Author: Jonas Bilinkevicius

Least squares line fitting in Delphi

Answer:

Example that finds least squares fit for y = Mx + c
1   
2   procedure LeastSquares(X, Y: array of Extended; var M: Extended; var C: Extended);
3   var
4     SumX, SumY, SumX2, SumXY: Extended;
5     n, i: Integer;
6   begin
7     if High(X) <> High(Y) then
8       raise
9         Exception.Create('LeastSquares() Error - Input X & Y arrays must be
10  			 of the same length'
11    n := High(X) + 1;
12    SumX := 0.0;
13    SumY := 0.0;
14    SumX2 := 0.0;
15    SumXY := 0.0;
16    for i := 0 to n - 1 do
17    begin
18      SumX := SumX + X[i];
19      SumY := SumY + Y[i];
20      SumX2 := SumX2 + (X[i] * X[i]);
21      SumXY := SumXY + (X[i] * Y[i]);
22    end;
23    if (n * SumX2) = (SumX * SumX) then
24      raise Exception.Create('LeastSquares() Error - X Values cannot all be the 
25  same'
26    M := ((SumY * SumX2) - (SumX * SumXY)) / ((n * SumX2) - (SumX * SumX));
27    C := ((n * SumXY) - (SumX * SumY)) / ((n * SumX2) - (SumX * SumX));
28  end;