// Instructions:
// (1) First display the points by compiling and executing.
// (2) Un-comment the least-squares section, add code to
//     apply least-squares. Then compile and execute.

import edu.gwu.lintool.*;

public class RegressionExample {

    public static void main (String[] argv)
    {
	// The data:
	int n = 8;
	double[] x = {1, 1.5, 2, 3.6, 5, 6.2, 8.5, 9};
	double[] y = {3.6, 3.9, 3.9, 5.1, 5.2, 6.0, 7.4, 7.2};

	// Display the points.
	DrawTool.display ();
	DrawTool.setXYRange (0,10, 0,10);
	for (int i=0; i<n; i++) {
	    DrawTool.drawPoint (x[i],y[i]);
	}

	// Put the data in a matrix:
        double[][] A = {
	    {1,   1},
	    {1.5, 1},
	    {2,   1},
	    {3.6, 1},
	    {5,   1},
	    {6.2, 1},
	    {8.5, 1},
	    {9.0, 1}
	};
	// The RHS vector b is just y
	double[] b = y;

	/*
	// INSERT YOUR CODE HERE for least squares
	// Compute the transpose of A:
	double[][] AT = 

	// Multiply A by AT (with AT on the left)
	double[][] ATA = 

	// Get the inverse of ATA:
	LinResult L = LinToolLibrary.inverse (ATA);
	if (L.Ainv == null) {
	    System.out.println ("No inverse exists for ATA");
	    System.exit (0);
	}

	// Compute approx solution x = ATA^-1 * A^T * b in two steps:
	// Step 1: first compute AT * b
	double[] ATb = 
	// Step 2: multiply the result on the left by ATA^-1
	double[] xhat = 

	// xhat[0] = m (slope)
	// xhat[1] = c (y-intercept)
	System.out.println ("xhat[0]=" + xhat[0] + " xhat[1]=" + xhat[1]);

	// Draw the line. Here drawLineFromEquation() expects the
	// line specified in ax+by+c format. To convert from y=mx+c,
	// observe that a=m, b=-1, c=c.
	DrawTool.setEquationLineColor ("blue");
	DrawTool.drawLineFromEquation (xhat[0], -1, xhat[1]);
	*/
    }

}