Graphical criterion for the detection of outliers in linear regression taking into account errors in both axes

Over the past few years linear regression taking into account the errors in both axes has become increasingly important in chemical analysis. It can be applied for instance in method comparison studies at several levels of concentration (where each of the two methods normally present errors of the same order of magnitude) or at calibration straight lines using reference materials as calibration standards, such as in X-ray fluorescence for analysing geological samples. However, the results obtained by using a regression line may be biased due to one or more outlying points in the experimental data set. These situations can be overcome by robust regression methods or techniques for detecting outliers. This paper presents a graphical criterion for detecting outliers using the bivariate least squares (BLS) regression method, which takes into account the heteroscedastic individual errors in both axes. This graphical criterion is based on a modification of Cookʹs well-known test for detecting outliers. This new technique has been checked using two simulated data sets where an outlier is added, and one real data set corresponding to a method comparison analysis.