# Test multiple linear restrictions simultaneously

`test_linear_restrictions.Rd`

`test_linear_restrictions`

takes a set of regression results and
tests multiple linear restrictions simultaneously.

## Arguments

- regresults
A list containing two items:

`coefficients`

, which is a vector of coefficient estimates, and`vcov`

, which is the variance-covariance matrix of the coefficient estimates.- R
A matrix of linear restrictions. Each row of

`R`

represents a different linear restriction. R should have the same number of columns as`length(regresults$coefficients)`

.- c
A vector of constants, equal to the number of rows in

`R`

. This is what we are testing that each linear restriction is equal to.

## Value

A list with the following items:

W: The Wald (chi-square) statistic

p_value: The p-value of the test

## Examples

```
# test both that the returns to one year of education are
# equal to ten years of age, and that the intercept is zero
model <- estimatr::lm_robust(earnwk ~ age + educ, data = cps)
R <- matrix(c(0, -10, 1, 1, 0, 0), nrow = 2, byrow = TRUE)
test_linear_restrictions(model, R)
#> $W
#> [1] 45.18291
#>
#> $p_value
#> [1] 1.54403e-10
#>
```