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

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 variabl...

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Vydáno v:Molecules (Basel, Switzerland) Ročník 29; číslo 6; s. 1248
Hlavní autoři: Lim, Jeong Sik, Kim, Yong Doo, Woo, Jin-Chun
Médium: Journal Article
Jazyk:angličtina
Vydáno: Switzerland MDPI AG 11.03.2024
MDPI
Témata:
Calibration
correlated independent variables
Independent variables
Monte Carlo simulation
ordinary least squares
Polynomials
Propagation
Regression analysis
Software
uncertainty evaluation
Germany
uncertainty evaluation
ordinary least squares
calibration
Monte Carlo simulation
correlated independent variables
ISSN:1420-3049, 1420-3049
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Shrnutí: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.
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Current address: Measurement Assurance Institute, Yuseong-gu, Daejeon 34113, Republic of Korea.
ISSN:1420-3049
1420-3049
DOI:10.3390/molecules29061248