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Re: OT: finding the weights used in weighted least squares regression
From: |
Kamaraju S Kusumanchi |
Subject: |
Re: OT: finding the weights used in weighted least squares regression |
Date: |
Wed, 27 Apr 2011 08:09:03 -0400 |
User-agent: |
KNode/4.4.7 |
James Sherman Jr. wrote:
> This seems like an ill-posed problem to me. (or in other words the answer
> is no, you can't solve for W or at least not a specific W).
>
I think so too! But I just wanted to make sure if I am missing something.
> 2) Ax ~=b, then if you want to solve for a W such that WAx = Wb, equates
> to W(Ax-b) = 0, which is to say that as long as Ax-b is in the null space
> of W (or that Ax-b is an eigenvector with eigenvalue 0) you are free to
> choose
> any W that satisfies this condition. This is in essence a linear system
> with n^2 unknowns (size of W) with only n equations.
FWIW, W is a diagonal matrix. So there are only n unknowns, not n^2.
Also when A is a long thin matrix and when the system is solved by least
squares, W(Ax-b) is not exactly zero. There is always a residual.
In other words, W(Ax-b) ~= 0.
thanks
--
Kamaraju S Kusumanchi
http://malayamaarutham.blogspot.com/
- OT: finding the weights used in weighted least squares regression, Kamaraju S Kusumanchi, 2011/04/26
- Re: OT: finding the weights used in weighted least squares regression, Ben Abbott, 2011/04/26
- Re: OT: finding the weights used in weighted least squares regression, Kamaraju S Kusumanchi, 2011/04/27
- Re: OT: finding the weights used in weighted least squares regression, James Sherman Jr., 2011/04/27
- Re: OT: finding the weights used in weighted least squares regression,
Kamaraju S Kusumanchi <=
- Re: OT: finding the weights used in weighted least squares regression, Ben Abbott, 2011/04/27
- Re: OT: finding the weights used in weighted least squares regression, Kamaraju S Kusumanchi, 2011/04/27
- Re: OT: finding the weights used in weighted least squares regression, Ben Abbott, 2011/04/27
- Re: OT: finding the weights used in weighted least squares regression, Kamaraju S Kusumanchi, 2011/04/27
- Re: OT: finding the weights used in weighted least squares regression, Mike Miller, 2011/04/28