# Multivariate Regression

Linear regression with a multivariate response variable

## Functions

 `mvregress` Multivariate linear regression `mvregresslike` Negative log-likelihood for multivariate regression `polytool` Interactive polynomial fitting `polyconf` Polynomial confidence intervals `plsregress` Partial least-squares (PLS) regression

## Examples and How To

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.

## Concepts

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.