Which statistic measures the influence of a single case by comparing model fits with and without that case?

Which statistic measures the influence of a single case by comparing model fits with and without that case?

• A. Cook's distance
• B. DFFit
• C. Leverage
• D. DFBETAS

Answer: (B)

The important idea here is how much a single observation changes its own predicted value when that observation is removed from the model. DFFIT measures exactly that: it compares the fitted value for the observation with the model that includes all data to the fitted value for the same observation when that case is excluded, typically standardizing the difference. This directly captures the influence of that one case on its own prediction. Other diagnostics look at different aspects of influence. Leverage flags observations with predictor values far from the center, Cook’s distance assesses the overall impact on all fitted values when a case is removed, and DFBETAS shows how much the estimated coefficients would change if the case were deleted. But the scenario described—how much the model’s fit for that particular observation changes when you remove it—is exactly what DFFIT conveys.

The important idea here is how much a single observation changes its own predicted value when that observation is removed from the model. DFFIT measures exactly that: it compares the fitted value for the observation with the model that includes all data to the fitted value for the same observation when that case is excluded, typically standardizing the difference. This directly captures the influence of that one case on its own prediction.

Other diagnostics look at different aspects of influence. Leverage flags observations with predictor values far from the center, Cook’s distance assesses the overall impact on all fitted values when a case is removed, and DFBETAS shows how much the estimated coefficients would change if the case were deleted. But the scenario described—how much the model’s fit for that particular observation changes when you remove it—is exactly what DFFIT conveys.