# 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).

## 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]

: $\mathbf{Y} = \mathbf{X}\mathbf{B} + \mathbf{U},$

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.

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