Exercise 2.11.3 Consider themodel yi = 1xi1 + 2xi2 + ei , ei s i.i.d. N(0, 2).

Exercise 2.11.3 Consider themodel yi = β1xi1 + β2xi2 + ei , ei s i.i.d. N(0, σ2).

Use the data given below to answer

(a) through (d). Show your work, i.e., do not use a regression or general linear models computer program.

(a) Estimate β1, β2, and σ2.

(b) Give 95% confidence intervals for β1 and β1 + β2.

(c) Perform an α = 0.01 test for H0 : β2 = 3.

(d) Find an appropriate P value for the test of H0 : β1 − β2 = 0.
obs. 1 2 3 4 5 6 7 8 y 82 79 74 83 80 81 84 81 x1 10 9 9 11 11 10 10 12 x2 15 14 13 15 14 14 16 13