I'm convinced that homoscedasticity (of errors) is not an assumption (at least not explicit) for OLS regression. Also, even though WLS is advocated for heteroscedastic errors, OLS is not particularly bad, at least when the heteroscedasticity is limited as has been discussed by Gung in his answer. However, let's say that I encounter, while fitting an OLS using a feature X and an outcome variable y, heteroscedastic errors and go on to transform the variables, say using log transformation on both - X and y - and thus be able to beget fairly homoscedastic errors. Should I now give the results of OLS credence? Is it even a good practice? Or should I use WLS regression instead?
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EDIT:
Earlier I took X and y for integer counts.