TABLE 13-10
You worked as an intern at We Always Win Car Insurance Company last summer. You noticed that individual car insurance premiums depend very much on the age of the individual, the number of traffic tickets received by the individual, and the population density of the city in which the individual lives. You performed a regression analysis in Microsoft Excel and obtained the following information:

-An interaction term in a multiple regression model may be used when
A) the coefficient of determination is small.
B) there is a curvilinear relationship between the dependent and independent variables.
C) neither one of two independent variables contribute significantly to the regression model.
D) the relationship between X₁ and Y changes for differing values of X₂.

Question

TABLE 13-10
You worked as an intern at We Always Win Car Insurance Company last summer. You noticed that individual car insurance premiums depend very much on the age of the individual, the number of traffic tickets received by the individual, and the population density of the city in which the individual lives. You performed a regression analysis in Microsoft Excel and obtained the following information:
 
-An interaction term in a multiple regression model may be used when
A) the coefficient of determination is small. 
B) there is a curvilinear relationship between the dependent and independent variables. 
C) neither one of two independent variables contribute significantly to the regression model. 
D) the relationship between X₁ and Y changes for differing values of X₂.

Quizplus · Accepted Answer

The purpose of an interaction term is to capture the effect of the interaction between two independent variables on the dependent variable. This is useful when the relationship between one independent variable (X₁) and the dependent variable (Y) changes for differing values of another independent variable (X₂). Therefore, option D is the correct choice. Option A is incorrect because the coefficient of determination (R²) is a measure of how well the independent variables explain the variation in the dependent variable, and it does not determine whether an interaction term is necessary. Option B is incorrect because a curvilinear relationship between the dependent and independent variables may be captured through the addition of polynomial terms, not interaction terms. Option C is incorrect because it refers to a situation where neither independent variable is significant in the regression model, whereas an interaction term is only added when both independent variables have a significant effect.

TABLE 13-10 You Worked as an Intern at We Always Win Car