How to perform a Breusch-Pagan test?

To perform a Breusch-Pagan test, first run a regression model and obtain the residuals.

The Breusch-Pagan test is used to determine if there is heteroscedasticity in a regression model. Heteroscedasticity occurs when the variance of the residuals is not constant across all levels of the independent variable(s). This violates one of the assumptions of linear regression, which is that the variance of the residuals is constant.

To perform a Breusch-Pagan test, first run a regression model and obtain the residuals. Then, run a regression of the squared residuals on the independent variables. The null hypothesis is that there is no heteroscedasticity, and the alternative hypothesis is that there is heteroscedasticity.

The test statistic is calculated as follows:

BP = n * R^2

where n is the sample size and R^2 is the coefficient of determination from the regression of the squared residuals on the independent variables.

The test statistic follows a chi-squared distribution with k degrees of freedom, where k is the number of independent variables in the original regression model. The p-value can be obtained from a chi-squared distribution table or using statistical software.

If the p-value is less than the significance level (usually 0.05), then we reject the null hypothesis and conclude that there is heteroscedasticity in the model. If the p-value is greater than the significance level, then we fail to reject the null hypothesis and conclude that there is no evidence of heteroscedasticity in the model.