Society of Actuaries (SOA) PA Practice Exam

What does the Scale-Location graph assess regarding residuals?

1. Correlation with the independent variables

2. Homoscedasticity of residuals

3. Distribution normality of predictor variables

4. Confounding variables in the data

The correct answer is: Homoscedasticity of residuals

The Scale-Location graph is a graphical representation used in regression analysis to assess the homoscedasticity of residuals, which refers to the consistency of variance in the residuals across all levels of the independent variable(s). When plotting the square root of the standardized residuals against the fitted values, this graph helps visualize if the residuals remain evenly spread throughout the range of predicted values. In a well-fitted model exhibiting homoscedasticity, the points should display a random scatter around the horizontal axis with no clear pattern. If there is a noticeable trend or funneling effect, this suggests heteroscedasticity, indicating that the variance of the residuals changes with the fitted values. Understanding this concept is crucial in regression diagnostics since violations of the homoscedasticity assumption can lead to inefficiencies in parameter estimates and affect statistical inference, resulting in unreliable hypothesis testing. The other options are related to different aspects of the regression analysis: correlation with independent variables pertains to multicollinearity diagnostics, distribution normality addresses the appraisal of the normal distribution of residuals, and confounding variables consideration deals with the effects of omitted variable bias. Each of these concepts is essential to linear regression as well, but they are assessed through different means rather