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,suppose the builder wants to test whether the coefficient on Income is significantly different from 0.What is the value of the relevant t-statistic?
A)-0.7630
B)3.2708
C)10.8668
D)60.0864

Question

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,suppose the builder wants to test whether the coefficient on Income is significantly different from 0.What is the value of the relevant t-statistic?
A)-0.7630 
B)3.2708 
C)10.8668 
D)60.0864

Quizplus · Accepted Answer

To test whether the coefficient on Income is significantly different from 0, we need to calculate the t-statistic, which is given by: 
t = b1 / (SEb1), where b1 is the coefficient on Income and SEb1 is its standard error.

From the output, we can see that the coefficient on Income is 2.2486 and its standard error is 0.6559. Therefore, 
t = 2.2486 / 0.6559 = 3.4275

The builder can reference Appendix Table 2 and find that a t-distribution with 47 degrees of freedom gives a critical value at the 5% level of significance of 2.013. Since our calculated t-statistic (3.4275) is greater than the critical value at the 5% level of significance, we can reject the null hypothesis that the coefficient on Income is equal to 0.

Thus, the value of the relevant t-statistic is 3.4275, which is closest to Option C (10.8668) after rounding it to four decimal places.

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