Analysis of the sensitivity to the systematic error in least-squares regression models

An algorithm that calculates the sensitivity to the systematic error of the fitted parameters of a least-squares regression model, with respect to the known parameters, is developed. The algorithm can be applied to mechanistic and empirical models, obtained by linear and non-linear regression, including principal component and partial least-squares. It can be useful in identifying those parameters or calibration regions that can influence other parameters and the response mostly, and thus, whose accuracy should be particularly procured. Other applications are the weighing of experimental points and the comparison of different models and regression methods in terms of its ability of amplifying as little as possible the systematic errors associated to both the known parameters and the selected regions along the independent variables. Both a simulated (a first order kinetics) and a real (two overlapped chromatographic peaks) experiments showed an excellent agreement between the systematic errors of the fitted parameters when calculated by leastsquares with respect to those predicted by the proposed algorithm.