We have already looked at the linear least squares fit, but that does not always produces a nice fit to the data. The least squares fit with a log ordinate tries to match up the data to the equation y = B * 10Mx using the least squares method.
In the code below, if there is no solution, the function returns M and B as 0.
public static void LeastSquaresFitLogOrdinate(Pnt[] points, int numPoints, ref double M, ref double B) { //Gives best fit of data to curve Y = B*(10^M)^X double x1, y1, xy, x2, J, LY; int i; x1 = 0.0; y1 = 0.0; xy = 0.0; x2 = 0.0; for (i = 0; i < numPoints; i++) { LY = Math.Log10(points[i].Y); x1 = x1 + points[i].X; y1 = y1 + LY; xy = xy + points[i].X * LY; x2 = x2 + points[i].X * points[i].X; } J = ((double)numPoints * x2) - (x1 * x1); if (J != 0.0) { M = (((double)numPoints * xy) - (x1 * y1)) / J; M = Math.Floor(1.0E3 * M + 0.5) / 1.0E3; B = ((y1 * x2) - (x1 * xy)) / J; B = Math.Floor(1.0E3 * B + 0.5) / 1.0E3; } else { M = 0; B = 0; } }
Comments