Example: Regression with User-supplied Basis Functions

In this example, we fit the polynomial . For this model, the user basis function is with and hasIntercept=true .

Data are generated using the model with .

using System;
using Imsl.Stat;
using Imsl.Math;

public class UserBasisRegressionEx2 : IRegressionBasis
{
    public double Basis(int index, double x)
    {
        // Notice zero-based indexing requires index be incremented
        return System.Math.Pow(x, index + 1);
    }

    public static void Main(string[] args)
    {
        double y = 0;
        double[] coef ;
        IRegressionBasis basis = new UserBasisRegressionEx2();
        UserBasisRegression ubr = 
            new UserBasisRegression(basis, 4, true);
        for (double x = 0; x < 10; x++)
        {
            y = 10.0 + x + 3 * System.Math.Pow(x, 3);
            ubr.Update(x, y, 1.0);
        }
        coef = ubr.GetCoefficients();
        PrintMatrix pm = new PrintMatrix("The regression coefficients are:");
        PrintMatrixFormat pmf = new PrintMatrixFormat();
        pmf.NumberFormat = "0.0";
        pm.Print(pmf, coef);
        
        // Print the Anova Table
        ANOVA anovaTable = ubr.ANOVA;
        
        System.Console.Out.WriteLine("Degrees Of Freedom For Model:          "
         + anovaTable.DegreesOfFreedomForModel);
        System.Console.Out.WriteLine("Degrees Of Freedom For Error:          "
         + anovaTable.DegreesOfFreedomForError);
        System.Console.Out.WriteLine("Total (Corrected) Degrees Of Freedom:  "
         + anovaTable.TotalDegreesOfFreedom);
        System.Console.Out.WriteLine("Sum Of Squares For Model:              "
         + anovaTable.SumOfSquaresForModel);
        System.Console.Out.WriteLine("Sum Of Squares For Error:              "
         + anovaTable.SumOfSquaresForError);
        System.Console.Out.WriteLine("Total (Corrected) Sum Of Squares:      "
         + anovaTable.TotalSumOfSquares);
        System.Console.Out.WriteLine("Model Mean Square:                     "
         + anovaTable.ModelMeanSquare);
        System.Console.Out.WriteLine("Error Mean Square:                     "
         + anovaTable.ErrorMeanSquare);
        System.Console.Out.WriteLine("F statistic:                           "
         + anovaTable.F);
        System.Console.Out.WriteLine("P value:                               "
         + anovaTable.P);
        System.Console.Out.WriteLine("R Squared (in percent):                "
         + anovaTable.RSquared);
        System.Console.Out.WriteLine("Adjusted R Squared (in percent):       "
         + anovaTable.AdjustedRSquared);
        System.Console.Out.WriteLine("Model Error Standard deviation:        "
         + anovaTable.ModelErrorStdev);
        System.Console.Out.WriteLine("Mean Of Y:                             "
         + anovaTable.MeanOfY);
        System.Console.Out.WriteLine("Coefficient Of Variation (in percent): "
         + anovaTable.CoefficientOfVariation);
    }
}

Output

The regression coefficients are:
    0    
0  10.0  
1  1.0   
2  0.0   
3  3.0   
4  0.0   

Degrees Of Freedom For Model:          4
Degrees Of Freedom For Error:          5
Total (Corrected) Degrees Of Freedom:  9
Sum Of Squares For Model:              5152488
Sum Of Squares For Error:              1.86264514923096E-09
Total (Corrected) Sum Of Squares:      5152488
Model Mean Square:                     1288122
Error Mean Square:                     3.72529029846191E-10
F statistic:                           3.45777616453632E+15
P value:                               8.69662785564134E-39
R Squared (in percent):                100
Adjusted R Squared (in percent):       99.9999999999999
Model Error Standard deviation:        1.93010111094261E-05
Mean Of Y:                             622
Coefficient Of Variation (in percent): 3.10305644846079E-06