312.final.2004 - Stat312 Final Exam Solutions Moo K Chung...

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Stat312: Final Exam SolutionsMoo K. Chung[email protected]December 17, 20041. We wish to fit data(x1, y1),· · ·,(xn, yn)with linear modelYj= 1 +βxj+²jwith²jN(0, σ2). Deriveeverything.(a) Find the maximum likelihood estimator forβ(10pts).(b) Estimateβby the least squares method (10pts).(c) Determine the distribution of the estimator given in (b) (10pts).

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