Which statistic measures the influence of deleting a case on a regression parameter estimate?

Which statistic measures the influence of deleting a case on a regression parameter estimate?

• A. DFFit
• B. DFBeta
• C. Diagonal
• D. Dichotomous

Answer: (B)

When you want to know how much deleting a single observation would change the estimated regression parameters, you look at DFBETAs. This statistic records, for each coefficient, how much that coefficient would shift if that observation were removed, often in standardized form. Large absolute DFBETAs signal that the observation has a strong influence on a particular parameter (like the intercept or a slope). This helps you pinpoint which cases are driving changes in the estimated relationships. By contrast, DFFITS assesses the impact of removing a case on the fitted value for that same case, not on the parameter estimates themselves. The diagonal of the hat matrix relates to leverage—how far an observation’s predictor values are from the center—indicating potential influence but not directly measuring parameter changes. A dichotomous statistic isn’t used for this purpose.

When you want to know how much deleting a single observation would change the estimated regression parameters, you look at DFBETAs. This statistic records, for each coefficient, how much that coefficient would shift if that observation were removed, often in standardized form. Large absolute DFBETAs signal that the observation has a strong influence on a particular parameter (like the intercept or a slope). This helps you pinpoint which cases are driving changes in the estimated relationships.

By contrast, DFFITS assesses the impact of removing a case on the fitted value for that same case, not on the parameter estimates themselves. The diagonal of the hat matrix relates to leverage—how far an observation’s predictor values are from the center—indicating potential influence but not directly measuring parameter changes. A dichotomous statistic isn’t used for this purpose.