Danilo -

What if you did a graphical residual analysis, with the predicted y values on the x-axis, and estimated residuals on the y-axis? You could try one regression for both genders together. If you color-code or otherwise delineate the points on the scatterplot by gender, that could indicate whether these data belong together or should be modeled separately.

You could also try modeling the sexes separately, and plot the two regression lines on the same chart. If each line had prediction interval limits plotted above and below it, you could see if the overlap between them is too great to model by gender. If the sample size for one sex is very small, the prediction interval limits for that line could be wide, and it may be obvious that you cannot model sexes separately, or at least not without more data. (A larger sample size reduces the model-part of the estimated variance of the prediction error, but not sigma for the estimated residuals.)

(A cross-validation of some sort could be used to check for overfitting.)

You might possibly want to try this without taking logs, which might help with interpretation of results.

For any regression of form y = y* + e, you might want to consider the following:

https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression

As part of that, please note

https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity,

and

https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity

and

https://www.researchgate.net/publication/333659087_Tool_for_estimating_coefficient_of_heteroscedasticityxlsx

Cheers - Jim