What is the term for the measure of the influence of a particular data case?

What is the term for the measure of the influence of a particular data case?

• A. Deleted residual
• B. Outlier
• C. Leverage
• D. Cook's distance

Answer: (A)

When assessing how much a single data point affects the regression results, the idea is to see what happens if that point is removed and the model is refitted. The deleted residual captures this by using the model estimated without that observation to predict its value, and then comparing that to the actual observed value. If this residual is large, removing the case would noticeably change the fitted values, meaning that data point has influence on the model. This focuses on the impact of deleting the case, rather than just how extreme the point is in terms of the observed response (outlier) or how far its predictor values lie from the center (leverage). While Cook’s distance combines residual size and leverage into a single influence metric, the per-case measure that directly reflects the influence of deleting that case is the deleted residual.

When assessing how much a single data point affects the regression results, the idea is to see what happens if that point is removed and the model is refitted. The deleted residual captures this by using the model estimated without that observation to predict its value, and then comparing that to the actual observed value. If this residual is large, removing the case would noticeably change the fitted values, meaning that data point has influence on the model. This focuses on the impact of deleting the case, rather than just how extreme the point is in terms of the observed response (outlier) or how far its predictor values lie from the center (leverage). While Cook’s distance combines residual size and leverage into a single influence metric, the per-case measure that directly reflects the influence of deleting that case is the deleted residual.