Comparison of prediction uncertainty in first order multivariate calibration methods

Most of the studies that are done in chemistry include measurements and numerical calculations and usually in these studies the results are reported quantitatively. Since no quantitative results are of any value unless they are accompanied by some estimate of the errors inherent in them [1], so calculating the error and its sources in these studies is very important. In every calibration a calibration diagram is obtained which is fitted by regression. The choice of regression method depends on the nature of the data. In this work, the three of the most important multivariate methods meaning Classical Least Squares (CLS), Principal Component Regression (PCR) and Partial least Squares (PLS), are compared based on their precision in prediction and various datasets, both simulated and real data, are used for this purpose. To do so, we needed equations for determining the concentration uncertainty in all three methods. In the literature we could only find these equations for PCR and PLS methods [2] and the ones for CLS were missing. So, we derived them ourselves. The simulated data include a series of diverse data in which the level of overlapping of spectrum of the components in chemical system is different and the effect of the intensity of the overlapping on the uncertainty of concentration prediction has been studied. The results showed that there is no significant difference in prediction uncertainties between mentioned methods and all methods had almost identical precisions. But also, one should consider the necessary conditions to perform methods and not only the prediction uncertainty or method simplicity.