  This paper presents a theory of error in cross-validation testing of
algorithms for predicting real-valued attributes. The theory justifies the
claim that predicting real-valued attributes requires balancing the conflicting
demands of simplicity and accuracy. Furthermore, the theory indicates precisely
how these conflicting demands must be balanced, in order to minimize
cross-validation error. A general theory is presented, then it is developed in
detail for linear regression and instance-based learning.
