Robust linear regression taking into account errors in the predictor and response variables

We developed a robust regression technique that is a generalization of the least median of squares (LMS) technique to the field in which the errors in both the predictor and the response variables are taken into account. This simple generalization is limited in the sense that the resulting straight line is found by using only two points from the initial data set. In this w ay a simulation step is added by using the Monte Carlo method to generate t he best robust regression line. We call this new technique 'bivariate least median of squares' (BLMS), following the notation of the LMS method. We ch ecked the robustness of the new regression technique by calculating its bre akdown point, which was 50%. This confirms the robustness of the BLMS regre ssion line. In order to show its applicability to the chemical field we tes ted it on simulated data sets and real data sets with outliers. The BLMS ro bust regression line was not affected by many types of outlying points in t he data sets.