/*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;