Using Cook's distance with a unity threshold, an observation is influential if which condition holds?

Using Cook's distance with a unity threshold, an observation is influential if which condition holds?

• A. Cook's distance > 1
• B. Cook's distance > 0
• C. Cook's distance > 4/n
• D. Cook's distance > 1e-3

Answer: (A)

Cook's distance tells you how much the estimated regression coefficients would change if you delete a single observation. When you use a unity threshold, an observation is considered influential if its Cook's distance exceeds 1. That means removing that point would cause a substantial shift in the fitted model, enough to warrant attention. This threshold is a simple, practical rule of thumb: it separates points that have a meaningful impact on the estimates from those with only a small, negligible effect. Other thresholds exist (for example, 4/n or very small numbers like 1e-3) but they are different heuristics or depend on context; the unity cutoff is the one described here.

Cook's distance tells you how much the estimated regression coefficients would change if you delete a single observation. When you use a unity threshold, an observation is considered influential if its Cook's distance exceeds 1. That means removing that point would cause a substantial shift in the fitted model, enough to warrant attention.

This threshold is a simple, practical rule of thumb: it separates points that have a meaningful impact on the estimates from those with only a small, negligible effect. Other thresholds exist (for example, 4/n or very small numbers like 1e-3) but they are different heuristics or depend on context; the unity cutoff is the one described here.