# Bootstrapping for multivariate linear regression models

## TL;DR

This paper extends bootstrap methods to multivariate linear regression models, enabling inference on the regression coefficient matrix with theoretical validation and practical examples.

## Contribution

It introduces multivariate bootstrap techniques for regression inference, extending Freedman's univariate methods without requiring proof, and validates them through simulations and real data.

## Key findings

- Bootstrap methods are valid for multivariate regression coefficients.
- Simulation studies support theoretical results.
- Real data example demonstrates practical applicability.

## Abstract

The multivariate linear regression model is an important tool for investigating relationships between several response variables and several predictor variables. The primary interest is in inference about the unknown regression coefficient matrix. We propose multivariate bootstrap techniques as a means for making inferences about the unknown regression coefficient matrix. These bootstrapping techniques are extensions of those developed in Freedman (1981), which are only appropriate for univariate responses. Extensions to the multivariate linear regression model are made without proof. We formalize this extension and prove its validity. A real data example and two simulated data examples which offer some finite sample verification of our theoretical results are provided.