This example uses the same data set as the first example, but Mallow's 
statistic is used as the criterion rather than 
. Note that when Mallow's 
statistic (or adjusted 
) is specified, MaximumBestFound
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 
criterion). In this example, the three best regressions are found to be (1, 2), (1, 2, 4), and (1, 2, 3).
using System;
using Imsl.Math;
using Imsl.Stat;
public class SelectionRegressionEx2
{
public static void Main(String[] args)
{
double[,] x = { {7.0, 26.0, 6.0, 60.0},
{1.0, 29.0, 15.0, 52.0},
{11.0, 56.0, 8.0, 20.0},
{11.0, 31.0, 8.0, 47.0},
{7.0, 52.0, 6.0, 33.0},
{11.0, 55.0, 9.0, 22.0},
{3.0, 71.0, 17.0, 6.0},
{1.0, 31.0, 22.0, 44.0},
{2.0, 54.0, 18.0, 22.0},
{21.0, 47.0, 4.0, 26},
{1.0, 40.0, 23.0, 34.0},
{11.0, 66.0, 9.0, 12.0},
{10.0, 68.0, 8.0, 12.0}
};
double[] y = new double[]{ 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};
SelectionRegression sr = new SelectionRegression(4);
sr.CriterionOption = Imsl.Stat.SelectionRegression.Criterion.MallowsCP;
sr.MaximumBestFound = 3;
sr.Compute(x, y);
SelectionRegression.SummaryStatistics stats = sr.Statistics;
for (int i = 1; i <= 4; i++)
{
double[] tmpCrit = stats.GetCriterionValues(i);
int[,] indvar = stats.GetIndependentVariables(i);
Console.Out.WriteLine("Regressions with "+i+" variable(s) (MallowsCP)");
for (int j = 0; j < tmpCrit.GetLength(0); j++)
{
Console.Out.Write(" " + tmpCrit[j] + " ");
for (int k = 0; k < indvar.GetLength(1); k++)
Console.Out.Write(indvar[j,k] + " ");
Console.Out.WriteLine("");
}
Console.Out.WriteLine("");
}
// Setup a PrintMatrix object for use in the loop below.
PrintMatrix pm = new PrintMatrix();
pm.SetColumnSpacing(9);
PrintMatrixFormat tst = new PrintMatrixFormat();
tst.SetNoColumnLabels();
tst.SetNoRowLabels();
tst.NumberFormat = "0.000";
for (int i = 0; i < 3; i++)
{
double[,] tmpCoef = stats.GetCoefficientStatistics(i);
Console.Out.WriteLine("\n\nRegressions with "+(i+1)+" variable(s) (MallowsCP)");
Console.Out.WriteLine("Variable Coefficient Standard Error t-statistic p-value");
pm.Print(tst, tmpCoef);
}
}
}
Regressions with 1 variable(s) (MallowsCP)
138.730833491674 4
142.486406936958 2
202.548769123445 1
315.154284140073 3
Regressions with 2 variable(s) (MallowsCP)
2.6782415983184 1 2
5.4958508247584 1 4
22.3731119646967 3 4
138.225919754638 2 4
198.094652569569 1 3
Regressions with 3 variable(s) (MallowsCP)
3.01823347348731 1 2 4
3.04127972306423 1 2 3
3.49682444234832 1 3 4
7.33747399565576 2 3 4
Regressions with 4 variable(s) (MallowsCP)
5 1 2 3 4
Regressions with 1 variable(s) (MallowsCP)
Variable Coefficient Standard Error t-statistic p-value
1.000 1.468 0.121 12.105 0.000
2.000 0.662 0.046 14.442 0.000
Regressions with 2 variable(s) (MallowsCP)
Variable Coefficient Standard Error t-statistic p-value
1.000 1.452 0.117 12.410 0.000
2.000 0.416 0.186 2.242 0.052
4.000 -0.237 0.173 -1.365 0.205
Regressions with 3 variable(s) (MallowsCP)
Variable Coefficient Standard Error t-statistic p-value
1.000 1.696 0.205 8.290 0.000
2.000 0.657 0.044 14.851 0.000
3.000 0.250 0.185 1.354 0.209
Link to C# source.