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

question 63

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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. 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 = β<sub>0</sub> + β<sub>1</sub>Prime + ε Model B: Balance = β<sub>0</sub> + β<sub>1</sub>Time + β<sub>2</sub>Prime + β<sub>3</sub>Time × Prime + ε Model C: Balance = β<sub>0</sub> + β<sub>1</sub>Prime + β<sub>2</sub>Time × 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, H<sub>0</sub>: β<sub>1</sub> = β<sub>3</sub> = 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 R<sup>2</sup>. B)  No, because Model B reduces then to Model A with a lower adjusted R<sup>2</sup>. C)  No, because Model B reduces than to Model A with lower R<sup>2</sup>. D)  Yes, because Model B reduces than to Model C with higher adjusted R<sup>2</sup>. 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?

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Functionalists

A perspective in psychology that focuses on how mental and behavioral processes function - how they enable the organism to adapt, survive, and flourish.

Specific Behaviors

Observable actions or reactions of an individual, often in response to external stimuli.

Adapt to Environment

The process by which organisms adjust to changes in their surroundings to survive and reproduce.

Psychoanalysis

A therapeutic approach founded by Sigmund Freud, focusing on unconscious processes as they are manifested in a person's present behavior.

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