I know how to find it for the regression slope, and also that $Var(Y_i)$ is $\sigma^2$, but what is $Var(\hat Y)$?
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5try writing $Var(\hat Y) = Var(X\hat \beta)$ and use what you know about $\hat \beta$. Does this help? – jld Jan 27 '17 at 16:47
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Add self study tag. – Michael R. Chernick Jan 27 '17 at 17:43
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Related: How are the standard errors of coefficients calculated in a regression? – Franck Dernoncourt Jan 28 '17 at 03:39