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We applied both the ordinary linear regression (OLR) and the new uncertainty weighted linear regression (UWLR) models for the calibration and comparison of a XRF machine through 59 geochemical reference materials (GRMs) and a procedure blank sample. The mean concentration and uncertainty data for the GRMs used for the calibrations (Supplementary Materials) (available here) filewere achieved from an up‐to‐date compilation of chemical data and their processing from well‐known discordancy and significance tests. The drift‐corrected XRF intensity and its uncertainty were determined from mostly duplicate pressed powder pellets. The comparison of the OLR (linear correlation coefficient r∼0.9523–0.9964 and 0.9771–0.9999, respectively, for before and after matrix correction) and UWLR models (r∼0.9772–0.9976 and 0.9970–0.9999, respectively) clearly showed that the latter with generally higher …