Regression with double-counting I am using regression to model production cost based on multiple regressors. Two of them are related, but may have different effects: number of products made and number of unique products made. I am worried about double-counting if I put both on the RHS. Is there a problem with including both? Or is there a method to correct for potential double-counting?
 A: The solution might be the following: having $N$ possible products, to consider $N$ regressors where each would quantify how many products have been produced in a specific category.
If this is not possible, you could use some of the feature selection approaches to test whether one of both parameters can be ignored. This strongly depends on the data: if each product is produced just once, then the number of unique products might play no role. On the other hand, if the vectors are not linearly dependent, I would use both of them: speaking about costs, you the costs can be lower if you produce 10 products of the same type than 1 product in 10 types: could be related to some setup of the machines. Thus, the final dependency could be:
(Number of unique)x(costs for preparing a machine to produce a different type) + (Number of all)x(costs for production an item).
However, there could be some nonlinear dependencies, too.
A: It’s completely acceptable to have correlated predictor variables. 
Your interpretation of the coefficients can get bizarre, since it doesn’t make sense to hold one variable constant while you take the derivative of the other unless they’re independent, but you’re fine for using correlated variables to make predictions.
You may find that it’s better to include only one of the two, but that comes down to both your knowledge of the process (having a hunch) and playing around with various models.
(When I say better with one instead of both, I mean out-of-sample, which I suggest checking for predictive modeling. In-sample, MSE will decrease if you add an additional parameter.)
