Exercise 2.11.4 Consider themodel yi = 1xi1 + 2xi2 + ei , ei s i.i.d. N(0, 2). There are 15 observations and the sum of

Exercise 2.11.4 Consider themodel yi = β1xi1 + β2xi2 + ei , ei s i.i.d. N(0, σ2).

There are 15 observations and the sum of the squared observations is Y Y = 3.03.

Use the normal equations given below to answer parts

(a) through (c).

(a) Estimate β1, β2, and σ2.

(b) Give 98% confidence intervals for β2 and β2 − β1.

(c) Perform an α = 0.05 test for H0 : β1 = 0.5.

The normal equations are



15.00 374.50 374.50 9482.75



β1

β2

=



6.03 158.25

.