Int. J. Metrol. Qual. Eng.
Volume 8, 2017
|Number of page(s)||10|
|Published online||27 November 2017|
Reversed inverse regression for the univariate linear calibration and its statistical properties derived using a new methodology
Quality Management Center, KEPCO NF,
242, Daedeok-daero 989 beon-gil
Accepted: 28 September 2017
Since simple linear regression theory was established at the beginning of the 1900s, it has been used in a variety of fields. Unfortunately, it cannot be used directly for calibration. In practical calibrations, the observed measurements (the inputs) are subject to errors, and hence they vary, thus violating the assumption that the inputs are fixed. Therefore, in the case of calibration, the regression line fitted using the method of least squares is not consistent with the statistical properties of simple linear regression as already established based on this assumption. To resolve this problem, “classical regression” and “inverse regression” have been proposed. However, they do not completely resolve the problem. As a fundamental solution, we introduce “reversed inverse regression” along with a new methodology for deriving its statistical properties. In this study, the statistical properties of this regression are derived using the “error propagation rule” and the “method of simultaneous error equations” and are compared with those of the existing regression approaches. The accuracy of the statistical properties thus derived is investigated in a simulation study. We conclude that the newly proposed regression and methodology constitute the complete regression approach for univariate linear calibrations.
Key words: bias / classical regression / error propagation / mean-data-point-based variance / population-regression-line-based variance / reversed inverse regression / simultaneous error equations / Taylor approximation
© P. Kang et al., published by EDP Sciences, 2017
This is an Open Access article distributed under the terms of 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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