1 /*Curve fitting problem by Least Squares

2 Nigel_Galloway@operamail.com

3 October 1st., 2007

4 */

5 set Sample;

6 param Sx {z in Sample};

7 param Sy {z in Sample};

8

9 var X;

10 var Y;

11 var Ex{z in Sample};

12 var Ey{z in Sample};

13

14 /* sum of variances is zero for Sx*/

15 variencesX{z in Sample}: X + Ex[z] = Sx[z];

16 zumVariancesX: sum{z in Sample} Ex[z] = 0;

17 /* sum of variances is zero for Sy*/

18 variencesY{z in Sample}: Y + Ey[z] = Sy[z];

19 zumVariancesY: sum{z in Sample} Ey[z] = 0;

20

21 solve;

22

23 param b1 := (sum{z in Sample} Ex[z]*Ey[z])/(sum{z in Sample} Ex[z]*Ex[z]);

24 printf "\nbest linear fit is:\n\ty = %f %s %fx\n\n", Y-b1*X, if b1 < 0 then "-" else "+", abs(b1);

25

26 data;

27

28 param:

29 Sample: Sx Sy :=

30 1 0 1

31 2 0.5 0.9

32 3 1 0.7

33 4 1.5 1.5

34 5 1.9 2

35 6 2.5 2.4

36 7 3 3.2

37 8 3.5 2

38 9 4 2.7

39 10 4.5 3.5

40 11 5 1

41 12 5.5 4

42 13 6 3.6

43 14 6.6 2.7

44 15 7 5.7

45 16 7.6 4.6

46 17 8.5 6

47 18 9 6.8

48 19 10 7.3

49 ;

50

51 end;