Mean-squared error (MSE) is used to analyse nine commonly used model-selection criteria (MSC) for their performance when selecting simplified models (SMs). Expressions are derived to enable exact calculations of the probability that a particular MSC will select a SM. For several common MSC, the relative propensities to select SMs are independent of model structure and data. It is shown that MSC that are effective in preventing overfitting are prone to underfitting when information content of the data is low. In a subsequent article, results are extended to develop a new MSE-based MSC for selecting nonlinear multi-response SMs.