Exercise 2.10.3 Consider the model yi = 1xi1 +2xi2 +ei, eis i.i.d. N(0, 2). Use the data

Exercise 2.10.3 Consider the model yi = β1xi1 +β2xi2 +ei, eis i.i.d. N(0,σ 2).

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 σ 2.

(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