# What are the three forms of the Park test for heteroskedasticity?

I understand the Park test for heteroskedasticity has three different forms. The best known one is in a log form: LN(Residual^2) = intercept + slope (LN(X)). The second one is in a linear form: Residual^2 = intercept + slope (X). In both cases if the regression coefficient of X (the independent variable you are testing for heteroskedasticity) then you have to reject the null hypothesis that residuals are homoskedastic relative to the levels of the tested independent variable X. Nevertheless, do you know how well established is the second form, the linear one? And, also what is the third form? For model variables I need to test, it is key that I can use the linear form because many of those variables are percent changes that can't be logged.

• Where did you see that the Park test has 3 forms? Can you provide a reference? – gung - Reinstate Monica Dec 10 '14 at 18:53
• The first form is a version of the spread vs level plot. IMHO it's an inferior choice because it does not use robust estimates of spread and it really shouldn't have an intercept, but for "nicely behaved" residuals and quick-and-dirty work it should be ok. As you note, it's applicable only when one intends to make Box-Cox transformations of a (necessarily) positive response variable. – whuber Dec 10 '14 at 19:20
• gung, the source I found mentioning the three forms of the test was not "well sourced." That's actually part of my question. Can one disclose what the 3d form is? And, based on good reference. – Sympa Dec 11 '14 at 22:41