# bothsidesmodel.hotelling: Test blocks of beta are zero. In msos: Data Sets and Functions Used in Multivariate Statistics: Old School by John Marden

## Description

Performs tests of the null hypothesis H0 : β^* = 0, where β^* is a block submatrix of β as in Section 7.2.

## Usage

 `1` ```bothsidesmodel.hotelling(x, y, z, rows, cols) ```

## Arguments

 `x` An N x P design matrix. `y` The N x Q matrix of observations. `z` A Q x L design matrix `rows` The vector of rows to be tested. `cols` The vector of columns to be tested.

## Value

A list with the following components:

Hotelling

A list with the components of the Lawley-Hotelling T^2 test (7.22)

T2

The T^2 statistic (7.19).

F

The F version (7.22) of the T^2 statistic.

df

The degrees of freedom for the F.

pvalue

The p-value of the F.

Wilks

A list with the components of the Wilks Λ test (7.37)

lambda

The Λ statistic (7.35).

Chisq

The χ ^2 version (7.37) of the Λ statistic, using Bartlett's correction.

df

The degrees of freedom for the χ ^2

.

pvalue

The p-value of the χ ^2

.

`bothsidesmodel`, `bothsidesmodel.chisquare`, `bothsidesmodel.df`, `bothsidesmodel.lrt`, and `bothsidesmodel.mle`.
 ```1 2 3 4 5 6``` ```# Finds the Hotelling values for example 7.3.1 data(mouths) x <- cbind(1, mouths[, 5]) y <- mouths[, 1:4] z <- cbind(c(1, 1, 1, 1), c(-3, -1, 1, 3), c(1, -1, -1, 1), c(-1, 3, -3, 1)) bothsidesmodel.hotelling(x, y, z, 1:2, 3:4) ```