I have a heavily positively skewed continuous outcome variable y. Therefore I log transformed it to achieve normality.
My interest is to assess the association between a few explanatory variables (one binary variable (Yes/No), one ordinal variable (0,1,2,3,4), two count variables) on y. I used generalised linear regression and treated the binary and the ordinal variables as categorical variables IN Proc GLM in SAS. The two count variables have many zeroes. The R squared is extremely small (~20%). The residual doesn't indicate severe departure from normality. Multicollinearity was assessed by using tolerance, variance inflation index and condition index. All this measures are around 1 so collinearity is not a problem here as far as I understand. However, there is an indication of heteroscedasticity from the residual vs predicted plot. As the predicted value increases, the variability of the residuals gets smaller.
Is being homoscedastic very important in my case? If so, how can it be resolved? I tried following the steps in this document, but the heteroscedasticity still presents.