bp.test: Breusch-Pagan Test for Heteroscedasticity

In visStatistics: Automated Selection and Visualisation of Statistical Hypothesis Tests

Breusch-Pagan Test for Heteroscedasticity

Description

Performs the Breusch-Pagan test for heteroscedasticity in linear regression models. Tests the null hypothesis that the error variance is constant (homoscedasticity) against the alternative that the error variance depends on the fitted values.

Usage

bp.test(model)

Arguments

model

A fitted linear model object (from lm()).

Details

The Breusch-Pagan test regresses the squared standardized residuals on the fitted values. The test statistic is:

BP = n \cdot R^2

where:

• n = sample size

• R^2 = coefficient of determination from auxiliary regression of e_i^2 on \hat{y}_i

Under the null hypothesis of homoscedasticity, the test statistic follows a chi-squared distribution: BP \sim \chi^2(p-1) where p is the number of parameters in the model (including intercept).

Large values of the test statistic (small p-values) provide evidence against homoscedasticity.

Value

An object of class "htest" with components:

statistic	the value of the chi-squared test statistic.
parameter	degrees of freedom.
p.value	the p-value of the test.
method	a character string indicating the test performed.
data.name	a character string giving the name of the model.

References

Breusch, T. S., and Pagan, A. R. (1979). A simple test for heteroscedasticity and random coefficient variation. Econometrica, 47(5), 1287-1294. DOI: 10.2307/1911963

Examples

# Example with homoscedastic errors
set.seed(123)
x <- runif(100)
y <- 2 + 3*x + rnorm(100, sd = 1)
model1 <- lm(y ~ x)
bp.test(model1)  # Should not reject (p > 0.05)

# Example with heteroscedastic errors (variance increases with x)
set.seed(456)
x <- runif(100)
y <- 2 + 3 *x + rnorm(100, sd = 0.5 + 2*x)
model2 <- lm(y ~ x)
bp.test(model2)  # Should reject (p < 0.05)

visStatistics documentation built on May 13, 2026, 1:08 a.m.