Consider the simple regression y i = x i + i where E[ | x] =

Consider the simple regression y_i= βx_i+ ε_iwhere E[ε | x] = 0 and E[ε²| x] = σ²

a. What is the minimum mean squared error linear estimator of β?

b. For the estimator in part a, show that ratio of the mean squared error of β to that of the ordinary least squares estimator b is

τ is the square of the population analog to the ??t ratio?? for testing the hypothesis that β = 0, which is given in (5-11). How do you interpret the behavior of this ratio as τ ?????

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MSE [B] MSE [b] where t2: (1+7?)' [o?/x'x]