Consider a linear regression model Y = Xβ + ε, with r regressors and an intercept, where X has full column rank and ε ~ Nn(0, σ2In). Let σ̂2 and σ̂2MLE respectively be the mean square error of residuals and the maximum likelihood estimator of σ2. Which of the following statements is true?

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Mathematics · Probability and Statistics

Verified Solution4 OptionsUpdated: October 2026👁️1 View

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Correct answer

Var(σ̂2MLE) < Var(σ̂2) if 1 ≤ r ≤ n - 2, n ≥ 3

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Answer 1

MSE(σ̂2MLE) > MSE(σ̂2) if r = 7, n = 12

Answer 2

Var(σ̂2MLE) < Var(σ̂2) if 1 ≤ r ≤ n - 2, n ≥ 3

Answer 3

Var(σ̂2MLE) > Var(σ̂2) if 2 ≤ r ≤ n - 2, n ≥ 12

Answer 4

MSE(σ̂2MLE) > MSE(σ̂2) if r = 2, n = 12

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