I need to perform a semi-log regression (or log-level regression) for sales data.
For that, i choosed a theoretical model which matches with my regression goal. It looks like the following:
Y = exp(X1)+exp(X2)+exp(X3).. and so on
Y=Absolute Number of sales for brand i
X1 = Baseprice for brand i
X2...XN = Baseprice for every other brand
I know that the model should lead to coefficients that can be interpreted as elasticities (I need to get Own- and Cross-Price-Elasticities). But my Coefficients are much greater than 1 and the R-Squared Value indicates an extremely bad fit for some brands.
Maybe i am completely wrong with the interpretation? Maybe the fool is in the data?
Please excuse the wide ranged question, but i really dont know where to start fitting the model, so i am very thankful for any advice