Chapter 16.2, Problem 10E

In a regression analysis involving 27 observations, the following estimated regression equation was developed.

$\hat{y}=25.2+5.5x_1$

For this estimated regression equation SST = 1550 and SSE = 520.

a. At α = .05, test whether x₁ is significant.

Suppose that variables x₂ and x₃ are added to the model and the following regression equation is obtained.

$\hat{y}=16.3+2.3x_1+12.1x_2-5.8x_3$

For this estimated regression equation SST = 1550 and SSE = 100.

b. Use an F test and a .05 level of significance to determine whether x₂ and x₃ together contribute significantly to the model.