Which statistic gauges the influence of an observed value on the predicted values in a regression model?

Which statistic gauges the influence of an observed value on the predicted values in a regression model?

• A. Leverage
• B. Hat values
• C. Cook's distance
• D. Influence

Answer: (A)

Cook's distance is the statistic that gauges how much the predicted values would change if a single observation were removed from the data. It combines how far an observation sits in predictor space (leverage) with how large its residual is. Observations with high leverage have the potential to influence the fit because their X-values are far from the center, but they only actually affect the predictions a lot if their residuals are sizable. Leverage, represented by hat values, flags those high–leverage points, but it doesn’t by itself measure the actual impact on the fitted values. The term influence describes the idea in general, but Cook's distance is the standard measure that directly quantifies that impact on predicted values. A point with a large Cook's distance indicates an influential observation whose presence materially changes the regression results.

Cook's distance is the statistic that gauges how much the predicted values would change if a single observation were removed from the data. It combines how far an observation sits in predictor space (leverage) with how large its residual is. Observations with high leverage have the potential to influence the fit because their X-values are far from the center, but they only actually affect the predictions a lot if their residuals are sizable. Leverage, represented by hat values, flags those high–leverage points, but it doesn’t by itself measure the actual impact on the fitted values. The term influence describes the idea in general, but Cook's distance is the standard measure that directly quantifies that impact on predicted values. A point with a large Cook's distance indicates an influential observation whose presence materially changes the regression results.