Cross-validated residuals measure the model's predictive ability and are used to calculate the PRESS statistic. Cross-validated residuals in PLS and least squares regression are conceptually similar, but their calculations differ.
In PLS, the cross-validated residuals are the differences between the actual responses and the cross-validated fitted values.
The cross-validated residual value varies based on how many observations are omitted each time the model is recalculated during cross-validation.
In least squares regression, the cross-validated residuals are calculated directly from the ordinary residuals.
| (i)|| observation omitted from the model calculation |
| yi ||response value|
| ||cross-validated fitted value|