One of the methods of doing Austrian economics is imaginary constructions of economic situations. When utilizing this method, the economist ponders how certain economic factors will affect other economic factors. For example, I want to think about how the rise in a price of a substitute good will affect the demand of the good in question. Another way to put it would be, how will a decrease in the price of chicken affect the demand of turkey. When doing this, the economist has to hold certain variables constant in a thought experiment. Using the chicken and turkey example, one must hold constant the fact that it is not November. This is a good tool when constructing economic theory, no one will deny that. However, the reason why Chicago School economists use regression is to find out the degree of which a price decrease in chicken will affect the demand in Turkey.
Consider how a Chicago School economist will handle this problem. First, they will make use of the imaginary construct the same way an Austrian economist would. Obviously, a decrease in the price of chicken should decrease the demand in turkey because they are substitute goods. Unless of course it is November where the demand of turkey sky rockets regardless of substitute goods. So at this point the Austrian and the Chicago Schooler should have arrived at the same point. Here is where regression comes in. The next step for the Chicago schooler is to collect chicken prices and quantities of turkey sold over the same geographical areas and time periods. This is where they will find the degree of how much price changes in chicken actually affect the demand in turkey. It might be very large or very small. What we can do to further test the affects the month of November variable has on this is introduce a "dummy variable," which basically tells us how much November increases the demand for turkey.
Why is this useful? If a firm selling chicken and turkey has found turkey sales are declining they can now make a better estimate of how much they need to increase the price of chicken in order to increase the demand of turkey. In my view, the theory is vitally important but the firm is more interested in the results produced by the regression. Another reason why regression is so useful is because it holds the other variables constant in order to see your imaginary construct as values. For example, if the price of chicken decreases by 50 cents the demand of turkey will decrease by .5%, holding all other variables constant.
Why Mises would claim that if we were to do a study using regression we learn nothing other than the amount price changes in chicken will affect the demand for turkey in that particular time period and geographical area is misguided at best. In my view, a firm can gain vast amounts of information by using regression methods. The firm learns how to change the demand for turkey by manipulating chicken prices, ceteris paribus. Obviously we cannot change them based on quantitative certainty but it gives important insight insight nonetheless.