Discovering Statistics Using IBM SPSS Statistics, 5th Ed. Practice Test

The process described is about testing how well a model would predict an observation if that observation hadn’t influenced the model itself. For each case, you remove that case, re-fit the model on the remaining data, and then use that reduced model to predict the excluded case. The value you obtain for that observation in this leave-one-out setup is what some software calls an adjusted or cross-validated predicted value. It represents the model’s prediction for a case when it wasn’t trained on that very case, giving a sense of how well the model generalizes to new data.

This is different from how DFFITS works, which focuses on the change in the fitted value for an observation when that observation is deleted (the difference between predictions with and without the case). It’s also different from Cook’s distance, which measures how much deleting a case would influence all fitted values in the model, not just the single predicted value for that case. The partial regression coefficient, meanwhile, is about the estimated effect of a predictor holding other variables constant, not about leaving cases out of the estimation.

So the value described—the predicted outcome for the excluded case after re-estimating the model without it—is best described as the adjusted predicted value.