Evaluation of the linearity of calibration dependence

Abstract

An example of the determination of glucose by means of spectrophotometry is used to illustrate a very fundamental question: assuming there is a response of the instrument (here: maximum of absorbance or peak area) to a changed level of concentration of an analyte (sometimes also a term analate is used), is this response linear or not quite linear? The corollary questions are for example: what criteria can be used to evaluate (or assess) the degree of linearity? Would that functional dependence be valid over the whole range of analyte concentrations or, if not, what other mathematical alternatives are available to construct a model which will be giving more reliable results? Using two sets of calibration data (each data set having 9 elements of concentration) and a regression equation of upto cubic order, three different models (linear, quadratic and cubic) were evaluated and their respective strengths and weaknesses discussed in detail. Generally, it was found that the best regression for both sets of calibration data gives the quadratic model. For the first set, the linear model upto glucose concentration 33 mmol/l is also acceptable. For the second set, however, the linear model can be used only as a crude approximation due to residua, which are autocorrelated. Although the results between the both sets are subtle, still care must be taken to apply models which give best results in terms of reliability over the concentration range of practical interest.