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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.
Such estimation methods include [12] Deming regression — assumes that the ratio δ = σ² ε /σ² η is known. This could be appropriate for example when errors in y and x are both caused by measurements, and the accuracy of measuring devices or procedures are known. The case when δ = 1 is also known as the orthogonal regression.
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.
DeFries–Fulker regression; de Moivre's law; De Moivre–Laplace theorem; Decision boundary; Decision theory; Decomposition of time series; Degenerate distribution; Degrees of freedom (statistics) Delaporte distribution; Delphi method; Delta method; Demand forecasting; Deming regression; Demographics; Demography. Demographic statistics ...
Several methods exist, considering: 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
George Box. The phrase "all models are wrong" was first attributed to George Box in a 1976 paper published in the Journal of the American Statistical Association.In the paper, Box uses the phrase to refer to the limitations of models, arguing that while no model is ever completely accurate, simpler models can still provide valuable insights if applied judiciously. [1]
Optimal instruments regression is an extension of classical IV regression to the situation where E[ε i | z i] = 0. Total least squares (TLS) [6] is an approach to least squares estimation of the linear regression model that treats the covariates and response variable in a more geometrically symmetric manner than OLS. It is one approach to ...