| Peer-Reviewed

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

Received: 27 December 2015     Accepted: 4 January 2016     Published: 4 February 2016
Views:       Downloads:
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.

Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 1, Issue 2)
DOI 10.11648/j.ijamtp.20150102.11
Page(s) 14-18
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Polynomial Regression, Calibration Curve, Analytical Chemistry

References
[1] WHO (World Health Organization). 2011. Guidelines for Drinking-water Quality. 4th ed. Geneva, Switzerland: World Health Organization.
[2] Guidelines Establishing Test Procedures for the Analysis of Pollutants. 2015. 40 CFR Part 136.
[3] Frisbie SH, Mitchell EJ, Yusuf AZ, Siddiq MY, Sanchez RE, Ortega R, Maynard DM, Sarkar B. 2005. The development and use of an innovative laboratory method for measuring arsenic in drinking water from western Bangladesh. Environ Health Perspect 113: 1196-1204.
[4] Neter J, Wasserman W, Kutner MH. 1985. Applied Linear Statistical Models. 2nd ed. Homewood, IL: Irwin.
[5] Buck Scientific, Inc. 2002. Buck Scientific 210VGP Atomic Absorption Spectrophotometer Operator’s Manual. East Norwalk, CT: Buck Scientific, Inc.
[6] Skoog, DA, West DM, Holler FJ, Crouch SR. 2014. Fundamentals of Analytical Chemistry. 9th ed. Belmont, CA: Brooks/Cole, Cengage Learning.
[7] Bencs L, Szakács O, Szoboszlai N, Ajtony Z, Bozsai G. 2003. Characteristics of atomic absorption calibration curves with transversely heated graphite furnace. J Anal At Spectrom 18: 105-110.
[8] Kántor T. 1988. Interpreting some analytical characteristics of thermal dispersion methods used for sample introduction in atomic spectrometry. Spectrochim Acta, Part B 43: 1299-1320.
[9] Berglund M, Frech W, Baxter DC, Radziuk B. 1993. A critical evaluation of a multielement ETAAS system using line sources and a transversely heated graphite atomizer with Zeeman effect background correction. Spectrochim Acta, Part B 48: 1381-1392.
[10] De Loos-Vollebregt MTC, Van Oosten P, De Koning MJ, Podmos J. 1993. Extension of the dynamic range in a. c. Zeeman electrothermal atomic absorption spectrometry. Spectrochim Acta, Part B 48: 1505-1515.
[11] APHA (American Public Health Association), American Water Works Association, Water Environment Federation. 2012. Standard Methods for the Examination of Water and Wastewater. 22nd ed. Washington, DC: American Public Health Association.
[12] ISO (International Organization for Standardization). 2001. ISO 8466-2: 2001, Water Quality - Calibration and Evaluation of Analytical Methods and Estimation of Performance Characteristics - Part 2: Calibration Strategy for Non-Linear Second-Order Calibration Functions. Geneva, Switzerland: International Organization for Standardization.
[13] Snedecor GW, Cochran WG. 1982. Statistical Methods. 7th ed. Ames, IA: The Iowa University Press.
Cite This Article
  • APA Style

    Seth H. Frisbie, Erika J. Mitchell, Kenneth R. Sikora, Marwan S. Abualrub, Yousef Abosalem. (2016). Using Polynomial Regression to Objectively Test the Fit of Calibration Curves in Analytical Chemistry. International Journal of Applied Mathematics and Theoretical Physics, 1(2), 14-18. https://doi.org/10.11648/j.ijamtp.20150102.11

    Copy | Download

    ACS Style

    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. Int. J. Appl. Math. Theor. Phys. 2016, 1(2), 14-18. doi: 10.11648/j.ijamtp.20150102.11

    Copy | Download

    AMA Style

    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. Int J Appl Math Theor Phys. 2016;1(2):14-18. doi: 10.11648/j.ijamtp.20150102.11

    Copy | Download

  • @article{10.11648/j.ijamtp.20150102.11,
      author = {Seth H. Frisbie and Erika J. Mitchell and Kenneth R. Sikora and Marwan S. Abualrub and Yousef Abosalem},
      title = {Using Polynomial Regression to Objectively Test the Fit of Calibration Curves in Analytical Chemistry},
      journal = {International Journal of Applied Mathematics and Theoretical Physics},
      volume = {1},
      number = {2},
      pages = {14-18},
      doi = {10.11648/j.ijamtp.20150102.11},
      url = {https://doi.org/10.11648/j.ijamtp.20150102.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20150102.11},
      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.},
     year = {2016}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Using Polynomial Regression to Objectively Test the Fit of Calibration Curves in Analytical Chemistry
    AU  - Seth H. Frisbie
    AU  - Erika J. Mitchell
    AU  - Kenneth R. Sikora
    AU  - Marwan S. Abualrub
    AU  - Yousef Abosalem
    Y1  - 2016/02/04
    PY  - 2016
    N1  - https://doi.org/10.11648/j.ijamtp.20150102.11
    DO  - 10.11648/j.ijamtp.20150102.11
    T2  - International Journal of Applied Mathematics and Theoretical Physics
    JF  - International Journal of Applied Mathematics and Theoretical Physics
    JO  - International Journal of Applied Mathematics and Theoretical Physics
    SP  - 14
    EP  - 18
    PB  - Science Publishing Group
    SN  - 2575-5927
    UR  - https://doi.org/10.11648/j.ijamtp.20150102.11
    AB  - 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.
    VL  - 1
    IS  - 2
    ER  - 

    Copy | Download

Author Information
  • Department of Chemistry and Biochemistry, Norwich University, Northfield, Vermont, USA

  • Better Life Laboratories, Inc., East Calais, Vermont, USA

  • Department of Chemistry and Biochemistry, Norwich University, Northfield, Vermont, USA

  • Department of Mathematics/Preparatory Program, Khalifa University, Abu Dhabi, United Arab Emirates

  • Department of Mathematics/Preparatory Program, Khalifa University, Abu Dhabi, United Arab Emirates

  • Sections