Multiple regression - Variance covariance matrix

emcos

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Jul 31, 2014
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I need to prove this result and I have no idea how! If anyone can help I would be really appreciative!
Thanks!

The variance-covariance matrix βhat is given by var(βhat) = (X Σ-1 X)-1. Prove this result.
Hint: Note that βhat = (X' Σhat-1 X )-1 X' Σhat-1y = Ay i.e a linear transformation of y, and that in general var(Ay) = AΣA’ where Σ = var(y).
 
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