Collect. Czech. Chem. Commun. 1995, 60, 2064-2073

Determination of Estimates of Parameters of Calibration Regression Straight Line with Objective Elimination of Remote Measurements

Vladimír Jehličkaa and Vladimír Machb

a Department of Mathematics, University of Pardubice, 530 09 Pardubice, Czech Republic
b Department of Analytical Chemistry, University of Pardubice, 530 09 Pardubice, Czech Republic


An alternative algorithm of calculation of estimates of parameters of calibration regression straight line with elimination of remote measurements has been elaborated for a function f(x) composed of linear-nonlinear or nonlinear-linear parts or, as the case may be, of nonlinear-linear-nonlinear parts. This algorithm makes it possible to objectively eliminate remote measurements and determine the interval <x1;x2> in which is located the linear part of dependence of output measured quantity y = f(x) with normal distribution N(f(x), σ2) on the input, i.e., independent variable x. For the procedure used for testing of remoteness of experimental points, a relation has been derived for calculation of the critical value of deviation of the point tested. The algorithm is finished by the calculation of parameters of the corresponding regression straight line and other statistical characteristics. On the basis of the algorithm suggested, a program has been assembled whose reliability was verified on a series of both model and practical examples.