/*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;