**Unformatted text preview: **y = β + β 1 x 1 + β 2 x 2 + ϵ , ϵ ∼ i.i.d. N (0 , σ 2 ) for the following data. y 1 5 4 4-1 x 1 1 2 1 3 3 3 x 2 1 1 2 1 2 3 (a) (10 points) Estimate β , β 1 , β 2 and σ 2 . (b) (5 points) Obtain 95% confidence interval of the mean response at x 1 = x 2 = 2. (c) (15 points) Obtain 99% confidence interval of β 1 − β 2 . (d) (5 points) Test H : β 1 = 0, H a : β 1 ̸ = 0 using α = 0 . 05. (e) (15 points) Test H : β 1 = 2 β 2 , H a : β 1 ̸ = 2 β 2 using α = 0 . 05. 2...

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- Fall '19