(a) It was stated that the LOOCV estimator \(\mathrm{CV}_{(n)}\) may have large variance "because the individual terms have positive covariances".

Why do they have positive covariances and why does that cause the variance of \(\mathrm{CV}_{(n)}\) to be large?

(b) It was stated that in \(k\)-fold cross-validation estimation of the MSE, "as \(k\) increases (approaching LOOCV), the bias of the MSE estimator decreases, but the variance of the MSE estimator increases."

Explain why this is the case.

(c) Explain why the cross-validated estimated MSE, \(\mathrm{CV}_{(k)}\) is in general larger that the estimated variance (even if the estimator is unbiased.)

Relate your explanation specifically to a regression model in which the fitted "Residual standard error" is 0.03249, yet the square root of the cross-validated estimated MSE is 0.03331.