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/*Curve fitting problem by Least Squares
Nigel_Galloway@operamail.com
October 1st., 2007
*/
set Sample;
param Sx {z in Sample};
param Sy {z in Sample};
var X;
var Y;
var Ex{z in Sample};
var Ey{z in Sample};
/* sum of variances is zero for Sx*/
variencesX{z in Sample}: X + Ex[z] = Sx[z];
zumVariancesX: sum{z in Sample} Ex[z] = 0;
/* sum of variances is zero for Sy*/
variencesY{z in Sample}: Y + Ey[z] = Sy[z];
zumVariancesY: sum{z in Sample} Ey[z] = 0;
solve;
param b1 := (sum{z in Sample} Ex[z]*Ey[z])/(sum{z in Sample} Ex[z]*Ex[z]);
printf "\nbest linear fit is:\n\ty = %f %s %fx\n\n", Y-b1*X, if b1 < 0 then "-" else "+", abs(b1);
data;
param:
Sample: Sx Sy :=
1 0 1
2 0.5 0.9
3 1 0.7
4 1.5 1.5
5 1.9 2
6 2.5 2.4
7 3 3.2
8 3.5 2
9 4 2.7
10 4.5 3.5
11 5 1
12 5.5 4
13 6 3.6
14 6.6 2.7
15 7 5.7
16 7.6 4.6
17 8.5 6
18 9 6.8
19 10 7.3
;
end;
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