Using Polynomial Regression to Objectively Test the Fit of Calibration Curves in Analytical Chemistry

Abstract

Calibration curves are commonly used for quantitative analysis in analytical chemistry to calculate the concentrations of chemicals in samples. Typically, the concentration of the analyte, the chemical being quantified, is the independent variable and is plotted on the x-axis. The detector response, the reading from the instrument, is the dependent variable and is plotted on the y-axis. A calibration curve is made by plotting the known concentration of analyte versus the detector response. After a calibration curve is made, the unknown concentration of analyte in any sample is calculated from its detector response. Unfortunately, there is no standard procedure for objectively testing the fit of calibration curves in analytical chemistry. For example, the World Health Organization (WHO) and the United States Environmental Protection Agency (U.S. EPA) do not provide guidance for testing the linearity or curvature of calibration curves. Moreover, this important topic is not broached in at least 5 of the leading analytical chemistry textbooks. However, there is a simple and effective way to fix this deficiency. In this paper, the use of polynomial regression to objectively test the fit of calibration curves in drinking water analysis is demonstrated. Polynomial regression was used to test the linearity of a representative calibration curve for the spectrophotometric determination of arsenic in drinking water by the arsenomolybdate method. And polynomial regression was used to test the curvature of a representative calibration curve for the determination of arsenic in drinking water by graphite furnace atomic absorption spectroscopy. Microsoft® Excel® 2010 and 2016, MiniTab® 17.2.1, and RStudio® 0.99.441 were used to calculate these calibration curves; in all cases, the calibration curves from these 3 programs agreed with each other to at least 3 significant figures.