Question: Problem 1 [26 points]: Consider simple linear regression y, : u + Ax, + 6,, with E(e,) =0 and Var(e,-) = 02 for i =

Problem 1 [26 points]: Consider simple linear regression y, : u + Ax, + 6,, with E(e,) =0 and Var(e,-) = 02 for i = 1, 2, ..., n. (a) [10 points] Based on matrix operations, simplify the Hat Matrix H : X(X' X)_1X' and show that 1 (1670(36- J_C) ' h..:+; ' '= I, n SXX for 1,} 1, 2, ..., n (b) [6 points] Based the fact that 02 +62 2 72a!) for any values a and b, show that p11, .,. ,-,-_n 2 or: )

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