I would like to estimate a multiple linear regression model $N$ observations (with $beta$ of length $k$):

$$Y = X beta + epsilon$$

subject, however, to some linear constraints on the coefficients. I.e a constraint of the form

$$M beta = 0$$

where (at least in my case) $M$ is of dimension $2 times k$ but more generally can be expressed as

$$M beta = c$$ where $M$ is of dimension $p times k$ with $p < N$ and $c$ of dimension $p times 1$.

I have not been able to find much about this online and would appreciate references to read up on this..

Thanks

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#### Best Answer

The slides from the website below give a very detailed procedure on how to transform your **equality constrained** least squares into simply an **unconstrained** least squares problem. It uses QR decomposition to split the normal equations into a part that depends on the constraints and another part that does not. I hope this proves useful!

The slides you're looking for are on 19,20 & 21.

See: http://folk.uio.no/inf9540/CLS.pdf (warning: .pdf)

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