1 /*Extended Yet Another Curve Fitting Solution (The poor man's RMA)

2

3 An extension of yacfs.mod adding a Weight parameter:

4 When set to 1 the model produces best fit by least squares with all error in y and none in x (YonX);

5 When set to zero the model produces best fit by least squares with all error in x and none in y (XonY);

6 When set to 0.5 the model assumes equal error in x and y producing results similar to fitting by Reduced Major Axis Analysis.

7

8 Nigel_Galloway@operamail.com

9 November 5th., 2009

10 */

11 set Sample;

12 param Sx {z in Sample};

13 param Sy {z in Sample};

14 param Weight := 0.5;

15

16 var a;

17 var b;

18 var p;

19 var q;

20

21 XonY1 :sum{z in Sample} q*Sy[z]*Sy[z] + sum{z in Sample} p*Sy[z] = sum{z in Sample} Sy[z]*Sx[z];

22 XonY2 :sum{z in Sample} q*Sy[z] + sum{z in Sample} p = sum{z in Sample} Sx[z];

23 YonX1 :sum{z in Sample} a*Sx[z]*Sx[z] + sum{z in Sample} b*Sx[z] = sum{z in Sample} Sy[z]*Sx[z];

24 YonX2 :sum{z in Sample} a*Sx[z] + sum{z in Sample} b = sum{z in Sample} Sy[z];

25

26 solve;

27

28 param W := Weight*a + (1-Weight)*(1/q);

29 printf "\nbest linear fit is:\n\ty = %f %s %fx\n\n", b*Weight - (1-Weight)*(p/q), if W < 0 then "-" else "+", abs(W);

30

31 data;

32

33 param:

34 Sample: Sx Sy :=

35 1 0 1

36 2 0.5 0.9

37 3 1 0.7

38 4 1.5 1.5

39 5 1.9 2

40 6 2.5 2.4

41 7 3 3.2

42 8 3.5 2

43 9 4 2.7

44 10 4.5 3.5

45 11 5 1

46 12 5.5 4

47 13 6 3.6

48 14 6.6 2.7

49 15 7 5.7

50 16 7.6 4.6

51 17 8.5 6

52 18 9 6.8

53 19 10 7.3

54 ;

55

56 end;