---
title: "LaTeX code for documentation files"
author: "Travis Loux"
date: "April 13, 2018"
output:
  pdf_document: default
  html_document: default
---

# coefficient_manova

$$
\mathbf{Y}_m = \beta_{m0} + \mathbf{X}_m \mathbf{B}_m
$$

$$
\mathbf{B}_1 = \mathbf{B}_2 = ... = \mathbf{B}_m
$$


# coef_welch

\begin{align*}
y_i &= \beta_{10} + \beta_{11}x_{i1} + \beta_{12}x_{i2} + \beta_{1i} \cr
y_i &= \beta_{20} + \beta_{21}x_{i1} + \beta_{22}x_{i2} + \beta_{2i} \cr
y_i &= \beta_{30} + \beta_{31}x_{i1} + \beta_{32}x_{i2} + \beta_{3i}
\end{align*}

$H_0: \beta_{11} = \beta_{21} = \beta_{31}$

$x_1$

$x_2$

