Used in regression analysis to indicate how well the model predicts responses for new observations, whereas R2 indicates how well the model fits your data. Predicted R2 can prevent overfitting the model and can be more useful than adjusted R2 for comparing models because it is calculated using observations not included in model estimation. Overfitting refers to models that appear to explain the relationship between the predictor and response variables for the data set used for model calculation but fail to provide valid predictions for new observations.
Predicted R2 is calculated by systematically removing each observation from the data set, estimating the regression equation, and determining how well the model predicts the removed observation. Predicted R2 ranges between 0 and 100% and is calculated from the PRESS statistic. Larger values of predicted R2 suggest models of greater predictive ability.
For example, you work for a financial consulting firm and are developing a model to predict future market conditions. The model you settle on looks promising because it has an R2 of 87%. However, when you calculate the predicted R2 you see that it drops to 52%. This may indicate an overfitted model and suggests that your model will not predict new observations nearly as well as it fits your existing data.