Curvilinear regression methods - Introduction

In many instrumental analysis methods the instrument response is proportional to the analyte concentration over substantial concentration ranges. The simplified calculations that result encourage analysts to take significant experimental precautions to achieve such linearity. Examples of such precautions include the control of the emission line width of a hollow-cathode lamp in atomic absorption spectrometry, and the size and positioning of the sample cell to minimize inner filter artefacts in molecular fluorescence spectrometry. However, many analytical methods (e.g. immunoassays and similar competitive binding assays) produce calibration plots that are intrinsically curved. Particularly common is the situation where the calibration plot is linear (or approximately so) at low analyte concentrations, but becomes curved at higher analyte levels. When curved calibration plots are obtained we still need answers to the questions listed in Section 5.2, but those questions will pose rather more formidable statistical problems than occur in linear calibration experiments. 

In the situation where a calibration plot is linear over part of its range and curved elsewhere, it is of great importance to be able to establish the range over which linearity can be assumed. Approaches to this problem are outlined in the following example. 

Investigate the linear calibration range of the following fluorescence experiment. 

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