Calculates the two-tailed p-values for the t-statistics for regression parameters.

MyOLSMultipleLinearRegression.java

import org.apache.commons.math3.distribution.TDistribution;
import org.apache.commons.math3.linear.RealMatrix;
import org.apache.commons.math3.stat.regression.OLSMultipleLinearRegression;
import org.apache.commons.math3.util.FastMath;

import java.util.Arrays;

public class MyOLSMultipleLinearRegression extends OLSMultipleLinearRegression {
    /**
     * <p>Calculates the two-tailed p-values for the t-statistics for regression parameters.
     * </p>
     *
     * <p>Data for the model must have been successfully loaded using one of
     * the {@code newSampleData} methods before invoking this method; otherwise
     * a {@code NullPointerException} will be thrown.</p>
     *
     * @param beta The [p,1] array representing regression parameters, typically returned from invoking
     *             {@code estimateRegressionParameters} method
     * @return The [n,1] array representing p-values
     * @throws org.apache.commons.math3.linear.SingularMatrixException if the design matrix is singular
     * @throws NullPointerException if the data for the model have not been loaded
     */
    public double[] calculateRegressionParametersPvalues(double[] beta) {
        RealMatrix xMatrix = this.getX();
        int numSamples = xMatrix.getRowDimension();
        int numParameters = xMatrix.getColumnDimension();
        RealMatrix betaVarianceMatrix = this.calculateBetaVariance();  // (X'X)^{-1}
        double regressionStandardError = this.estimateRegressionStandardError();  // sqrt{r'r/(n-p)}
        double[] pValues = new double[numParameters];
        TDistribution tDist = new TDistribution(null, numSamples - numParameters);
        for (int i=0; i<numParameters; i++) {
            double tStats = (beta[i] /
                    (FastMath.sqrt(betaVarianceMatrix.getEntry(i, i)) * regressionStandardError));
            pValues[i] = 2 * (1 - tDist.cumulativeProbability(FastMath.abs(tStats)));
        }
        return pValues;
    }

    /**
     * Calculates the two-tailed p-values for the t-statistics for regression parameters. Convenient method for
     * {@link MyOLSMultipleLinearRegression#calculateRegressionParametersPvalues(double[])} if
     * {@code estimateRegressionParameters} has not been invoked beforehand.
     */
    public double[] calculateRegressionParametersPvalues() {
        double[] beta = this.estimateRegressionParameters();
        return calculateRegressionParametersPvalues(beta);
    }
}

class Demo {
    public static void main(String[] args) {
        MyOLSMultipleLinearRegression regression = new MyOLSMultipleLinearRegression();
        regression.newSampleData(new double[]{0, 1, 2, 3}, new double[][]{{1, 2}, {3, -1}, {6, 5}, {9, 8}});
        double[] beta = regression.estimateRegressionParameters();
        System.out.println("regression parameters: " + Arrays.toString(beta));
        System.out.println("p-values: " + Arrays.toString(regression.calculateRegressionParametersPvalues(beta)));
    }
}