# Machine Learning | Multivariate Linear Regression

This is similar to linear regression but instead of having single dependent variable Y, we have multiple output variables. It may be written as,
Y = XB + U ,
where Y is a matrix with series of multivariate measurements (each column being a set of measurements on one of the dependent variables), X is a matrix of observations on independent variables 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. U is the regularisation factor.

Representing it in the old form,

E( \beta_ 0, \beta_ 1, \beta_ 2, \beta_ 3, .. \beta_ m) = \sum_{i=1}^{n} (h_ \theta (x_ i) - y_ i)
##### Multivariate Linear Regression vs Multiple Linear Regression

In Multivariate regression there are more than one dependent variable with different variances (or distributions). The predictor variables may be one or multiple.
In Multiple regression, there is just one dependent variable i.e. y. But, the predictor variables or parameters are multiple.