Cross-validation sample sizes

The squared cross-validity coefficient is a measure of the predictive validity of a sample linear prediction equation. It provides a more realistic assessment of the usefulness of the equation than the squared multiple-correlation coefficient. The squared cross-validity coefficient cannot be larger than the squared multiple-correlation coefficient; its size is affected by the number of predictor variables and the size of the sample. Sample-size tables are presented that should result in very small discrepancies between the squared multiple correlation and the squared cross-validity correlation, thus facilitating the selection of sample size for predictive studies. Index terms: cross-validity coefficient, least-squares regression, multiple correlation, prediction, sample size.