Society of Actuaries (SOA) PA Practice Exam

What does an interaction describe in statistical modeling?

1. A situation where two variables have an additive effect

2. A scenario where one variable affects another independently

3. A case where the effect of one variable depends on another variable's state

4. An overall correlation between multiple independent variables

The correct answer is: A case where the effect of one variable depends on another variable's state

The correct understanding of an interaction in statistical modeling is that it describes a situation where the effect of one variable on the outcome variable is dependent on the value of another variable. This means that the relationship between the independent variable and the dependent variable changes when another independent variable changes. For instance, consider a model assessing the impact of study hours and tutoring on students' test scores. If the effect of tutoring on test scores increases with more study hours, then there is an interaction between study hours and tutoring. Thus, an interaction indicates that the combined influence of the variables on the outcome is not simply additive; instead, it reveals a more complex relationship where the impact of one variable is modified by another. The other choices do not accurately capture this concept. The additive effect describes a straightforward cumulative impact without interaction, independent effects imply that the variables do not influence each other at all, and an overall correlation refers to relationships among multiple independent variables without demonstrating causality or dependency between them.