A Researcher Wants to Examine How the Remaining Balance on $100,000

Multiple Choice

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 = β₀ + β₁Prime + ε
Model B: Balance = β₀ + β₁Time + β₂Prime + β₃Time × Prime + ε
Model C: Balance = β₀ + β₁Prime + β₂Time × Prime + ε,
Are summarized in the following table. Note: 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: β₁ = β₃ = 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 has the highest R².
B) No, because Model B reduces then to Model A with a lower adjusted 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.