I know that it's not right to enter variables having multicollinearity (high correlation) into a regression analysis. But if I'm using backward stepwise regression could I add all the highly correlated predictors and expect the best predictors to remain in the model at the end or the analysis could go awry? My experience with my own data resulted in removal of the redundant (with multicollinearity) variables thus it seems there's no problem, but I want to report my method and I want to know whether I did it right or it resulted just by chance. So to say briefly:
Is it right to enter variables with multicollinearity into a backward stepwise regression analysis?