/*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;