/*Extended Yet Another Curve Fitting Solution (The poor man's RMA)

   An extension of yacfs.mod adding a Weight parameter:

     When set to 1 the model produces best fit by least squares with all error in y and none in x (YonX);

     When set to zero the model produces best fit by least squares with all error in x and none in y (XonY);

     When set to 0.5 the model assumes equal error in x and y producing results similar to fitting by Reduced Major Axis Analysis.

   Nigel_Galloway@operamail.com

   November 5th., 2009

 */

 set Sample;

 param Sx {z in Sample};

 param Sy {z in Sample};

 param Weight := 0.5;

 var a;

 var b;

 var p;

 var q;

 XonY1 :sum{z in Sample} q*Sy[z]*Sy[z] + sum{z in Sample} p*Sy[z] = sum{z in Sample} Sy[z]*Sx[z];

 XonY2 :sum{z in Sample} q*Sy[z] + sum{z in Sample} p = sum{z in Sample} Sx[z];

 YonX1 :sum{z in Sample} a*Sx[z]*Sx[z] + sum{z in Sample} b*Sx[z] = sum{z in Sample} Sy[z]*Sx[z];

 YonX2 :sum{z in Sample} a*Sx[z] + sum{z in Sample} b = sum{z in Sample} Sy[z];

 solve;

 param W := Weight*a + (1-Weight)*(1/q);

 printf "\nbest linear fit is:\n\ty = %f %s %fx\n\n", b*Weight - (1-Weight)*(p/q), if W < 0 then "-" else "+", abs(W);

 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;