Title: errors-in-variables regression
Long Title: IUPAC Gold Book - errors-in-variables regression
DOI: 10.1351/goldbook.10150
Status: current

Definition
Least squares regression in which both the response variable and predictor variable have measurement error.

Notes
1) The model for EIV regression is \[\left\{\matrix{c_{i} = \alpha + \beta x_{i}^{*} + \varepsilon_{i} \cr x_{i} = x_{i}^{*} + \eta_{i} \cr}\right.\] where \(x^{*}\) is the true value of the predictor variable, \(c_{i}\) concentration and \(\varepsilon\) and \(\eta\) are errors.
2) When the errors \(\varepsilon\) and \(\eta\) have the same variance the method is called orthogonal regression and minimises the perpendicular distance of a point to the regression line.
3) Total least squares regression is performed by singular value decomposition.

Related Term
- singular value decomposition: https://goldbook.iupac.org//terms/view/10115

Source
- PAC, 2016, 88, 407. 'Vocabulary of concepts and terms in chemometrics (IUPAC Recommendations 2016)' on page 434 (https://doi.org/10.1515/pac-2015-0605)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/10150/html
- json: https://goldbook.iupac.org/terms/view/10150/json
- xml: https://goldbook.iupac.org/terms/view/10150/xml

Citation: Citation: 'errors-in-variables regression' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.10150
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Accessed: 2026-07-24T05:18:16+00:00