We use the OLS estimator in the usual regression model, and the unbiased estimator of variance

Question:

We use the OLS estimator βˆ in the usual regression model, and the unbiased estimator of variance σˆ 2. Which of the following statements are true, and why?

(i) cov(β) = σ2(X

X)−1.

(ii) cov(β)ˆ = σ2(X

X)−1.

(iii) cov(βˆ|X) = σ2(X

X)−1.

(iv) cov(βˆ|X) = ˆσ2(X
X)−1.
(v) cov (βˆ|X) = ˆσ2(X
X)−1.

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