ChadFulton/OOP - OLS Example

## OOP - OLS Example
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "# ^ shows plots in the notebook\n",
    "\n",
    "import numpy as np              # Numeric library\n",
    "from scipy.stats import norm, t # Normal and t distributions\n",
    "from tabulate import tabulate   # Library for printing tables\n",
    "import statsmodels.api as sm    # Get the Star98 dataset\n",
    "dta = sm.datasets.star98.load_pandas().data\n",
    "\n",
    "import matplotlib.pyplot as plt # Plotting library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class OLS(object): # <-- this is a \"Class\"\n",
    "    def __init__(self, y, x, significance_level=0.05):\n",
    "        self.y = y\n",
    "        self.x = x\n",
    "        self.n = y.shape[0]\n",
    "        \n",
    "        # Calculate regression results\n",
    "        self.beta_hat = np.dot(np.linalg.pinv(x), y)\n",
    "        self.fitted = np.dot(x, self.beta_hat)\n",
    "        self.resid = y - self.fitted\n",
    "        self.dof = self.n - x.shape[1]\n",
    "        self.s2 = np.inner(self.resid, self.resid) / self.dof\n",
    "        self.cov = self.s2 * np.linalg.inv(np.dot(x.T, x))\n",
    "        \n",
    "        # Compute standard errors, t-stats, P>|t|, 95% Conf. Interval\n",
    "        self.std_err = np.diagonal(self.cov)**0.5\n",
    "        self.t_stats = self.beta_hat / self.std_err\n",
    "        self.p_values = t.sf(np.abs(self.t_stats), self.dof) * 2\n",
    "        critical_value = t.ppf(1 - significance_level / 2, self.dof)\n",
    "        self.lower_conf = self.beta_hat - critical_value * self.std_err\n",
    "        self.upper_conf = self.beta_hat + critical_value * self.std_err\n",
    "        \n",
    "    def aic(self):  # <-- this is a \"method\" (a function belonging to a class)\n",
    "        return (\n",
    "            np.log (np.inner(self.resid, self.resid) / self.n) +\n",
    "            2 * self.x.shape[1] / self.n\n",
    "        )\n",
    "        \n",
    "    def summary(self):\n",
    "        # Print results\n",
    "        header = ['', 'Coef.', 'Std. Err.', 't', 'P>|t|', '[95% Conf.', 'Interval]']\n",
    "        results = np.c_[\n",
    "            ['intercept','PTRATIO'],\n",
    "            self.beta_hat, self.std_err, self.t_stats,\n",
    "            self.p_values, self.lower_conf, self.upper_conf\n",
    "        ]\n",
    "        return tabulate(results, header, floatfmt='.3f')\n",
    "        \n",
    "    def residual_diagnostics(self):\n",
    "        # Plots: residual diagnostics\n",
    "        fig, axes = plt.subplots(1, 2, figsize=(12,4))\n",
    "\n",
    "        # QQ-plot\n",
    "        sresid = self.resid.sort(inplace=False)\n",
    "        dist = norm.fit(sresid)\n",
    "        eos = norm.ppf((np.arange(1, self.n+1) - 0.5) / self.n)\n",
    "        axes[0].plot(eos, (sresid - dist[0]) / dist[1], 'ko', alpha=0.2)\n",
    "        axes[0].plot([-4,4],[-4,4], 'r')\n",
    "        axes[0].set(title='Normal Q-Q Plot',\n",
    "                    xlabel='Theoretical quantiles',\n",
    "                    ylabel='Sample quantiles')\n",
    "\n",
    "        # Histogram\n",
    "        axes[1].hist(self.resid)\n",
    "        axes[1].set(title='Histogram of residuals',\n",
    "                    xlabel='Residuals', \n",
    "                    ylabel='Frequency');\n",
    "        \n",
    "        return axes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              Coef.    Std. Err.       t    P>|t|    [95% Conf.    Interval]\n",
      "---------  --------  -----------  ------  -------  ------------  -----------\n",
      "intercept  -834.800      382.544  -2.182    0.030     -1587.600      -82.000\n",
      "PTRATIO      53.089       16.947   3.133    0.002        19.739       86.440\n",
      "AIC = 12.95\n"
     ]
    },
    {
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       "AZOn5CUPj4xGAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10de63a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mod1 = OLS(dta['NABOVE'], np.c_[np.ones(dta.shape[0]), dta['PTRATIO']])\n",
    "print mod1.summary()\n",
    "print \"AIC = %.2f\" % mod1.aic()\n",
    "mod1.residual_diagnostics();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             Coef.    Std. Err.       t    P>|t|    [95% Conf.    Interval]\n",
      "---------  -------  -----------  ------  -------  ------------  -----------\n",
      "intercept  -13.361        1.958  -6.825    0.000       -17.214       -9.509\n",
      "PTRATIO      5.954        0.630   9.454    0.000         4.714        7.193\n",
      "AIC = 0.22\n"
     ]
    },
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1121b0310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mod2 = OLS(np.log(dta['NABOVE']), np.c_[np.ones(dta.shape[0]), np.log(dta['PTRATIO'])])\n",
    "print mod2.summary()\n",
    "print \"AIC = %.2f\" % mod2.aic()\n",
    "mod2.residual_diagnostics();"
   ]
  }
 ],
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