My model is an OLS with a single independent variable on cross-sectional data (n=3500). The relation is linear and there's a very good fit and there are no outliers, but the residuals' variance increases as x increases, clearly visible as a fan-shape in a residual-versus-predicted plot, so there's an issue with heteroskedasticity (which the Breusch-Pagan test confirms). The residuals' variance seems to be normally distributed and indeed symmetric above and below any value of x. I then calculated robust standard errors.
This model has two objectives:
- To predict y for out-of-sample values of x. That's why transforming the variables to reduce heteroskedasticity won't help much: I'll have to de-transform the results back to their original units and the variance in the errors will return.
- To convey the message that in this model specification there is heteroskedasticity with a specific pattern that as x increases, the variance in the errors increases too, making predictions of high value x's less reliable but within a certain calculable range (i.e. confidence intervals).
My questions are:
- can I use robust standard errors to calculate confidence intervals for out-of-sample x's?
- I'd like to plot the in-sample and out-of-sample variables together with the regression line and 95% confidence intervals obtained through robust standard errors. Is there any special issue to be aware of, or can they be plotted just like regular CIs?
- Just out of curiosity I also tried bootstrapped standard errors, which came out remarkably similar to the robust standard errors. Is there any reason to prefer one over the other?
- Is there any other way to deal with heteroskedasticity in a case like this without introducing another independent variable?
I hope these questions make sense, if not please bear with me as I'm quite new at this and I'd like to learn why. Thank you!