# Why is a Breusch-Pagan test returning significant heteroskedasticity when the fitted value chart indicates homoskedasticity?

I was working the results of a regression equation and I wanted to test to see if there was significant heteroskedasticity in the residuals. Checking the results of the graph of fitted values versus residuals using plot() produced a straight line that is almost exactly zero for most of the resulting graph and the data fits rather closely.

However, a studentized Breusch-Pagan test of the residuals using the bptest() function indicated significant heteroskedasticity (BP = 8.4085, df = 1, p = 0.0037). I can't figure out why the Breusch-Pagan test is returning significant heteroskedasticity. The regression doesn't look heteroskedastic, the regression line is pretty consistent overall but there are a few outliers in the right half of the graph. There isn't a clearly non-linear pattern like increasing variance in residuals with increasing fitted values like one would expect from heteroskedastic results. So then why is the Breush-Pagan test telling me that I have significant heteroskedasticity in my regression?

• Try other tests as well, see if they differ. For example, what does a White test for heteroskedasticity say or are the coefficients of power > 1 significant when regressing residuals on fitted values? Dec 30, 2020 at 11:02

But tests for model specification are mostly irrelevant. If the BP test "passed", it is simply a Type II error, because heteroscedasticity is true in reality when $$Y$$ and $$X$$ are related. Rather than test for heteroscedasticity, why not just model it? Then you will have a better idea as to the size of the effect. Use that information, along with subject matter considerations, supplemented with simulation study as needed, to decide whether to ignore it.