SimpleLinearRegression.java

package com.compomics.util.math.statistics.linear_regression.regressions;

import com.compomics.util.math.BasicMathFunctions;
import com.compomics.util.math.statistics.linear_regression.RegressionStatistics;
import java.util.ArrayList;

/**
 * Performs a simple linear regression. 
 * TODO: replace with the Apache implementation
 *
 * @author Marc Vaudel
 */
public class SimpleLinearRegression {

    /**
     * Returns a simple linear regression. Note: r calculation is not
     * implemented.
     *
     * @param x the x series
     * @param y the y series
     *
     * @return a simple linear regression
     */
    public static RegressionStatistics getLinearRegression(ArrayList<Double> x, ArrayList<Double> y) {

        if (x == null) {
            throw new IllegalArgumentException("null given as x for linear regression.");
        }
        if (y == null) {
            throw new IllegalArgumentException("null given as y for linear regression.");
        }
        if (x.size() != y.size()) {
            throw new IllegalArgumentException("Attempting to perform linear regression of lists of different sizes.");
        }
        int n = x.size();
        if (n <= 1) {
            throw new IllegalArgumentException("Attempting to perform linear regression of a vectore of size " + n + ".");
        }

        Double sumXY = 0.0;
        Double sumX = 0.0;
        Double sumX2 = 0.0;
        Double sumY = 0.0;
        Double x0 = x.get(0);
        boolean newX = false;
        for (int i = 0; i < n; i++) {
            Double xi = x.get(i);
            if (!newX && !xi.equals(x0)) {
                newX = true;
            }
            Double yi = y.get(i);
            sumXY += (xi * yi);
            sumX += xi;
            sumX2 += (xi * xi);
            sumY += yi;
        }

        if (!newX) {
            throw new IllegalArgumentException("Attempting to perform the linear regression of a vertical line or a point.");
        }

        Double xMean = sumX / n;
        Double yMean = sumY / n;
        Double a = (sumXY - (xMean * sumY)) / (sumX2 - (sumX * sumX / n));
        Double b = yMean - (a * xMean);
        Double ssTot = 0.0;
        Double ssRes = 0.0;
        ArrayList<Double> deltasSquare = new ArrayList<Double>(x.size());

        for (int i = 0; i < x.size(); i++) {
            Double xi = x.get(i);
            Double yi = y.get(i);
            Double fi = (a * xi) + b;
            Double diffY = yi - yMean;
            ssTot += (diffY * diffY);
            Double diffF = yi - fi;
            ssRes += (diffF * diffF);
            Double deltaY = yi - b;
            Double ai = deltaY / xi;
            Double deltaA = ai - a;
            Double deltaSquare = (xi * xi) + (deltaY * deltaY);
            deltaSquare *= deltaA * deltaA;
            deltaSquare /= (1 + (ai * ai));
            deltaSquare /= (1 + (a * a));
            deltasSquare.add(deltaSquare);
        }

        Double rSquared = 1.0;
        if (ssTot > 0) {
            rSquared = 1 - (ssRes / ssTot);
        }

        Double meanDelta = BasicMathFunctions.mean(deltasSquare);
        Double medianDelta = BasicMathFunctions.median(deltasSquare);

        return new RegressionStatistics(a, b, rSquared, meanDelta, medianDelta);
    }
}