SCENARIO 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 1 | X 2 ) = 3297.7917
-Referring to Scenario 14-4,which of the following values for the level of significance is the smallest for which at least one explanatory variable is significant individually?
A)0.005
B)0.010
C)0.025
D)0.050

Question

SCENARIO 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 1 | X 2 ) = 3297.7917
-Referring to Scenario 14-4,which of the following values for the level of significance is the smallest for which at least one explanatory variable is significant individually?
A)0.005 
B)0.010 
C)0.025 
D)0.050

Quizplus · Accepted Answer

To determine the smallest level of significance at which at least one explanatory variable is significant individually, we need to look at the p-values for the coefficients of Income and Size. From the output, we can see that the p-value for the coefficient of Income is 0.071 (<0.1) and the p-value for Size is 0.000 (<0.1). This indicates that Size is significant individually, but Income is not significant individually at the 0.10 level of significance.

To determine the smallest level of significance at which at least one explanatory variable is significant individually, we need to keep decreasing the level of significance until we find a level at which at least one p-value for the coefficients of Income or Size is less than the level of significance. Going from the highest level of significance (0.10) to the lowest, we find that at the 0.005 level of significance, the p-value for Size is still less than the level of significance (0.000 < 0.005), indicating that Size is significant individually. Therefore, the smallest level of significance for which at least one explanatory variable is significant individually is 0.005. Thus, the answer is A) 0.005.

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