/*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;