Regressió lineal amb errors en ambdos eixosaplicació a la calibració i a la comparació de métodes analítics

Abstract

An important subject in analytical chemistry is the comparison of analytical methods at different levels of concentration using linear regression. As the two methods normally have associated errors, the regression line should be found using what is known as regression methods that take into account the errors in both axes. Another field in which these regression methods can be applied is in linear calibration, since there are some analytical techniques (for instance, X-ray fluorescence), in which the calibration line is found with certified reference materials (CRM) of the analyte of interest, each of which presents associated uncertainties to the concentration values. To find the regression line, we used the bivariate least squares (BLS) regression method, which takes into account the individual errors in both axes, and we developed the following tests: · individual tests on the coefficients of the regression line Useful for detecting constant or proportional errors. We developed and validated the expressions for calculating the probabilities of  error taking into account the selected  probabilities of error and the bias set by the analyst. · joint confidence interval on the coefficients of the regression line This test can be used to compare two analytical methods, when one wants to check whether the intercept of the regression line significantly differs from zero and simultaneously if the slope significantly differs from unity. We have developed and validated the joint confidence interval for the coefficients of the BLS regression method, and the joint confidence interval for the coefficients of the MLS (multivariate least squares) regression method. The latter is useful for comparing more than two analytical methods. · confidence intervals in prediction Useful for finding the concentration value and its confidence interval from the instrumental response. It is also used in method comparison studies when one wants to know the confidence interval of a sample from the results of the same sample analysed by another method.