Centre of the Universe

When analysing data it is often useful to find an equation to show the relationship in a certain set of data. The linear least squares fit tries to do exactly that.

Given a set of data points, it tries to find a straight line with the equation y = Mx + B which best fits the data, using the least squares technique, which works out the squares of the deviations of each point and then tries to minimize those.

		public static void LeastSquaresFitLinear(Pnt[] points, int numPoints, ref double M, ref double B)
		{
			//Gives best fit of data to line Y = MC + B
			double x1, y1, xy, x2, J;
			int i;

			x1 = 0.0;
			y1 = 0.0;
			xy = 0.0;
			x2 = 0.0;

			for (i = 0; i < numPoints; i++)
			{
				x1 = x1 + points[i].X;
				y1 = y1 + points[i].Y;
				xy = xy + points[i].X * points[i].Y;
				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;
			}
		}

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