# Multivariate Regression Algorithm

A Multivariate Regression Algorithm is a regression algorithm that can be implemented into a Multivariate Regression System (to solve a multivariate regression task).

**AKA:**Multiple Dependent Variables Regression Algorithm**Example(s):****Counter-Example(s):****See:**Design Matrix, Multivariate Normal Distribution, Generalized Linear Models, ANOVA, ANCOVA, MANOVA, MANCOVA, t-Test, F-Test, Multivariate Hypothesis Testing.

## References

### 2014

- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/General_linear_model Retrieved:2014-11-13.
- The
**general linear model**is a statistical linear model.It may be written as

^{[1]}: [math]\mathbf{Y} = \mathbf{X}\mathbf{B} + \mathbf{U},[/math]

where Y

**is a matrix with series of multivariate measurements,**X**is a matrix that might be a design matrix,**B is a matrix containing parameters that are usually to be estimated and**U**is a matrix containing errors or 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 models may be used to relax assumptions about

**Y**and U.The general linear model incorporates a number of different statistical models: ANOVA, ANCOVA, MANOVA, MANCOVA, ordinary linear regression, t-test and F-test. The general linear model is a generalization of multiple linear regression model to the case of more than one dependent variable. If

**Y**, B, and**U**were column vectors, the matrix equation above would represent multiple linear regression.Hypothesis tests with the general linear model can be made in two ways: multivariate or as several independent univariate tests.

In multivariate tests the columns of

**Y**are tested together, whereas in univariate tests the columns of Y are tested independently, i.e., as multiple univariate tests with the same design matrix.

- The

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### 2013

- (Hidalgo & Goodman, 2013) ⇒ Bertha Hidalgo, and Melody Goodman. (2013). “Multivariate Or Multivariable Regression?.” In: American journal of public health, 103(1).
- QUOTE: Most regression models are described in terms of the way the outcome variable is modeled: in linear regression the outcome is continuous, logistic regression has a dichotomous outcome, and survival analysis involves a time to event outcome. Statistically speaking, multivariate analysis refers to statistical models that have 2 or more dependent or outcome variables, and multivariable analysis refers to statistical models in which there are multiple independent or response variables.

### 1982

- (Chamberlain, 1982) ⇒ Gary Chamberlain (1982). “Multivariate regression models for panel data.” In: Journal of Econometrics, 18(1).