I am trying to test whether my regression has an issue of heteroscedasticity. After running a regression, I can clearly see that the residual plot has a pattern. After taking a log of the dependent variable the pattern is much, much reduced. The White's test on the original formula returns a p-value of 0.0004 before the transformation (the model with strong pattern in residuals), and a p-value of 0.08 after the log transformation.
I can see that the second model has less heteroscedasticity on the plot, but how do I interpret the results of White's test? Does the first value mean that we can reject that there is heteroscedasticity at (100-0.0004)% significance, while in the second model, we can reject it at, say, 95% confidence?