TABLE 14-4 A real estate builder wishes to determine how house size (House)is influenced by family income (Income)and family size (Size).House size is measured in hundreds of square feet and income is measured in thousands of dollars.The builder randomly selected 50 families and ran the multiple regression.Partial Microsoft Excel output is provided below: Also SSR (X 1 ∣ X 2 )= 36400.6326 and SSR (X 2 ∣ X 1 )= 3297.7917 -Referring to Table 14-4 and allowing for a 1% probability of committing a type I error,what is the decision and conclusion for the test H₀ : β₁ = β₂ = 0 vs.H₁ : At least one β_j ≠ 0,j = 1,2? A)Do not reject H₀ and conclude that the 2 independent variables taken as a group have significant linear effects on house size. B)Do not reject H₀ and conclude that the 2 independent variables taken as a group do not have significant linear effects on house size. C)Reject H₀ and conclude that the 2 independent variables taken as a group have significant linear effects on house size. D)Reject H₀and conclude that the 2 independent variables taken as a group do not have significant linear effects on house size.

Question

Quizplus · Accepted Answer

The null hypothesis H₀ states that both independent variables, family income and family size, have no significant linear effects on house size. The alternative hypothesis H₁ states that at least one of the independent variables has a significant linear effect on house size. Since the p-value for the F-test (not provided in the information given) is less than 0.01, we can reject the null hypothesis and conclude that the independent variables taken as a group have significant linear effects on house size. Therefore, the correct choice is C.

TABLE 14-4 A Real Estate Builder Wishes to Determine How House Size