In a linear regression, should I include independent variables that is already known to be predictive of the dependent variable? I own an online shop and I'm trying to find the factors that would predict the profitability of a merchandise. To do this, I ran a linear regression with profit as the dependent variable. For the independent variables, I used all the data that I have recorded about each merchandise, which included things like the number of competitors, competitors' prices, year of production, etc. The idea is to create a list of criteria to determine if I should or should not sell a certain merchandise.
However, the result is always obvious: the selling price and buying cost are the only significant predictors (there are other statistically significant variables, but their beta is very low). Since they would obviously affect the profit, should I exclude them?
I did try to exclude them and the result is a lot more interesting, but I don't know if they are valid. I've also tried swapping the dependent variable from profit to the selling price and their results are identical.
 A: $$ \text{profit} = (\text{price}-\text{cost})\times\text{sales}. $$
I don't think it makes sense to regress profit on price or cost. Or sales, for that matter. We know the relationship above.
Instead, work on understanding the three drivers above. For instance, as a first approximation, you can treat cost as fixed, since you may only get to negotiate it in the medium term. That leaves us with your selling price and sales.
And of course price will have an impact on sales.
So I would recommend forecasting future sales, using price as a driver, e.g., using regression. Play around with different possible price points and find the one that maximized profit per the formula above. Feel free to include other drivers like your competitors' prices in the sales forecast (but note that you will of course need to forecast future competitors' prices).
The problem: if you are running this analysis to determine if you should or should not sell a certain merchandise, then you will most likely not yet have any data on the particular product you are looking at. So a straightforward regression approach won't help. Instead, look for "similar" products with known historical sales to train your models.
A: I think something that might help is slightly rephrase the question. I agree for profitability, the largest difference in buying vs selling price would be a good indicator (or perhaps the only indicator you might need), but that's hardly insightful. What I would do is to normalize the profit by the buying or selling prices. For example for each product, compute something like
Profit/(Buying Price) or Profit/(selling price)
And regress on the other facts. So a large coefficient would now tell you what is important for getting more profit for each dollar in the buying/selling price. 
