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.
Which of the following three models would you choose to make the predictions of the remaining loan balance?

Question

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.
Which of the following three models would you choose to make the predictions of the remaining loan balance?

Quizplus · Accepted Answer

Model C is the best choice because it includes both the dummy variable for prime loans and the interaction between time and prime loans. This allows us to account for the different effects of prime and subprime loans on the remaining balance over time. Model A only includes the dummy variable for prime loans, while Model B includes both variables and interaction but also includes an extraneous variable that does not significantly contribute to the model (time). Therefore, Model C is the most parsimonious and appropriate model.

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