package com.imsl.test.example.stat;

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

/**
 * <p>Fits a regression to a polynomial with user defined basis functions.
 * </p>
 * <p>
 * In this example, we fit the polynomial \(y = c_0 + c_1 x + c_2 x^2 \cdots +
 * c_4 x^4 + \varepsilon\). For this model, the user basis function is \(f_i (x)
 * = x^{i + 1}\) with \(i = 0,1, \cdots ,nBasis = 4\) and
 * <code>hasIntercept=true</code>.
 * </p>
 * <p>
 * Data are generated using the model \(y = 10 + 2x + 5x^3\) with \(x = 0,1,
 * \cdots 9\).</p>
 *
 *
 *
 * @see <a href="UserBasisRegressionEx2.java">Code</a>
 * @see <a href="doc-files/UserBasisRegressionEx2.out">Output</a>
 */

public class UserBasisRegressionEx2 {

    public static void main(String args[]) {
        class Basis implements RegressionBasis {

            @Override
            public double basis(int index, double x) {
                // Notice zero-based indexing requires index be incremented
                return Math.pow(x, index + 1);
            }
        }

        UserBasisRegression ubr
                = new UserBasisRegression(new Basis(), 4, true);

        for (double x = 0; x < 10; x++) {
            double y = 10.0 + x + 3 * Math.pow(x, 3);
            ubr.update(x, y, 1.0);
        }

        // Print the regression coefficients
        double coef[] = ubr.getCoefficients();
        new PrintMatrix("The regression coefficients are:").print(coef);

        // Print the Anova Table
        ANOVA anovaTable = ubr.getANOVA();

        System.out.println("Degrees Of Freedom For Model:          "
                + anovaTable.getDegreesOfFreedomForModel());
        System.out.println("Degrees Of Freedom For Error:          "
                + anovaTable.getDegreesOfFreedomForError());
        System.out.println("Total (Corrected) Degrees Of Freedom:  "
                + anovaTable.getTotalDegreesOfFreedom());
        System.out.println("Sum Of Squares For Model:              "
                + anovaTable.getSumOfSquaresForModel());
        System.out.println("Sum Of Squares For Error:              "
                + anovaTable.getSumOfSquaresForError());
        System.out.println("Total (Corrected) Sum Of Squares:      "
                + anovaTable.getTotalSumOfSquares());
        System.out.println("Model Mean Square:                     "
                + anovaTable.getModelMeanSquare());
        System.out.println("Error Mean Square:                     "
                + anovaTable.getErrorMeanSquare());
        System.out.println("F statistic:                           "
                + anovaTable.getF());
        System.out.println("P value:                               "
                + anovaTable.getP());
        System.out.println("R Squared (in percent):                "
                + anovaTable.getRSquared());
        System.out.println("Adjusted R Squared (in percent):       "
                + anovaTable.getAdjustedRSquared());
        System.out.println("Model Error Standard deviation:        "
                + anovaTable.getModelErrorStdev());
        System.out.println("Mean Of Y:                             "
                + anovaTable.getMeanOfY());
        System.out.println("Coefficient Of Variation (in percent): "
                + anovaTable.getCoefficientOfVariation());
    }
}