LinearRegression.java

package uk.ac.babraham.BamQC.Utilities;
/**
 *  The <tt>LinearRegression</tt> class performs a simple linear regression
 *  on an set of <em>N</em> data points (<em>y<sub>i</sub></em>, <em>x<sub>i</sub></em>).
 *  That is, it fits a straight line <em>y</em> = α + β <em>x</em>,
 *  (where <em>y</em> is the response variable, <em>x</em> is the predictor variable,
 *  α is the <em>y-intercept</em>, and β is the <em>slope</em>)
 *  that minimizes the sum of squared residuals of the linear regression model.
 *  It also computes associated statistics, including the coefficient of
 *  determination <em>R</em><sup>2</sup> and the standard deviation of the
 *  estimates for the slope and <em>y</em>-intercept.
 *  
 *  Source code: http://algs4.cs.princeton.edu/14analysis/LinearRegression.java
 *  (GPLv3 License)
 *
 *  @author Robert Sedgewick
 *  @author Kevin Wayne
 */
public class LinearRegression {
    private final int N;
    private final double intercept, slope;
    private final double R2;
    private final double svar, svar0, svar1;

   /**
     * Performs a linear regression on the data points <tt>(y[i], x[i])</tt>.
     *
     * @param  x the values of the predictor variable
     * @param  y the corresponding values of the response variable
     * @throws IllegalArgumentException if the lengths of the two arrays are not equal
     */
    public LinearRegression(double[] x, double[] y) {
        if (x.length != y.length) {
            throw new IllegalArgumentException("Array lengths are not equal");
        }
        N = x.length;

        // first pass
        double sumx = 0.0, sumy = 0.0;
        for (int i = 0; i < N; i++)
            sumx  += x[i];
        for (int i = 0; i < N; i++) {
		}
        for (int i = 0; i < N; i++)
            sumy  += y[i];
        double xbar = sumx / N;
        double ybar = sumy / N;

        // second pass: compute summary statistics
        double xxbar = 0.0, yybar = 0.0, xybar = 0.0;
        for (int i = 0; i < N; i++) {
            xxbar += (x[i] - xbar) * (x[i] - xbar);
            yybar += (y[i] - ybar) * (y[i] - ybar);
            xybar += (x[i] - xbar) * (y[i] - ybar);
        }
        slope  = xybar / xxbar;
        intercept = ybar - slope * xbar;

        // more statistical analysis
        double rss = 0.0;      // residual sum of squares
        double ssr = 0.0;      // regression sum of squares
        for (int i = 0; i < N; i++) {
            double fit = slope*x[i] + intercept;
            rss += (fit - y[i]) * (fit - y[i]);
            ssr += (fit - ybar) * (fit - ybar);
        }

        int degreesOfFreedom = N-2;
        R2    = ssr / yybar;
        svar  = rss / degreesOfFreedom;
        svar1 = svar / xxbar;
        svar0 = svar/N + xbar*xbar*svar1;
    }

   /**
     * Returns the <em>y</em>-intercept α of the best of the best-fit line <em>y</em> = α + β <em>x</em>.
     *
     * @return the <em>y</em>-intercept α of the best-fit line <em>y = α + β x</em>
     */
    public double intercept() {
        return intercept;
    }

   /**
     * Returns the slope β of the best of the best-fit line <em>y</em> = α + β <em>x</em>.
     *
     * @return the slope β of the best-fit line <em>y</em> = α + β <em>x</em>
     */
    public double slope() {
        return slope;
    }

   /**
     * Returns the coefficient of determination <em>R</em><sup>2</sup>.
     *
     * @return the coefficient of determination <em>R</em><sup>2</sup>,
     *         which is a real number between 0 and 1
     */
    public double R2() {
        return R2;
    }

   /**
     * Returns the standard error of the estimate for the intercept.
     *
     * @return the standard error of the estimate for the intercept
     */
    public double interceptStdErr() {
        return Math.sqrt(svar0);
    }

   /**
     * Returns the standard error of the estimate for the slope.
     *
     * @return the standard error of the estimate for the slope
     */
    public double slopeStdErr() {
        return Math.sqrt(svar1);
    }

   /**
     * Returns the expected response <tt>y</tt> given the value of the predictor
     * variable <tt>x</tt>.
     *
     * @param  x the value of the predictor variable
     * @return the expected response <tt>y</tt> given the value of the predictor
     *         variable <tt>x</tt>
     */
    public double predict(double x) {
        return slope*x + intercept;
    }

   /**
     * Returns a string representation of the simple linear regression model.
     *
     * @return a string representation of the simple linear regression model,
     *         including the best-fit line and the coefficient of determination
     *         <em>R</em><sup>2</sup>
     */
    @Override
	public String toString() {
        String s = "";
        s += String.format("%.2f N + %.2f", slope(), intercept());
        return s + "  (R^2 = " + String.format("%.3f", R2()) + ")";
    }


}