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Approximated Uncertainty Propagation of Correlated Independent Variables Using the Ordinary Least Squares Estimator

Molecules (Basel, Switzerland), 2024-03, Vol.29 (6), p.1248 [Peer Reviewed Journal]

COPYRIGHT 2024 MDPI AG ;2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. ;2024 by the authors. 2024 ;ISSN: 1420-3049 ;EISSN: 1420-3049 ;DOI: 10.3390/molecules29061248 ;PMID: 38542885

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  • Title:
    Approximated Uncertainty Propagation of Correlated Independent Variables Using the Ordinary Least Squares Estimator
  • Author: Lim, Jeong Sik ; Kim, Yong Doo ; Woo, Jin-Chun
  • Subjects: Calibration ; correlated independent variables ; Independent variables ; Monte Carlo simulation ; ordinary least squares ; Polynomials ; Propagation ; Regression analysis ; Software ; uncertainty evaluation
  • Is Part Of: Molecules (Basel, Switzerland), 2024-03, Vol.29 (6), p.1248
  • Description: For chemical measurements, calibration is typically conducted by regression analysis. In many cases, generalized approaches are required to account for a complex-structured variance-covariance matrix of (in)dependent variables. However, in the particular case of highly correlated independent variables, the ordinary least squares (OLS) method can play a rational role with an approximated propagation of uncertainties of the correlated independent variables into that of a calibrated value for a particular case in which standard deviation of fit residuals are close to the uncertainties along the ordinate of calibration data. This proposed method aids in bypassing an iterative solver for the minimization of the implicit form of the squared residuals. This further allows us to derive the explicit expression of budgeted uncertainties corresponding to a regression uncertainty, the measurement uncertainty of the calibration target, and correlated independent variables. Explicit analytical expressions for the calibrated value and associated uncertainties are given for straight-line and second-order polynomial fit models for the highly correlated independent variables.
  • Publisher: Switzerland: MDPI AG
  • Language: English
  • Identifier: ISSN: 1420-3049
    EISSN: 1420-3049
    DOI: 10.3390/molecules29061248
    PMID: 38542885
  • Source: DOAJ Directory of Open Access Journals
    GFMER Free Medical Journals
    PubMed Central
    Alma/SFX Local Collection
    ProQuest Central
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