There are two basic ways of estimating prediction uncertainty, namely, error propagation or resampling strategies. Error propagation leads to closed-form expressions where some hypotheses are made but which provide a platform for evaluating the different sources of uncertainty. Resampling is essentially a "black box" approach which, however, is often more accurate because fewer assumptions and approximations are made. Some analytical expressions can be found in the literature for error propagation method, but all consider local linearization and other important assumptions. Particularly, the errors in the predictors are assumed to be independent and to have constant variance. This latter assumption is never fulfilled in spectroscopy. So, this paper proposes a new expression for prediction uncertainty estimation based on the error propagation strategy, using as few as possible assumptions.