Question

Consider a portion of simple linear regression results,

y^ = 104.93 + 24.73x₁; SSE = 407,297; n = 30

In an attempt to improve the results, two explanatory variables are added. The relevant regression results are the following:

y^ = 4.80 + 19.21x₁ – 25.62x₂ + 6.64x₃; SSE = 344,717; n = 30.

[You may find it useful to reference the F table.]

a. Formulate the hypotheses to determine whether x₂ and x₃ are jointly significant in explaining y.

• H₀: β₂ = β₃ = 0; H_A: At least one of the coefficients is nonzero.

• H₀: β₁ = β₂ = β₃ = 0; H_A: At least one of the coefficients is nonzero.

• H₀: β₂ = β₃ = 0; H_A: At least one of the coefficients is greater than zero.

b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

b-2. Find the p-value.

• p-value 0.10
• 0.05 p-value < 0.10
• 0.025 p-value < 0.05
• 0.01 p-value < 0.025

• p-value < 0.01

c. At the 1% significance level, What is the conclusion to the test?

Answer 1

a)

H₀: β₂ = β₃ = 0; H_A: At least one of the coefficients is nonzero.

b-1)

sample size n=			30
SSE for complete model :SSEc =			344717
SSE for reduced model :SSER =			407297
c =coefficients in complete model =			3
r =coefficient in reduced model =			1
Partial F=((SSEr-SSEc)/(c-r))/(SSEc/(n-c-1)) =					2.360

b-2)

p-value > 0.10

c) fail to reject Ho

we cannot conclude that  At least one of the coefficients is nonzero.