package stdlib;
public class XLinearRegression {
  private final int N;
  private final double beta0, beta1;
  private final double R2;
  private final double svar, svar0, svar1;

  public XLinearRegression(double[] x, double[] y) {
    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];
    //for (int i = 0; i < N; i++) sumx2 += x[i]*x[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);
    }
    beta1 = xybar / xxbar;
    beta0 = ybar - beta1 * 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 = beta1*x[i] + beta0;
      rss += (fit - y[i]) * (fit - y[i]);
      ssr += (fit - ybar) * (fit - ybar);
    }

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

  // y = beta1*x + beta0
  // y = slope*x + intercept  [ rename to slope and intercept ]
  public double beta0() { return beta0; }
  public double beta1() { return beta1; }

  // R^2
  public double R2() { return R2; }

  // standard error of beta0 and beta1
  public double beta0StdErr() { return Math.sqrt(svar0); }
  public double beta1StdErr() { return Math.sqrt(svar1); }

  // predict a value of y, given a value of x
  public double predict(double x) {
    return beta1*x + beta0;
  }

  public String toString() {
    String s = "";
    s += String.format("%.2f N + ", beta1());
    s += String.format("%.2f ", beta0());
    return s + " (R^2 = " + String.format("%.3f", R2()) + ")";
  }


}