Society of Actuaries (SOA) PA Practice Exam

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What does Cook's distance measure in a Residuals vs Leverage graph?

Effectiveness of the model
Influential points relative to model fitting
Variance of residuals
Distribution of selected predictors

The correct answer is: Influential points relative to model fitting

Cook's distance measures the influence of each data point on the overall regression model. In the context of a Residuals vs Leverage graph, it specifically identifies points that significantly affect the fitted model. High values of Cook's distance indicate that a data point has the potential to disproportionately affect the estimates of the regression coefficients. This means that such points may be influential in determining the shape and position of the regression line, suggesting they should be examined more closely. By analyzing Cook's distance, practitioners can effectively identify which observations may be outliers or leverage points that could unduly influence the results, allowing for better model diagnostics and potentially more robust conclusions.