Reversed inverse regression for the univariate linear calibration and its statistical properties derived using a new methodology

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...

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Main Authors: Kang Pilsang, Koo Changhoi, Roh Hokyu
Format: Article
Language:English
Published: EDP Sciences 2017-01-01
Series:International Journal of Metrology and Quality Engineering
Subjects:
Online Access:https://www.metrology-journal.org/articles/ijmqe/full_html/2017/01/ijmqe170016/ijmqe170016.html
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spelling doaj-0804bf94d0d64d3bb62e4fa9fe14e0852021-09-02T20:54:13ZengEDP SciencesInternational Journal of Metrology and Quality Engineering2107-68472017-01-0182810.1051/ijmqe/2017021ijmqe170016Reversed inverse regression for the univariate linear calibration and its statistical properties derived using a new methodologyKang PilsangKoo ChanghoiRoh HokyuSince 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.https://www.metrology-journal.org/articles/ijmqe/full_html/2017/01/ijmqe170016/ijmqe170016.htmlbiasclassical regressionerror propagationmean-data-point-based variancepopulation-regression-line-based variancereversed inverse regressionsimultaneous error equationstaylor approximation
collection DOAJ
language English
format Article
sources DOAJ
author Kang Pilsang
Koo Changhoi
Roh Hokyu
spellingShingle Kang Pilsang
Koo Changhoi
Roh Hokyu
Reversed inverse regression for the univariate linear calibration and its statistical properties derived using a new methodology
International Journal of Metrology and Quality Engineering
bias
classical regression
error propagation
mean-data-point-based variance
population-regression-line-based variance
reversed inverse regression
simultaneous error equations
taylor approximation
author_facet Kang Pilsang
Koo Changhoi
Roh Hokyu
author_sort Kang Pilsang
title Reversed inverse regression for the univariate linear calibration and its statistical properties derived using a new methodology
title_short Reversed inverse regression for the univariate linear calibration and its statistical properties derived using a new methodology
title_full Reversed inverse regression for the univariate linear calibration and its statistical properties derived using a new methodology
title_fullStr Reversed inverse regression for the univariate linear calibration and its statistical properties derived using a new methodology
title_full_unstemmed Reversed inverse regression for the univariate linear calibration and its statistical properties derived using a new methodology
title_sort reversed inverse regression for the univariate linear calibration and its statistical properties derived using a new methodology
publisher EDP Sciences
series International Journal of Metrology and Quality Engineering
issn 2107-6847
publishDate 2017-01-01
description 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.
topic bias
classical regression
error propagation
mean-data-point-based variance
population-regression-line-based variance
reversed inverse regression
simultaneous error equations
taylor approximation
url https://www.metrology-journal.org/articles/ijmqe/full_html/2017/01/ijmqe170016/ijmqe170016.html
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AT koochanghoi reversedinverseregressionfortheunivariatelinearcalibrationanditsstatisticalpropertiesderivedusinganewmethodology
AT rohhokyu reversedinverseregressionfortheunivariatelinearcalibrationanditsstatisticalpropertiesderivedusinganewmethodology
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