F Statistic Issue

f-stat

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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n",
      "%load_ext rmagic"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Load library, load data, standardize `MET`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "library('MASS')\n",
      "data <- read.csv('/home/william/class/appm4570/stateExpenditures.csv')\n",
      "data$MET <- (data$MET - mean(data$MET))/sd(data$MET)\n",
      "data$MET2 <- data$MET^2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 50
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Linear regression on data. Using same small model from other code."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "fit_full <- lm(EX ~ ECAB + MET + MET2 + GROW + YOUNG + OLD + WEST, data=data)\n",
      "fit_small <- lm(EX ~ ECAB + MET2 + WEST, data=data)\n",
      "k <- 7\n",
      "l <- 3\n",
      "print(coefficients(fit_full))\n",
      "print('============')\n",
      "print(coefficients(fit_small))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "(Intercept)        ECAB         MET        MET2        GROW       YOUNG \n",
        " 44.5614507   1.3954201  -5.0542271  22.4342650   0.6953360   0.6076015 \n",
        "        OLD        WEST \n",
        "  4.1207839  34.0730785 \n",
        "[1] \"============\"\n",
        "(Intercept)        ECAB        MET2        WEST \n",
        "  97.732033    1.519929   22.548872   39.550509 \n"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Find SSE of both fits"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "sse_full <- deviance(fit_full)\n",
      "sse_small <- deviance(fit_small)\n",
      "print(c('SSE FULL:', sse_full))\n",
      "print(c('SSE SMALL:', sse_small))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "[1] \"SSE FULL:\"        \"50155.0203618758\"\n",
        "[1] \"SSE SMALL:\"       \"54718.1056200931\"\n"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Calculate $f$ statistic, \n",
      "\n",
      "\\begin{equation}\n",
      "    \\frac{\\left( \\text{SSE}_l - \\text{SSE}_k \\right) / (k - l)}\n",
      "    {\\text{SSE}_k / \\left[ n - (k + l) \\right]}\n",
      "\\end{equation}"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "((sse_small - sse_full) / (k - l)) /\n",
      "(sse_full / (48 - (k + l)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "[1] 0.8643065\n"
       ]
      }
     ],
     "prompt_number": 56
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "pf(0.95, 4, 40)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "[1] 0.5546512\n"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
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  }
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