1. (a) Suppose we have the simple linear model Yi = Bo + B1x; + ei, i = 1, ...,n, E[e;] = 0, var(e;) = o², cov(e;, e;) = 0, i + j. Write down the model using suitable matrix notation, and provide a condition for both Bo and B, to be linearly estimable. (b) Show that the least squares estimate of 31 under the model when B, = 0 is known sgven by β - Ση/ ΣL ή (c) Find the bias of Bị when in fact B, # 0. (d) Derive expressions for the variance of Bi and the variance of the least squares estimate B1 obtained when 3o is not known. Comment on which estimator has the smallest variance, whether or not this contradicts the Gauss-Markov Theorem.

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