Algorithm for the line of best fit for a two-dimensional dataset
Deming regression. The red lines show the error in both x and y. This is different from the traditional least squares method, which measures error parallel to the y axis. The case shown, with deviations measured perpendicularly, arises when errors in x and y have equal variances.
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 special case of total least squares, which allows for any number of predictors and a more complicated error structure.
Deming regression is equivalent to the maximum likelihood estimation of an errors-in-variables model in which the errors for the two variables are assumed to be independent and normally distributed, and the ratio of their variances, denoted δ, is known.[1] In practice, this ratio might be estimated from related data-sources; however the regression procedure takes no account for possible errors in estimating this ratio.
The Deming regression is only slightly more difficult to compute than the simple linear regression. Most statistical software packages used in clinical chemistry offer Deming regression.
The model was originally introduced by Adcock (1878) who considered the case δ = 1, and then more generally by Kummell (1879) with arbitrary δ. However their ideas remained largely unnoticed for more than 50 years, until they were revived by Koopmans (1936) and later propagated even more by Deming (1943). The latter book became so popular in clinical chemistry and related fields that the method was even dubbed Deming regression in those fields.[2]
In statistics, Demingregression, named after W. Edwards Deming, is an errors-in-variables model that tries to find the line of best fit for a two-dimensional...
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linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where...
distance to reach a road, quantifying the scatter on a graph, etc. In Demingregression, a type of linear curve fitting, if the dependent and independent...
Nonparametric regression Isotonic regression Semiparametric regression Local regression Total least squares regressionDemingregression Errors-in-variables...
used for estimating the unknown regression coefficients in a standard linear regression model. In PCR, instead of regressing the dependent variable on the...
^{\mathsf {T}}\mathbf {y} .} Optimal instruments regression is an extension of classical IV regression to the situation where E[εi | zi] = 0. Total least...
as well as non-linear regression, logistic regression, and multivariate statistics. Survival analysis includes Cox regression (Proportional hazards model)...
HarperCollins (1995), p. 1087. also 14th ed. (1989). Yang, Lihui; An, Deming; Jessica Anderson Turner (2008). Handbook of Chinese Mythology. Oxford University...
including t-tests, regression models, design of experiments, and much else, use least squares methods applied using linear regression theory, which is based...
Zabell 1992 Deming, W. Edwards (1952). Lectures on statistical control of quality (Rev. 2nd ed.). Nippon Kagaku Gijutsu Remmei. OCLC 2518026. Deming, W. Edwards...
innovation came to the attention of W. Edwards Deming, then working at the Hawthorne facility. Deming later worked at the United States Department of...
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Quality Engineers focus on optimizing product quality which W. Edwards Deming defined as: Quality = Results of work efforts Total costs {\displaystyle...
special form such as a linear regression or neural network. These have special analysis methods. In particular linear regression techniques are much more efficient...
calibration techniques such as partial-least squares regression, or principal component regression (and near countless other methods) are then used to...
sampling, using a random coefficient regression model. Lohr presents conditions under which the GLS estimator of the regression slope has a design effect less...
and the specification limit is drawn. All these losses are, as W. Edwards Deming would describe them, unknown and unknowable, but Taguchi wanted to find...
Archived (PDF) from the original on 27 July 2018. Retrieved 5 September 2018. Deming S (2011). "The Economic Importance of Indian Opium and Trade with China...
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