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I have the following matrices: $$ X'X $$ $$X'y$$$$ y'y $$

I know that the B matrix can be computed as follows : $$ B = (X'X)^{-1}X'y $$

If I want to perform a t test for a specific B, say $$B_{1}$$, I know that I must follow the formula : $$ t = \frac{B_{1} - B_{0}}{se(B_{1})} $$

However, if I only have the 3 aforementioned matrices, how can I compute the standard error of a given B?

1 Answers1

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If $\epsilon$ designate your residuals, estimator variance matrix is given by $Var(\hat{\beta}) = \sigma^2(X'X)^{-1}, \sigma^2 = Var(\epsilon)$ in my class notes but I can't demonstrate it so can't be a 100% sure.

EDIT : this thread gives (and proves) $Var(\beta_1) = \frac{\sigma^2}{\sum\limits_i (x_i - \bar{x})^2}$ so I guess my notes are still good enough :)

Riff
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