How to deal with semi-discrete regressors? I've aggregated a dataset based on some research I've done regarding Battery Electric Vehicles. Three of my regressors however are throwing me off: Available BEV models in the market, Estimated Average BEV purchase price, and Estimated_Average_purchased_BEV_range. Because these numbers didn't change very often from quarter to quarter, I get QQ-plots that look step-like. I tried including an image, but I'm guessing I can't post images just yet.
From my reading, it seems like normalizing discrete variables isn't necessary. I don't think these are truly discrete variables, but since they resemble them should I treat them as such?
Thank you, and sorry that I'm terribly confused!
 A: Regression analysis is undertaken conditional on the regressors, so it is not really a problem what distribution these values have.  If they are bunched into groups of values that recur over multiple periods, that is fine.  Regression can accommodate continuous regressors with unique values, or discrete regressors, or binary regressors, and even a fixed column of ones for the intercept term.
Depending on the full set of regressors, the presence of one or more regressors which recur at the same values may lead to some bunching on the regressor axes in your diagnostic plots; that does not invalidate the regression or change the interpretation of the plots.  However, it would be strange to see exact step-like behaviour in the QQ plots, since this plot compares the empirical quantiles of the residuals to their assumed model form.  The residuals are affected both by the regressors but also by the response variable, so if you are getting stepping behaviour in this plot, it is likely to be because you have a response variable that is also taking on the same value over multiple periods.  (This would be something worth checking.)  If this is the case then it falsifies the assumption of independent normally distributed error terms, but your regression results might be robust to this.
