# LinearRegression.java

Below is the syntax highlighted version of LinearRegression.java from §9.7 Optimization.

```
/******************************************************************************
*  Compilation:  javac LinearRegression.java StdIn.java
*  Execution:    java LinearRegression < data.txt
*
*  Reads in a sequence of pairs of real numbers and computes the
*  best fit (least squares) line y  = ax + b through the set of points.
*  Also computes the correlation coefficient and the standard errror
*  of the regression coefficients.
*
*  Note: the two-pass formula is preferred for stability.
*
******************************************************************************/

public class LinearRegression {

public static void main(String[] args) {
int MAXN = 1000;
int n = 0;
double[] x = new double[MAXN];
double[] y = new double[MAXN];

// first pass: read in data, compute xbar and ybar
double sumx = 0.0, sumy = 0.0, sumx2 = 0.0;
while(!StdIn.isEmpty()) {
sumx  += x[n];
sumx2 += x[n] * x[n];
sumy  += y[n];
n++;
}
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);
}
double beta1 = xybar / xxbar;
double beta0 = ybar - beta1 * xbar;

// print results
StdOut.println("y   = " + beta1 + " * x + " + beta0);

// analyze results
int df = n - 2;
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 = beta1*x[i] + beta0;
rss += (fit - y[i]) * (fit - y[i]);
ssr += (fit - ybar) * (fit - ybar);
}
double R2    = ssr / yybar;
double svar  = rss / df;
double svar1 = svar / xxbar;
double svar0 = svar/n + xbar*xbar*svar1;
StdOut.println("R^2                 = " + R2);
StdOut.println("std error of beta_1 = " + Math.sqrt(svar1));
StdOut.println("std error of beta_0 = " + Math.sqrt(svar0));
svar0 = svar * sumx2 / (n * xxbar);
StdOut.println("std error of beta_0 = " + Math.sqrt(svar0));

StdOut.println("SSTO = " + yybar);