Breusch-Pagan Test for Detecting Heteroscedasticity in Regression Models

Tests the null hypothesis of homoscedasticity (constant error variance) against heteroscedasticity using the Koenker variant of the Breusch-Pagan test. The test statistic is \(BP = n \cdot R^2\) from an auxiliary regression of squared residuals on fitted values, asymptotically distributed as \(\chi^2\) with \(k\) degrees of freedom, where \(k\) is the number of predictors.

Usage

bpTest(fit)

Arguments

fit

a fitted lm() object.

Value

An object of class "htest" with the following components:

statistic

the BP test statistic.

parameter

degrees of freedom.

p.value

p-value based on the \(\chi^2\) distribution.

method

character string describing the test.

data.name

the formula of the fitted model.

References

Breusch, T.S. and Pagan, A.R. (1979). A simple test for heteroscedasticity and random coefficient variation. Econometrica, 47, 1287–1294.

Koenker, R. (1981). A note on studentizing a test for heteroscedasticity. Journal of Econometrics, 17, 107–112.

See also

lm()

Other test.regression: breuschGodfreyTest(), durbinWatsonTest(), hosmerLemeshowTest(), leCessieTest()

Examples

fit <- lm(Sepal.Length ~ Sepal.Width, data = iris)
bpTest(fit)
#> 
#> 	Breusch-Pagan test (Koenker)
#> 
#> data:  Sepal.Length ~ Sepal.Width
#> BP = 0.78243, df = 1, p-value = 0.3764
#>