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In statistics, Deming regression, named after W. Edwards Deming, is an errors-in-variables model that tries to find the line of best fit for a two-dimensional data set. It differs from the simple linear regression in that it accounts for errors in observations on both the x - and the y - axis.
It is a generalization of Deming regression and also of orthogonal regression, and can be applied to both linear and non-linear models. The total least squares approximation of the data is generically equivalent to the best, in the Frobenius norm , low-rank approximation of the data matrix.
In Deming regression, a type of linear curve fitting, if the dependent and independent variables have equal variance this results in orthogonal regression in which the degree of imperfection of the fit is measured for each data point as the perpendicular distance of the point from the regression line.
Linear errors-in-variables models were studied first, probably because linear models were so widely used and they are easier than non-linear ones. Unlike standard least squares regression (OLS), extending errors in variables regression (EiV) from the simple to the multivariable case is not straightforward, unless one treats all variables in the same way i.e. assume equal reliability.
Deming regression (total least squares) also finds a line that fits a set of two-dimensional sample points, but (unlike ordinary least squares, least absolute deviations, and median slope regression) it is not really an instance of simple linear regression, because it does not separate the coordinates into one dependent and one independent ...
Procedures for method evaluation and method comparison include ROC curve analysis, [6] Bland–Altman plot, [7] as well as Deming and Passing–Bablok regression. [ 8 ] The software also includes reference interval estimation, [ 9 ] meta-analysis and sample size calculations.
How to Calculate Deming Regression ... Incorrect Least-Squares Regression Coefficients in Method-Comparison Analysis P. Joanne Cornbleet and Nathan Gochman Clin Chem ...
Vertical distance: Simple linear regression; Resistance to outliers: Robust simple linear regression; Perpendicular distance: Orthogonal regression (this is not scale-invariant i.e. changing the measurement units leads to a different line.) Weighted geometric distance: Deming regression