Multivariate Linear Regression

Abstract

This chapter will show that multivariate linear regression with $m \ge 2$ response variables is nearly as easy to use, at least if m is small, as multiple linear regression which has 1 response variable. For multivariate linear regression, at least one predictor variable is quantitative. Plots for checking the model, including outlier detection, are given. Prediction regions that are robust to nonnormality are developed. For hypothesis testing, it is shown that the Wilks’ lambda statistic, Hotelling Lawley trace statistic, and Pillai’s trace statistic are robust to nonnormality.