Error Bars in Chemometrics: What Do They Really Mean?

Spectroscopic calibration models, particularly those using multivariate regression methods, often operate in conditions where predictor variables are highly collinear, reference methods have their own measurement error, and sample matrices vary widely. These realities violate the assumptions of ordinary least squares (OLS) and complicate uncertainty estimation. This tutorial compares classical analytical error propagation with Bayesian and resampling methods such as bootstrapping and jackknifing. The discussion emphasizes interpreting coefficient standard errors, confidence intervals for predictions, and prediction uncertainty in contexts such as near-infrared (NIR), infrared (IR), Raman, and ultraviolet–visible (UV–vis) spectroscopy. Numerical examples and derivations are presented in matrix notation, enabling direct application by experienced practitioners.