Society of Actuaries (SOA) PA Practice Exam

What do influential data points have in common in a Residuals vs Leverage graph?

1. High residuals and low leverage

2. Low influence on the model

3. High leverage and high residuals

4. None of the above

The correct answer is: High leverage and high residuals

In a Residuals vs Leverage graph, influential data points typically exhibit the characteristics of having both high leverage and high residuals. High leverage points have values of the independent variable that are significantly different from the mean of the independent variable, potentially exerting a strong influence on the slope of the regression line. High residuals indicate that the difference between the observed value and the predicted value is large, suggesting that these points do not conform well to the model established by the other data points. When both of these conditions are present—high leverage points that also show significant deviation from the predicted values—they are designated as influential because they can disproportionately affect the results of the regression analysis. Removing such points can lead to changes in the overall model fit and summary statistics, underscoring their importance in the context of regression diagnostics. On the other hand, the characteristics described in the other options do not adequately capture the nature of influential points in this context. For instance, high residuals paired with low leverage would suggest that the points are not particularly influential on the regression line, as their leverage is insufficient to substantially affect the modeling outcomes. Similarly, points with low influence are characterized by both low leverage and low residuals, meaning they do not significantly alter the model