Re: OT: finding the weights used in weighted least squares regression

[Kamaraju S Kusumanchi]

Ben Abbott wrote:
> 
> If I understand what you'd like to do, I think the solution is ...
> 
> W = (A*(A\b)-b) ./ (A*x-b)
> 

No. This is not the solution. Consider the following example

octave:10> n=5, m=2, W = diag(rand(n,1)), A = rand(n,m), b = rand(n,1), x = 
(W*A) \ (W*b), (A*(A\b)-b) ./ (A*x-b)
n =  5
m =  2
W =

   0.63718   0.00000   0.00000   0.00000   0.00000
   0.00000   0.75466   0.00000   0.00000   0.00000
   0.00000   0.00000   0.69982   0.00000   0.00000
   0.00000   0.00000   0.00000   0.08992   0.00000
   0.00000   0.00000   0.00000   0.00000   0.94621

A =

   0.833095   0.568790
   0.792483   0.536521
   0.702069   0.588282
   0.036704   0.529085
   0.238762   0.427252

b =

   0.86356
   0.77943
   0.77652
   0.98000
   0.49344

x =

   0.32941
   0.97441

ans =

     2.07510
    -7.79993
     2.55568
     0.23533
   112.87186


Hence W is not same as (A*(A\b)-b) ./ (A*x-b) .

thanks
-- 
Kamaraju S Kusumanchi
http://malayamaarutham.blogspot.com/