/*************************************************************************
 *  Compilation:  javac -classpath jama.jar:. MultipleLinearRegression.java
 *  Execution:    java  -classpath jama.jar:. MultipleLinearRegression
 *  Dependencies: jama.jar
 *  
 *  Compute least squares solution to X beta = y using Jama library (which
 *  uses LU if matrix is square or QR decomposition otherwise).
 *  Assumes X has full column rank.
 *  
 *       http://math.nist.gov/javanumerics/jama/
 *       http://math.nist.gov/javanumerics/jama/Jama-1.0.1.jar
 *
 *************************************************************************/

import Jama.Matrix;

public class MultipleLinearRegression {

    public static void main(String[] args) { 

        // generate random n-by-p matrix
        int n = Integer.parseInt(args[0]);
        int p = Integer.parseInt(args[1]);
        Matrix X = Matrix.random(n, p);
        Matrix y = Matrix.random(n, 1);

        // solve least squares problem using Jama
        Matrix beta = X.solve(y);
        Matrix residuals = X.times(beta).minus(y);

        // print results
        System.out.println("X = ");
        X.print(9, 4);
        System.out.println("y = ");
        y.print(9, 4);
        System.out.println("beta = ");
        beta.print(9, 4);
        System.out.println("X beta - y = ");
        residuals.print(9, 4);

        // error variance
        double s2 = residuals.norm2() / (n - p - 1);
        System.out.println("error variance = " + s2);

    }


}