According to Hoaglin and Welsch, a case is potentially influential if its leverage value exceeds what threshold?

• A. greater than three times the average (3(k+1)/n)
• B. greater than twice the average (2(k+1)/n)
• C. greater than four times the average (4(k+1)/n)
• D. greater than the average (1*(k+1)/n)

Answer: (B)

Leverage tells you how far an observation’s predictor values lie from the center of the predictor space. An observation with high leverage has the potential to pull the regression line toward itself, even if its outcome value isn’t extreme. The average leverage across all cases is p/n, where p is the number of parameters in the model (including the intercept). So, with k predictors plus an intercept, p = k+1 and the average is (k+1)/n.

Hoaglin and Welsch recommend flagging observations whose leverage exceeds twice the average, i.e., h_ii > 2(k+1)/n. This threshold—twice the average leverage—helps identify cases that are unusually distant in predictor space and thus potentially influential on the fitted model. Using this rule avoids flagging typical points while catching those that could disproportionately affect the results.

So, a case is potentially influential when its leverage value exceeds two times the average leverage.