Cross-validation calculates the predictive ability of potential models to help you determine the appropriate number of components to retain in your model. Cross-validation is best if you do not know the optimal number of components. When the data contain multiple response variables, Minitab validates the components for all responses at the same time.
After doing steps 1 - 5 for each model, Minitab selects the model with the number of components that produces the highest predicted R^{2} and lowest PRESS. With multiple response variables, Minitab selects the model with the highest average predicted R^{2} and lowest average PRESS.
If you do not use cross-validation, Minitab sets the number of components to 10 or to the number of predictors in your model, whichever is less.
In PLS regression, the cross-validated fitted value is the predicted response for each observation in your data set, calculated individually, so the observation can be excluded from the model used to calculate the predicted response for that observation. The cross-validated fitted values are calculated during cross-validation and vary based on how many observations are omitted each time the model is recalculated.
Use cross validated fitted values to identify how well your model predicts data. Cross-validated fitted values are similar to ordinary fitted values, which identify how well your model fits the data.
In PLS regression, 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.
The residuals measure the model's predictive ability. Minitab uses cross-validated residuals to calculate the PRESS statistic.