[Machine Learning] some concept about the CV

Cross-validation VS SSE

CV is not designed to improve the fit on the training data, but it won't necessarily make it worse either. Cross-validation cannot guarantee improving the SSE on unseen data, although it often helps.

Cross-validation VS best prediction

The purpose of cross-validation is to pick the tree that will perform the best on a test set. So we would expect the model we made with the "best" cp to perform best on a test set.

complexity of the model

Trying different combinations of variables in linear regression controls the complexity of the model. This is similar to trying different numbers of splits in a tree, which is also controlling the complexity of the model.