According to Belsey et al., deleting a case will damage the precision of some model parameters if CVR exceeds which threshold?

• A. If CVR > 1 + [3(k + 1)/n], deleting the case will damage the precision of some model parameters.
• B. If CVR < 1 − [3(k + 1)/n], deleting the case will damage the precision of some model parameters.
• C. If CVR > 1 + [3(k + 1)/n], deleting the case will damage the precision of some model parameters.
• D. If CVR is between 1 − [3(k + 1)/n] and 1 + [3(k + 1)/n], deleting the case will have no impact on precision.

Answer: (C)

When assessing whether removing a single observation will hurt the precision of the model’s parameter estimates, you look at a diagnostic statistic called the Case-Deletion Variance Ratio (CVR). CVR compares how precise the parameter estimates would be if that case were dropped versus if all cases are kept. If this ratio gets large, it means that deleting the case would significantly change (and typically worsen) the precision of some parameters.

The guideline from Belsey et al. says that deleting a case damages precision when CVR exceeds 1 plus three times (k + 1) divided by n, where k is the number of predictors and n is the sample size. So the critical threshold is 1 + 3(k + 1)/n. If your CVR is above this value, you’d expect the precision of some model parameters to deteriorate upon removing that case.

In other words, a CVR well above that upper bound flags an influential case in terms of precision. If CVR stays within the interval around 1 (roughly between 1 − 3(k + 1)/n and 1 + 3(k + 1)/n), deleting the case is not expected to meaningfully affect precision.