package com.imsl.test.example.stat;

import java.text.*;
import com.imsl.stat.*;
import com.imsl.math.*;

/**
 * <p>
 * Finds the best regressions using Mallow's \(C_p\) criterion.
 * </p>
 *
 * <p>
 * This example uses the same data set as example
 * {@link SelectionRegressionEx1}, but Mallow's \(C_p\) statistic is used as the
 * criterion rather than \(R^2\). Note that when Mallow's \(C_p\) statistic (or
 * adjusted \(R^2\)) is specified, the method <code>setMaximumBestFound</code>
 * is used to indicate the total number of "best" regressions (rather than
 * indicating the number of best regressions per subset size, as in the case of
 * the \(R^2\) criterion). In this example, the three best regressions are found
 * to be \((1, 2), (1, 2, 4)\), and \((1, 2, 3)\).</p>
 *
 *
 * @see <a href="SelectionRegressionEx2.java">Code</a>
 * @see <a href="doc-files/SelectionRegressionEx2.out">Output</a>
 */
public class SelectionRegressionEx2 {

    public static void main(String[] args) throws Exception {
        double x[][] = {
            {7., 26., 6., 60.},
            {1., 29., 15., 52.},
            {11., 56., 8., 20.},
            {11., 31., 8., 47.},
            {7., 52., 6., 33.},
            {11., 55., 9., 22.},
            {3., 71., 17., 6.},
            {1., 31., 22., 44.},
            {2., 54., 18., 22.},
            {21., 47., 4., 26},
            {1., 40., 23., 34.},
            {11., 66., 9., 12.},
            {10.0, 68., 8., 12.}
        };

        double y[] = {
            78.5, 74.3, 104.3, 87.6,
            95.9, 109.2, 102.7, 72.5,
            93.1, 115.9, 83.8, 113.3,
            109.4
        };

        String criterionOption;
        MessageFormat critMsg
                = new MessageFormat("Regressions with {0} variable(s) ({1})");
        MessageFormat critLabel
                = new MessageFormat("   Criterion               Variables");
        MessageFormat coefMsg = new MessageFormat("Best Regressions with"
                + " {0} variable(s) ({1})");
        MessageFormat coefLabel = new MessageFormat("Variable   Coefficient"
                + "   Standard Error  t-statistic   p-value");

        SelectionRegression sr = new SelectionRegression(4);
        sr.setCriterionOption(SelectionRegression.MALLOWS_CP_CRITERION);
        sr.setMaximumBestFound(3);
        sr.compute(x, y);
        SelectionRegression.Statistics stats = sr.getStatistics();

        criterionOption = "Mallows Cp";

        for (int i = 1; i <= 4; i++) {
            double[] tmpCrit = stats.getCriterionValues(i);
            int[][] indvar = stats.getIndependentVariables(i);

            Object p[] = {new Integer(i), criterionOption};
            System.out.println(critMsg.format(p));
            Object p1[] = {null};
            System.out.println(critLabel.format(p1));

            for (int j = 0; j < tmpCrit.length; j++) {
                System.out.print("     " + tmpCrit[j] + "        ");
                for (int k = 0; k < indvar[j].length; k++) {
                    System.out.print(indvar[j][k] + "   ");
                }
                System.out.println("");
            }
            System.out.println("");
        }

        for (int i = 0; i < 3; i++) {
            System.out.println("");

            double[][] tmpCoef = stats.getCoefficientStatistics(i);

            Object p[] = {new Integer(tmpCoef.length), criterionOption};
            System.out.println(coefMsg.format(p));
            Object p2[] = {null};
            System.out.println(coefLabel.format(p2));

            PrintMatrix pm = new PrintMatrix();
            pm.setColumnSpacing(10);
            NumberFormat nf = NumberFormat.getInstance();
            nf.setMinimumFractionDigits(4);
            PrintMatrixFormat tst = new PrintMatrixFormat();
            tst.setNoColumnLabels();
            tst.setNoRowLabels();
            tst.setNumberFormat(nf);
            pm.print(tst, tmpCoef);
            System.out.println();
            System.out.println();
        }
    }
}