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Hello there, I have a issue in building the Weighted Matrix for my next system of equations:

2x+y=2

-x+3y=1

x+2y=3

A=2 1 b=2

-1 3 1

1 2 3

And I can solve this by means of OLS But my means of WLS I have this formulas from a book:

b=Ax+e

e=b-Ax

C=e*e' % (covariance_matrix)

W=C^-1 % (weight matrix)

But the thing is det(C)=0 and and thus, the inverse it does not exist and I don't think the last 2 formulas for C and W are correct. Can someone explain to me step by step how to build the Weight Matrix just having the matrix A and b? I know this my be too simple but I need a little bit of guidance.

Thank you in advance

*NOTE: 1). I have read the theory regarding WLS and its rational approach. But I understand faster with a practical example, step by step.

2). I would like not to use any matlab-built in functions (for the sake of learning).

Wenwen He
on 8 Aug 2016

Hello,have you solved this question?

Wenwen He
on 8 Aug 2016

mahmood hassan
on 10 Nov 2018

Edited: mahmood hassan
on 10 Nov 2018

Hi, According to Wikipedia the Weighted least squares (WLS), is a generalization of ordinary least squares and linear regression in which the errors covariance matrix is allowed to be different to an identity matrix. WLS is also a specialization of generalized least squares in which the above matrix is diagonal. https://en.wikipedia.org/wiki/Weighted_least_squares

if you use this it will not goes to the singularity

- b=Ax+e
- e=b-Ax
- C=diag(e*e') % (covariance_matrix)
- W=diag(C)^-1 % (weight matrix)

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