Abstract: A new method to estimate case specific prediction uncertainty for univariate trilinear partial least squares (tri-PLS1) regression is introduced. This method is, from a theoretical point of view, the most exact finite sample approximation to true prediction uncertainty that has been reported up till now. Using the new method, different error sources can be propagated, which is an advantage that cannot be offered by data driven approaches such as the bootstrap. In a concise example, it is illustrated how the method can be applied. In the Appendix, efficient algorithms are presented to compute the estimates required.