Below is the syntax highlighted version of LinearRegression.java.
/****************************************************************************** * Compilation: javac LinearRegression.java * Execution: java LinearRegression * Dependencies: none * * Compute least squares solution to y = beta * x + alpha. * Simple linear regression. * ******************************************************************************/ package edu.princeton.cs.algs4; /** * The {@code LinearRegression} 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. * * @author Robert Sedgewick * @author Kevin Wayne */ public class LinearRegression { private final double intercept, slope; private final double r2; private final double svar0, svar1; /** * Performs a linear regression on the data points {@code (y[i], x[i])}. * * @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"); } int n = x.length; // first pass double sumx = 0.0, sumy = 0.0, sumx2 = 0.0; for (int i = 0; i < n; i++) { sumx += x[i]; sumx2 += x[i]*x[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; double 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 {@code y} given the value of the predictor * variable {@code x}. * * @param x the value of the predictor variable * @return the expected response {@code y} given the value of the predictor * variable {@code x} */ 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> */ public String toString() { StringBuilder s = new StringBuilder(); s.append(String.format("%.2f n + %.2f", slope(), intercept())); s.append(" (R^2 = " + String.format("%.3f", R2()) + ")"); return s.toString(); } } /****************************************************************************** * Copyright 2002-2022, Robert Sedgewick and Kevin Wayne. * * This file is part of algs4.jar, which accompanies the textbook * * Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne, * Addison-Wesley Professional, 2011, ISBN 0-321-57351-X. * http://algs4.cs.princeton.edu * * * algs4.jar is free software: you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation, either version 3 of the License, or * (at your option) any later version. * * algs4.jar is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with algs4.jar. If not, see http://www.gnu.org/licenses. ******************************************************************************/