Volume 1, Issue 2, July 2015, Page: 14-18
Using Polynomial Regression to Objectively Test the Fit of Calibration Curves in Analytical Chemistry
Seth H. Frisbie, Department of Chemistry and Biochemistry, Norwich University, Northfield, Vermont, USA; Better Life Laboratories, Inc., East Calais, Vermont, USA
Erika J. Mitchell, Better Life Laboratories, Inc., East Calais, Vermont, USA
Kenneth R. Sikora, Department of Chemistry and Biochemistry, Norwich University, Northfield, Vermont, USA
Marwan S. Abualrub, Department of Mathematics/Preparatory Program, Khalifa University, Abu Dhabi, United Arab Emirates
Yousef Abosalem, Department of Mathematics/Preparatory Program, Khalifa University, Abu Dhabi, United Arab Emirates
Received: Dec. 27, 2015;       Accepted: Jan. 4, 2016;       Published: Feb. 4, 2016
DOI: 10.11648/j.ijamtp.20150102.11      View  4978      Downloads  122
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.
Keywords
Polynomial Regression, Calibration Curve, Analytical Chemistry
To cite this article
Seth H. Frisbie, Erika J. Mitchell, Kenneth R. Sikora, Marwan S. Abualrub, Yousef Abosalem, Using Polynomial Regression to Objectively Test the Fit of Calibration Curves in Analytical Chemistry, International Journal of Applied Mathematics and Theoretical Physics. Vol. 1, No. 2, 2015, pp. 14-18. doi: 10.11648/j.ijamtp.20150102.11
Copyright
Copyright © 2015 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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