A researcher wants to examine how the remaining balance on $100,000 loans taken 10 to 20 years ago depends on whether the loan was a prime or subprime loan. He collected a sample of 25 prime loans and 25 subprime loans and recorded the data in the following variables:Balance = the remaining amount of loan to be paid off (in $),Time = the time elapsed from taking the loan,Prime = a dummy variable assuming 1 for prime loans, and 0 for subprime loans.The regression results obtained for the models:Model A: Balance = ?0 + ?1Prime + ?Model B: Balance = ?0 + ?1Time + ?2Prime + ?3Time × Prime + ?Model C: Balance = ?0 + ?1Prime + ?2Time × Prime + ?,are summarized in the following table.VariableModel AModel BModel CIntercept88,020 (t = 77.89)90,269
(t = 24.35)88,020 (t = 81.19)TimeN/A?148 (t = ?0.64)N/APrime?18,000 (t = ?11.26)-28,493 (t = ?5.36)?26,244 (t = ?6.66)Time × PrimeN/A662 (t = 2.03)514 (t = 2.27) SSE1,532,480,0001,369,126,0911,381,128,299R20.72540.75470.7526Adjusted R20.71980.73880.7421Note: The values of relevant test statistics are shown in parentheses below the estimated coefficients.Suppose that at the 5% significance level you do not reject the null hypothesis, H0: ?1 = ?3 = 0, when testing the joint significance of Time and Time × Prime in Model B. Should you delete both Time and Time × Prime from Model B?
A. No, because Model B reduces then to Model A with a lower adjusted R2.
B. No, because Model B has the highest R2.
C. No, because Model B reduces than to Model A with lower R2.
D. Yes, because Model B reduces than to Model C with higher adjusted R2.
Answer: A
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