Suppose that the regression model is y , where has a zero mean, constant variance, and equal correlation, , across observations Then Cov i , j 2 if i j Prove that the least squares estimator of is inconsistent Find the characteristic roots of and show that Condition 2 after Theorem 9 2 is violated ...

The covariance matrix is The matrix X is a column of 1s so the least squares est ...

Suppose that the regression model is y = + , where has a zero mean,

Question:

Suppose that the regression model is y = μ + ε, where ε has a zero mean, constant variance, and equal correlation, ρ, across observations. Then Cov[ε_i, ε_j] = σ²ρ if i = j. Prove that the least squares estimator of μ is inconsistent. Find the characteristic roots of and show that Condition 2 after Theorem 9.2 is violated.