Elimination of outlying values prior to evaluating experimental data by linear regression analysis

Abstract

In this ariticle,an algorithm for eliminating outlying values prior to estimating linear regression parameters is described. By using such an algorithm,one can objectively exclude outlying values from experimental measurements and determine an interval (x1, x2) covering a linear relation y =f(x) between the output variable with a normal distribution N(f(x),sigma2) and the independent variable x.The theoretical part concerns the derivation of a mathematical equation which allows to identify the outlying values and to determine the critical deviation of a point under testing. In the experimental section, the usefulness of the algorithm proposed is demenstrated on the evaluation of linear regression parameters of a calibration plot and for calculating the equivalence point of selected titration curves. The derived algorithm can generally be applied to evaluation of the concentration dependences of various physico-chemical variables such as absorbance,polarographic wave-height,conductivity,refraction,optical rotation,etc.A method utilising this algorithm can be used e.g. for analysing the titration end-points in conductometry,amperometry,spectrosphotometry,radiometry or thermometry.The algorithm proposed is especially suitable for evaluating a set with small number of experimental data and for processing such sets that comprise two linear segments with insignificantly different slopes ot the corresponding regression lines.