Breusch-Pagan Test

Performs the Breusch-Pagan test against heteroskedasticity.

Usage

BreuschPaganTest(formula, varformula = NULL, studentize = TRUE, data = list())

Arguments

formula

a symbolic description for the model to be tested (or a fitted "lm" object).

varformula

a formula describing only the potential explanatory variables for the variance (no dependent variable needed). By default the same explanatory variables are taken as in the main regression model.

studentize

logical. If set to TRUE Koenker's studentized version of the test statistic will be used.

data

an optional data frame containing the variables in the model. By default the variables are taken from the environment which BreuschPaganTest is called from.

Details

The Breusch-Pagan test fits a linear regression model to the residuals of a linear regression model (by default the same explanatory variables are taken as in the main regression model) and rejects if too much of the variance is explained by the additional explanatory variables.

Under \(H_0\) the test statistic of the Breusch-Pagan test follows a chi-squared distribution with parameter (the number of regressors without the constant in the model) degrees of freedom.

Examples can not only be found on this page, but also on the help pages of the data sets bondyield, currencysubstitution, growthofmoney, moneydemand, unemployment, wages.

Value

A list with class "htest" containing the following components:

statistic

the value of the test statistic.

p.value

the p-value of the test.

parameter

degrees of freedom.

method

a character string indicating what type of test was performed.

data.name

a character string giving the name(s) of the data.

References

T.S. Breusch & A.R. Pagan (1979), A Simple Test for Heteroscedasticity and Random Coefficient Variation. Econometrica 47, 1287–1294

R. Koenker (1981), A Note on Studentizing a Test for Heteroscedasticity. Journal of Econometrics 17, 107–112.

W. Kraemer & H. Sonnberger (1986), The Linear Regression Model under Test. Heidelberg: Physica

See also

lm, ncvTest

Author

Achim Zeileis <Achim.Zeileis@R-project.org>

Examples

## generate a regressor
x <- rep(c(-1,1), 50)

## generate heteroskedastic and homoskedastic disturbances
err1 <- rnorm(100, sd=rep(c(1,2), 50))
err2 <- rnorm(100)

## generate a linear relationship
y1 <- 1 + x + err1
y2 <- 1 + x + err2

## perform Breusch-Pagan test
BreuschPaganTest(y1 ~ x)
#> 
#> 	studentized Breusch-Pagan test
#> 
#> data:  y1 ~ x
#> BP = 7.2534, df = 1, p-value = 0.007077
#> 
BreuschPaganTest(y2 ~ x)
#> 
#> 	studentized Breusch-Pagan test
#> 
#> data:  y2 ~ x
#> BP = 3.9268e-05, df = 1, p-value = 0.995
#>