Interpretation of the coefficient of a dummy variable in a regression with log-transformed outcome I want to interpret the models (2) Pool variable. It equals 1 if the house has a pool and 0 if not. The relation between the dependent variable and the Pool variable is a log-linear that means ∆y/y = b1*∆X whereby X is a dummy variable D so the change ∆D can only be 1 or -1 if I am not wrong. So if a house has a pool the price will rise by 7.1% and if house has already a pool and it gets destroyed or something like this the price will decrease by 7.1%. Is this interpretation correct?


The interpretation of the coefficient of pool in the second model is: Compared to houses that have no pool, the geometric mean of the price for houses with pools is $100(\exp(0.071) - 1)\% = 7.36\,\%$ higher, all else being held constant. In other words, $\exp(\beta)$ is the ratio of the geometric means of pool/no pool (or generally, current level/reference level of the categorical variable). For more information, see this page.
