Multivariate Linear Regression

Linear regression with a multivariate response variable

When you need to include more than one response variable in a regression model, use a multivariate linear regression model. A multivariate linear regression model expresses a d-dimensional continuous response vector as a linear combination of predictor terms plus a vector of error terms with a multivariate normal distribution. You can use mvregress to create a multivariate linear regression model.

Partial least-squares (PLS) regression is a dimension reduction method that constructs new predictor variables that are linear combinations of the original predictor variables. To fit a PLS regression model that has multiple response variables, use plsregress.

Note

A multivariate linear regression model is different from a multiple linear regression model, which models a univariate continuous response as a linear combination of exogenous terms plus an independent and identically distributed error term. To fit a multiple linear regression model, use fitlm or fitrlinear.

Functions

`mvregress`	Multivariate linear regression
`mvregresslike`	Negative log-likelihood for multivariate regression
`plsregress`	Partial least-squares (PLS) regression

Topics

Set Up Multivariate Regression Problems
To fit a multivariate linear regression model using mvregress, you must set up your response matrix and design matrices in a particular way.
Multivariate General Linear Model
This example shows how to set up a multivariate general linear model for estimation using mvregress.
Fixed Effects Panel Model with Concurrent Correlation
This example shows how to perform panel data analysis using mvregress.
Longitudinal Analysis
This example shows how to perform longitudinal analysis using mvregress.
Partial Least Squares Regression and Principal Components Regression
Apply partial least squares regression (PLSR) and principal components regression (PCR), and explore the effectiveness of the two methods.
Multivariate Linear Regression
Large, high-dimensional data sets are common in the modern era of computer-based instrumentation and electronic data storage.
Estimation of Multivariate Regression Models
When you fit multivariate linear regression models using mvregress, you can use the optional name-value pair 'algorithm','cwls' to choose least squares estimation.
Partial Least Squares
Partial least squares (PLS) constructs new predictor variables as linear combinations of the original predictor variables, while considering the observed response values, leading to a parsimonious model with reliable predictive power.