n",
      "Date:                Tue, 14 Nov 2017   Prob (F-statistic):           2.02e-18\n",
      "Time:                        10:52:38   Log-Likelihood:                -160.59\n",
      "No. Observations:                  42   AIC:                             327.2\n",
      "Df Residuals:                      39   BIC:                             332.4\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -6.3174      3.680     -1.717      0.094       -13.760     1.125\n",
      "income         0.9307      0.154      6.053      0.000         0.620     1.242\n",
      "education      0.2846      0.121      2.345      0.024         0.039     0.530\n",
      "==============================================================================\n",
      "Omnibus:                        3.811   Durbin-Watson:                   1.468\n",
      "Prob(Omnibus):                  0.149   Jarque-Bera (JB):                2.802\n",
      "Skew:                          -0.614   Prob(JB):                        0.246\n",
      "Kurtosis:                       3.303   Cond. No.                         158.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "subset = ~prestige.index.isin([\"conductor\", \"RR.engineer\", \"minister\"])\n",
    "prestige_model2 = ols(\"prestige ~ income + education\", data=prestige, subset=subset).fit()\n",
    "print(prestige_model2.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
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bI444gnXr1vGnP/2JuXPndim56i4VuRBJAPX+EBEREem5JUuWMG3aNB566CEuvPBCXn75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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116ccbdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "fig = sm.graphics.plot_partregress_grid(prestige_model, fig=fig)"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}