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. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Polynomial Regression, Calibration Curve, Analytical Chemistry
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| [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. |
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| [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. |
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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
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
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
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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}
}
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 -
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