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/*Quadratic Curve Fitting Solution
Find a plausable quadratic fit to a sample of points
Nigel_Galloway@operamail.com
February 1st., 2009
*/
set Sample;
param Sx {z in Sample};
param Sy {z in Sample};
var a;
var b;
var c;
equalz1 :sum{z in Sample} a*Sx[z]*Sx[z]*Sx[z]*Sx[z] + sum{z in Sample} b*Sx[z]*Sx[z]*Sx[z] + sum{z in Sample} c*Sx[z]*Sx[z] = sum{z in Sample} Sy[z]*Sx[z]*Sx[z];
equalz2 :sum{z in Sample} a*Sx[z]*Sx[z]*Sx[z] + sum{z in Sample} b*Sx[z]*Sx[z] + sum{z in Sample} c*Sx[z] = sum{z in Sample} Sy[z]*Sx[z];
equalz3 :sum{z in Sample} a*Sx[z]*Sx[z] + sum{z in Sample} b*Sx[z] + sum{z in Sample} c = sum{z in Sample} Sy[z];
solve;
printf "\nbest quadratic fit is:\n\ty = %f %s %fx %s %fx^2\n\n", c, if b < 0 then "-" else "+", abs(b), if a < 0 then "-" else "+", abs(a);
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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