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Assume linear model y=Xβ+ε Assume cov(ε)=σ2I (I is the identity matrix) Show that cov(β-hat) = σ2(XTX)-1...

Assume linear model y=Xβ+ε

Assume cov(ε)=σ2I (I is the identity matrix)

Show that cov(β-hat) = σ2(XTX)-1 and discuss its meaning

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Answer #1

This is var cov matrix of estimated beta coefficients.

First we find the inverse of (x'x) matrix then multiply by sigma square will give the variances and covariance of beta hat.

Off diagonal elements will give covariance and diagonal elements will give variance

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