Abstract An assessment of least median of squares (LMS) regression is made based on two exploration geochemical data sets: one from Norway in which Cu, Pb, Zn, Cd, Fe and Mn were analyzed on 25 stream sediment samples, and the other from the Torrington district, N.S.W., Australia, in which U, Cu, Pb, Zn, Fe, Mn and LOI (loss on ignition) were determined on 73 stream sediment samples, together with F, pH and conductivity on stream water samples from the same sites. The Norwegian data were subjected to regression analysis of Zn on Fe and Mn to screen the scavenging effect of the major elements on Zn. A regression of U on LOI, Mn and conductivity was carried out for the Torrington data to discriminate U anomalies related to mineralization from those that are results of secondary environmental factors. Two regression methods, namely, ordinary least squares (OLS) and reweighted least squares (RLS) based on the LMS estimator were used, and the results obtained compared. Regression equations and associated statistics derived for the OLS and LMS-based RLS estimators differ for both data sets. In particular, the statistics of interest increase markedly for the most part from nonsignificant at the 5% level for OLS to highly significant for RLS. Similarly, the goodness-of-fit improves from OLS to RLS with the latter being more reliable and trustworthy because it is not affected by the outliers. The LMS-based RLS regression yields high-contrast residual values for both strong and subtle anomalies related to mineralization. In contrast, OLS regression produces low-contrast residual values for the strong anomalies while failing to detect many subtle but geochemically meaningful anomalies. On the other hand, both OLS and LMS-based RLS succeed in indicating false anomalies related to secondary environmental factors for both data sets.