Society of Actuaries (SOA) PA Practice Exam

What does the Residuals versus Fitted graph help assess?

1. Normality of the residuals

2. Homogeneity of variance and linearity

3. Influential data points

4. The significance of predictors

The correct answer is: Homogeneity of variance and linearity

The Residuals versus Fitted graph is an important diagnostic tool in regression analysis. It is primarily used to assess two key assumptions of the regression model: homogeneity of variance (also known as homoscedasticity) and the linearity of the relationship between the independent and dependent variables. When plotting the residuals against the fitted values, we look for patterns. If the residuals are randomly scattered around zero, it suggests that the variance of the residuals is constant across all levels of the fitted values, which indicates homogeneity of variance. Conversely, if we observe a systematic pattern (such as a funnel shape, which indicates that the residuals spread out or contract as fitted values increase), this can suggest the presence of heteroscedasticity, violating the assumption of constant variance. Additionally, if the residuals show a linear pattern, it may imply that the linear relationship is not adequately modeling the data. Any curvature observed in the residuals plot may indicate that a nonlinear model may be more appropriate. While this graph can give some insight into influential data points, the primary focus is on evaluating the assumptions related to variance and the fit of the linear model. Thus, the correct choice highlights its role in assessing both homogeneity of variance and