@Carl Love 

Thank you very much, works fine!

I checked the code for Dual in Maple18 and found:
 

proc(b) option
  option `Copyright (c) 1990 by the University of Waterloo. All rights reserved.`;
  local substitutions;
  substitutions := {'false' = 'true', 'true' = 'false', `&or` = `&and`, `&and` = `&or`, `&nor` = `&nand`, `&nand` = `&nor`, `&iff` = `&xor`, `&xor` = `&iff`, `&implies` = (x, y)->`&implies`(`&not`(x), `&not`(y))};
  eval(Sanitize(b), substitutions);
end proc;

Seems the error lies in the " `&implies` = (x, y)->`&implies`(`&not`(x), `&not`(y)) ", which should be " `&implies` = (x, y)->`&not`(`&implies`((y), (x))) "
 

Best regards,
  Anthei

@Carl Love 

I see.

Thanks again,

Anthei

@acer 

Thats strange, because Maple 18 gives same error.

@Carl Love 

Yes, that would be correct.

Thanks for your answer,

Anthei

@mmcdara 

Thanks for your answer!

Yes, that settles it for LinearFit() (w * residual^2).

Interestingly, I applied your script to NonlinearFit() and it seems to use the other weighing scheme (i.e. w^2 * residual^2);
That doesn't make sense to me.

Please find attached a modified version of your script.

Best regards,

 Anthrazius

Weighed_Least_Squares_2.mw