Take the linear model Y=X*beta+e, where e~Nn(0, sigma^2 * I), and it has MLE beta.hat(adsbygoogle = window.adsbygoogle || []).push({});

First, find the distribution of (beta.hat-beta)' * X'*X * (beta.hat-beta), where t' is t transpose. I think I've done this. I think it's a sigma^2 chi-squared (n-p) distribution.

Next, Hence find a (1-a)-level confidence set for beta based on a root with an F distribution. I can't do this to save my life. I'm aware that an F distribution is the ratio of two chi-squareds, but where the hell I'm going to get another chi squared from I have no idea. Also, we're dealing in -vectors- and I don't know how,what,why any confidence set is going to be or even look like, and I've no idea how to even try to get one.

-Any- help would be appreciated. Thanks

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# A hideous Linear Regression/confidence set question

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