Question

A real estate analyst estimates the following regression, relating a house price to its square footage (Sqft):

PriceˆPrice^ = 48.36 + 52.50Sqft; SSE = 56,018; n = 50

In an attempt to improve the results, he adds two more explanatory variables: the number of bedrooms (Beds) and the number of bathrooms (Baths). The estimated regression equation is

PriceˆPrice^ = 28.71 + 40.44Sqft + 10.58Beds + 16.44Baths; SSE = 48,937; n = 50

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

a. Choose the appropriate hypotheses to determine whether Beds and Baths are jointly significant in explaining Price.

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

• 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.

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.

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

• p-value < 0.01

• p-value0.10
• 0.05p-value < 0.10

c. At the 5% significance level, what is the conclusion to the test?

• Reject H₀Beds and Baths are jointly significant in explaining Price.
• Reject H₀Sqft Beds and Baths are jointly significant in explaining Price.
• Do not reject H₀ SqftBeds and Baths are not jointly significant in explaining Price.
• Do not reject H₀Beds and Baths are not jointly significant in explaining Price.

Answer 1