Least squares regression in which both the response variable and predictor variable have measurement error.
Notes: - 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.
- 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.
- Total least squares regression is performed by singular value decomposition.
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)