Society of Actuaries (SOA) PA Practice Exam

What is a common way to visually assess model assumptions?

1. A box plot of residuals

2. A Residuals Versus Fitted Graph

3. A scatter plot of predictor variables

4. A pie chart of prediction outcomes

The correct answer is: A Residuals Versus Fitted Graph

A Residuals Versus Fitted Graph is a fundamental tool in regression analysis used to visually assess model assumptions, particularly the assumption of homoscedasticity and the linearity of the relationship between the dependent and independent variables. In this graph, the fitted values (predicted values) from the model are plotted on the x-axis, while the residuals (the differences between observed and predicted values) are plotted on the y-axis. When the residuals are randomly scattered around the horizontal line at zero with no discernible pattern, it indicates that the model’s assumptions are met. Specifically, this can demonstrate that the variance of the residuals is constant (homoscedastic), and that the model does not exhibit any systematic error. If there are patterns or trends visible in the plot (such as a funnel shape or curvature), it suggests violations of these assumptions, indicating that the model may need refinement or that a different modeling approach might be necessary. In contrast, while a box plot of residuals can provide some insight into the distribution and potential outliers of residuals, it is not as effective for assessing the relationship between residuals and fitted values. A scatter plot of predictor variables is useful for examining relationships among predictors themselves but does not directly