Has the Heteroskedasticity been resolved? - r

Question

I created a linear regression model of two continuous variables Income and Expense. The former is the independent variable and the latter is the dependent. I initially found that there was heteroskedasticity in the model after looking at the spread of the data and then calculating a post-estimation function (Breusch-Pagan test) which calculated that p-value < 2.2e-16. Since this was less than the significance level of 0.05 I rejected the null hypothesis that there was homoskedasticity and concluded that heteroskedasticity does exist.
In trying to correct the heteroskedasticity I used the box-cox transformation on the dependent variable using the following code:
lmodI = lm(LCF2010$expense ~ LCF2010$income, data=newexcel) #my original Original model
boxcox(lmodI, lambda = seq(0,0.5,0.1)) #Found the ideal lambda value to be 0.35
newexcel <- cbind(newexcel, newexcel$expense^0.35) #Added the new variable to the original dataframe
names(newexcel)[14] <- "Yprime" #Changed the column name to "Yprime"
lmodINew <- lm(Yprime ~ income, data=newexcel) #Created the new linear model
I then decided to compare the old model to the new to see if I had corrected the heteroskedasticity - creating the following diagnostic plots:
original model:
new model:
I also ran the Breusch-Pagan test for the new model and found that the p-value stayed the same at p-value < 2.2e-16. This and the fact that I couldnt see much of a difference between the two diagnostic plots has confused me as I expected the method I used to fix the heteroskedasticity.
I expected the p-value for the new model to be higher than 0.05 so I couldn't reject the null hypothesis and thus have homoskedasticity. Have I done something wrong during the box-cox transformation?

Answer 1

From your plots it seems you have a couple of hundred of observations. Remember that the Breusch-Pagan test is essentially the number of observations times R-squared, where the R-squared comes from the auxiliary regression of the residuals on the regressors (see eqn. [8.16] in Wooldridge 2015). If n is large, this statistic will always reject the null hypothesis.