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: <math>\mathbf{Y} = \mathbf{X}\mathbf{B} + \mathbf{U},</math>
where '''Y''' is a [[Matrix (mathematics)|matrix]] with series of multivariate measurements (each column being a set of measurements on one of the [[dependent variable]]s), '''X''' is a matrix of observations on [[independent variable]]s that might be a [[design matrix]] (each column being a set of observations on one of the independent variables), '''B''' is a matrix containing parameters that are usually to be estimated and '''U''' is a matrix containing [[Errors and residuals in statistics|errors]] (noise). The errors are usually assumed to be uncorrelated across measurements, and follow a [[multivariate normal distribution]]. If the errors do not follow a multivariate normal distribution, [[generalized linear model]]s may be used to relax assumptions about '''Y''' and '''U'''.
The general linear model incorporates a number of different statistical models: [[Analysis of variance|ANOVA]], [[Analysis of covariance|ANCOVA]], [[Multivariate analysis of variance|MANOVA]], [[Multivariate analysis of covariance|MANCOVA]], ordinary [[linear regression]], [[t-test|''t''-test]] and [[F-test|''F''-test]]. The general linear model is a generalization of multiple linear regression to the case of more than one dependent variable. If '''Y''', '''B''', and '''U''' were [[column vector]]s, the matrix equation above would represent multiple linear regression.
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== Comparison to generalized linear model ==
The general linear model and the [[generalized linear model]] (GLM)<ref name=":0">{{Cite book |last1=McCullagh |first1=P. |author1-link=Peter McCullagh |last2=Nelder |first2=J. A. |author2-link=John Nelder |date=January 1, 1983 |chapter=An outline of generalized linear models |title=Generalized Linear Models |pages=21–47 |publisher=Springer US |isbn=9780412317606 |doi=10.1007/978-1-4899-3242-6_2 |doi-broken-date=13 December 2024}}</ref><ref>Fox, J. (2015). ''Applied regression analysis and generalized linear models''. Sage Publications.</ref> are two commonly used families of [[Statistics|statistical methods]] to relate some number of continuous and/or categorical [[Dependent and independent variables|predictors]] to a single [[Dependent and independent variables|outcome variable]].
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|[[Wolfram Language]] & [[Mathematica]] function
|LinearModelFit[]<ref>[http://reference.wolfram.com/language/ref/LinearModelFit.html LinearModelFit], Wolfram Language Documentation Center.</ref>
|GeneralizedLinearModelFit[]<ref>[http://reference.wolfram.com/language/ref/GeneralizedLinearModelFit.html GeneralizedLinearModelFit], Wolfram Language Documentation Center.</ref>
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|[[EViews]] command
|ls<ref>[http://www.eviews.com/help/helpintro.html#page/content%2Fcommandcmd-ls.html ls], EViews Help.</ref>
|glm<ref>[http://www.eviews.com/help/helpintro.html#page/content%2Fcommandcmd-glm.html glm], EViews Help.</ref>
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|statsmodels Python Package
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== References ==
▲ |last1=Christensen |first1=Ronald |year=2020 |title=Plane Answers to Complex Questions: The Theory of Linear Models |___location=New York |publisher=Springer |edition=5th |isbn=978-3-030-32096-6}}
* {{cite book |last1=Wichura |first1=Michael J. |year=2006 |title=The coordinate-free approach to linear models |series=Cambridge Series in Statistical and Probabilistic Mathematics |publisher=Cambridge University Press |___location=Cambridge |pages=xiv+199 |isbn=978-0-521-86842-6 |mr=2283455}}
* {{Cite book |editor1-last=Rawlings |editor1-first=John O. |editor2-last=Pantula |editor2-first=Sastry G. |editor3-last=Dickey |editor3-first=David A. |year=1998
{{Statistics}}
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