# semi-log (log linear) regression model

I know there are different reasons for choosing a particular model (e.g. log log, semi log, lin log).

I read somewhere that the semi log (where only the log of Y is taken) corresponds to a multiplicative/additive relationship.

My dependent variable are market shares which growths/operates multiplicatively (I believe) and most of my independent variables are dummies & some variables are related to culture (which is expected to change slowly).

I am not sure if these reasons are good/strong enough for choosing a semi log model?

Also how would you interpret dummy variables in a semi log regression where only the logarithm of Y is taken?

• log Y as a linear function of some predictors corresponds to an exponential model. If it helps to call that multiplicative-additive, so be it. As market share presumably can't exceed 1, using the exponential model won't (can't) be a tremendously plausible model unless the shares are all $\ll 1$. I'd expect something more like logit in general terms. – Nick Cox May 2 '17 at 15:32
• Indicator variables (dummy variables in your terminology) have shift and tilt effects in the space in which they are fitted. You leave them as they come; there is no question of transforming them. – Nick Cox May 2 '17 at 15:35
• @NickCox the highest share would be 40 percent (thus 0,4) – Jennifer4 May 2 '17 at 15:43
• Plotting exponential and logistic functions will give you some insight into the approximation (probably quite good). Naturally, if the outcome is shares that add to 1, across subsets of observations, or the entire dataset, then that constraint might be important too. – Nick Cox May 2 '17 at 15:57
• Sorry I don't completely understand what you mean. – Jennifer4 May 2 '17 at 17:38