# What is criterion for Breusch-Pagan test?

Could someone explain to me what is criterion for interpretation of Breusch-Pagan test?

I have applied ncvTest test from the package car in R on a simple linear regression with one predictor variable e.g. lm(weight~size). I have the following result:

Chisquare = 7.182687 Df = 1 p = 0.007361039

I see in other questions that p = 0.073459 implies heteroscedasticity while p = 0.6283239 and p-value = 0.858 imply homoscedascity. By looking at these samples I would assume that my result set is heteroscedasticit, but I would like to know is p value only criterion and is there some boundary value for yes/no decision (i.e. some p value between 0.007 and 0.6).

Does Chisquare value matters?

The Breush-Pagan test creates a statistic that is chi-squared distributed and for your data that statistic=7.18. The p-value is the result of the chi-squared test and (normally) the null hypothesis is rejected for p-value < 0.05. In this case, the null hypothesis is of homoskedasticity and it would be rejected.

For any hypothesis test, the decision rule is:

• If p-value < level of significance (alpha); then null hypothesis is rejected.
• If p-value > level of significance (alpha); then we fail to reject the null hypothesis.

Level of significance (alpha) is chosen by the researcher. How to chose alpha (also known as probability of rejecting the null when it is true/type_I error) is altogether a different issue. It depends on "how sure you want to be before rejecting a null" Most common value of alpha is 0.05

Now, for BP test, the null assumes homoskedasticity. So if p_val < 0.05 (or your chosen alpha value); you reject the null and infer the presence of heteroskedasticity and if p_val > 0.05 (or your chosen alpha value); you fail to reject the null and conclude there may not be heteroskedasticity.

Note: A weakness of the BP test is that it assumes the heteroskedasticity is a linear function of the independent variables. Failing to find evidence of heteroskedasticity with the BP doesn’t rule out a nonlinear relationship between the independent variable(s) and the error variance.

White test provides a flexible functional form that’s useful for identifying nearly any pattern of heteroskedasticity. It allows the independent variable to have a nonlinear and interactive effect on the error variance.

So most commonly used test for homoskedasticity is White test.