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

question 58

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.
Using Model B, what is the null hypothesis for testing the joint significance of the variable Time and the interaction variable Time × Prime?

• A) H₀: β₁ = β₂ = β₃ = 0
• B) H₀: β₁ = 0 and β₃ = 0
• C) H₀: β₁ = 0 or β₃ = 0
• D) H₀: β₁ ≠ 0 or β₃ ≠ 0

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