observations we have x1,12 x2,12 5 −2 = . x1,13 x2,13 3 −7 Answer Some preliminary algebra: x1 x1 x1 x2 XX= = x2 x1 x2 x2 Therefore (X X )−1 = β1 β2 1 3 2 1 1 2 2 −1 −1 2 1 3 . . 1 1 = 1 3 1 3 = (X X )−1 X y = 2 −1 −1 2 . Question 1 (cont) Answer y MX y y y − y X (X X )−1 X y εε ˆˆ = = 11 − 2 9 9 2 −1 1 4 1 1 1 3 − 3 −1 2 1 9 4−2 3 s2 = = 2 = = 9 27 We’ll start with (b), and then do (a), because (a) builds on (b). Question 1 (b) Answer (b) Want to find 80% prediction…
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