Design matrix

In statistics, a design matrix, also known as model matrix or regressor matrix and often denoted by X, is a matrix of values of explanatory variables 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 models, e.g., the general linear model.[1][2][3] It can contain indicator variables (ones and zeros) that indicate group membership in an ANOVA, or it can contain values of continuous variables.

The design matrix contains data on the independent variables (also called explanatory variables) in statistical models which attempt to explain observed data on a response variable (often called a dependent variable) in terms of the explanatory variables. The theory relating to such models makes substantial use of matrix manipulations involving the design matrix: 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 designs and statistical models, e.g., ANOVA, ANCOVA, and linear regression.[citation needed]

References

  1. ^Everitt, B. S. (2002). Cambridge Dictionary of Statistics (2nd ed.). Cambridge, UK: Cambridge University Press. ISBN 0-521-81099-X.
  2. ^Box, G. E. P.; Tiao, G. C. (1992) [1973]. Bayesian Inference in Statistical Analysis. New York: John Wiley and Sons. ISBN 0-471-57428-7. (Section 8.1.1)
  3. ^Timm, Neil H. (2007). Applied Multivariate Analysis. Springer Science & Business Media. p. 107.
  4. ^Johnson, Richard A; Wichern, Dean W (2001). Applied Multivariate Statistical Analysis. Pearson. pp. 111–112. ISBN 0131877151.
  5. ^“Basic Concepts for Multivariate Statistics p.2” (PDF). SAS Institute.

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