Editing Design matrix (section)

{{Short description|Matrix of values of explanatory variables}}
In [[statistics]] and in particular in [[regression analysis]], a '''design matrix''', also known as '''model matrix''' or '''regressor matrix''' and often denoted by '''X''', is a [[matrix (mathematics)|matrix]] of values of [[explanatory variable]]s of a set of objects. Each row represents an individual object, with the successive columns corresponding to the variables and their specific values for that object. The design matrix is used in certain [[statistical model]]s, e.g., the [[general linear model]].<ref>{{cite book |last=Everitt |first=B. S. |year=2002 |title=Cambridge Dictionary of Statistics |edition=2nd |location=Cambridge, UK |publisher=Cambridge University Press |isbn=0-521-81099-X }}</ref><ref>{{cite book |last1=Box |first1=G. E. P. |author-link=George E. P. Box|author2-link=George Tiao |last2=Tiao |first2=G. C. |year=1992 |orig-year=1973 |title=Bayesian Inference in Statistical Analysis |location=New York |publisher=John Wiley and Sons |isbn=0-471-57428-7 }} (Section 8.1.1)</ref><ref>{{cite book |last=Timm |first=Neil H. |title=Applied Multivariate Analysis |publisher=Springer Science & Business Media |year=2007 |page=107 |isbn=9780387227719 |url=https://books.google.com/books?id=vtiyg6fnnskC&pg=PA107 }}</ref> It can contain [[indicator variable]]s (ones and zeros) that indicate group membership in an [[ANOVA]], or it can contain values of [[continuous variable]]s.

The design matrix contains data on the [[independent variable]]s (also called explanatory variables), in a statistical model that is intended to explain observed data on a response variable (often called a [[dependent variable]]). The theory relating to such models uses the design matrix as input to some [[linear algebra]] : see for example [[linear regression]]. A notable feature of the concept of a design matrix is that it is able to represent a number of different [[experimental design]]s and statistical models, e.g., [[ANOVA]], [[ANCOVA]], and linear regression.{{citation needed|date=April 2013}}