According to Stevens, what threshold is suggested as a cutoff for undue influence using leverage?

According to Stevens, what threshold is suggested as a cutoff for undue influence using leverage?

• A. greater than half the average (0.5*(k+1)/n)
• B. greater than the average (k+1)/n
• C. greater than three times the average (3(k+1)/n)
• D. greater than four times the average (4(k+1)/n)

Answer: (C)

In regression diagnostics, leverage shows how far an observation’s predictor values are from the center of the predictor space. The average leverage across all observations is p/n, where p is the number of parameters in the model (k predictor variables plus the intercept, so p = k + 1). Stevens recommends using a cutoff of three times that average to flag undue influence due to leverage: h_i > 3(k+1)/n. Observations with such high leverage have predictor values that are unusually far from the mean, giving them the potential to disproportionately pull the estimated regression coefficients, even if their residuals aren’t large. This threshold is a practical balance—smaller cutoffs would flag too many points, while larger ones could miss truly influential cases. To apply it, compute each observation’s leverage h_i, compare to 3(k+1)/n, and scrutinize any that exceed the threshold, possibly using additional diagnostics like Cook’s distance for a fuller picture of influence. For example, with k = 5 predictors and n = 100 observations, the average leverage is (5+1)/100 = 0.06, so the cutoff is 3 × 0.06 = 0.18.

In regression diagnostics, leverage shows how far an observation’s predictor values are from the center of the predictor space. The average leverage across all observations is p/n, where p is the number of parameters in the model (k predictor variables plus the intercept, so p = k + 1). Stevens recommends using a cutoff of three times that average to flag undue influence due to leverage: h_i > 3(k+1)/n. Observations with such high leverage have predictor values that are unusually far from the mean, giving them the potential to disproportionately pull the estimated regression coefficients, even if their residuals aren’t large. This threshold is a practical balance—smaller cutoffs would flag too many points, while larger ones could miss truly influential cases. To apply it, compute each observation’s leverage h_i, compare to 3(k+1)/n, and scrutinize any that exceed the threshold, possibly using additional diagnostics like Cook’s distance for a fuller picture of influence. For example, with k = 5 predictors and n = 100 observations, the average leverage is (5+1)/100 = 0.06, so the cutoff is 3 × 0.06 = 0.18.