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 a 10% significance level, you do not reject the null hypothesis, H₀: β₁ = 0, when testing the individual significance of Time in Model B. Would you delete Time from Model B?

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.
Suppose that at a 10% significance level, you do not reject the null hypothesis, H₀: β₁ = 0, when testing the individual significance of Time in Model B. Would you delete Time from Model B?

Quizplus · Accepted Answer

The fact that the coefficient on Time is not statistically significant does not necessarily mean that it should be removed from the model. However, Model C, which includes the interaction term between Time and Prime, has a higher adjusted R-squared than Model B, indicating that it explains more of the variation in the data while still avoiding overfitting. Therefore, removing Time from Model B and using Model C instead is a reasonable choice.

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