Breusch-Pagan Test

Publication Date :

23 Jan, 2025

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Table Of Contents

Importance

The main purpose of the breusch-pagan test hypothesis is to find out heteroskedasticity. The state of systematic variations in the residuals' distribution or the model's error term is known as heteroskedasticity. A model's dispersion is dependent on at least one independent variable. This exists if there is residual variance present in the model. This gives the model more business and, as a result, raises the possibility of the model deviating from actual and effective outcomes. Through this, the results obtained become more reliable.

What Is Breusch-Pagan Test?

The Breusch-Pagan test is a statistical method for determining the presence of heteroscedasticity in a regression model using null and alternative hypotheses. The null hypothesis (H0) implies homoscedasticity, while the alternative hypothesis (HA) suggests heteroscedasticity, where the variance of the residual distribution is unequal.

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Conditions in which the residual variance is not equal over a certain range of measured values are referred to as heteroskedasticity. The test consists of regressing the original regression model's squared residuals on the predictor variables and evaluating the significance of the obtained coefficients. Heteroskedasticity is said to be present when the coefficients exhibit a statistically significant deviation from zero.

Key Takeaways

The Breusch-Pagan test is a statistical method for determining the presence of heteroskedasticity in a model. Trevor Breusch and Adrian Pagan developed it in 1979 to check if a linear regression model has heteroskedasticity.
The process entails fitting the data to a linear regression model, collecting the residuals, and squaring them.
The White test and the BP test both deal with finding heteroskedasticity. However, they differ in their approaches, with the White test allowing for more general heteroscedasticity patterns.

Breusch-Pagan Test Explained

The Breusch-Pagan test is a statistical method used to determine the presence of heteroskedasticity in a model. The test was developed in 1979 by Trevor Breusch and Adrian Pagan to check if a linear regression model has heteroskedasticity. It checks whether the variance of errors in the regression depends on the values of the independent variables and assumes normal error terms. Predictors, the model's fitted values, and a subset of independent variables can all be used to execute the test. Multiple tests and p-value correction options, such as the Bonferroni, Holm, and Sidak methods, are also included.

The process entails fitting the data to a linear regression model, collecting the residuals, and squaring them. It further involves regressing the squared residuals on the original models' predictor variables and determining the significance of coefficients. P-values below a cutoff point, often 0.05, signify heteroskedasticity. Because of its sensitivity to multicollinearity, it is advised to resolve it prior to administering the test.

The BP test assumes homoskedasticity, and if p_val < 0.05, it infers heteroskedasticity. If p_val > 0.05, it fails to reject the null, indicating the absence of heteroskedasticity. However, the test's weakness is that it assumes heteroskedasticity is a linear function of independent variables. So, failing to find evidence doesn't rule out a nonlinear relationship between independent variables and the error variance.

Examples

Let us look at a few examples to understand the concept of the breusch-pagan test for heteroskedasticity better.

Example #1

Dan is a researcher. Let's say Dan wishes to look at how age (an independent variable) and consumer spending (a dependent variable) relate to each other for various income groups. Dan suspects the presence of heteroscedasticity after doing a regression analysis. They use the BP test to verify this and confirm it through the breusch-pagan test calculator. The test would support heteroscedasticity, and suitable strategies are needed to address it if it reveals a substantial link between the squared residuals and the ages.

Example #2

ABC Ltd is an independent research organization. Researchers detect heteroscedasticity in a study investigating the relationship between gender (the dependent variable) and education (the independent variable) among a sample of participants. They investigate the connection between the squared residuals and education using the BP test. They use an online breusch-pagan test calculator for it. A substantial result from the test points to heteroscedasticity and the need for additional research using the right techniques to consider the fluctuating error variance. They might make decisions on a range of issues, including policy, based on the findings and their comprehension of variance.