Interpretation of log transformed predictor
I have a regression equation (below). In the raw form, my Y dependent variable is in days (length of stay in days). I transformed the dependent variable using a natural log transformation. I want to know how to interpret the equation’s coefficients. Would I say, for the year variable, that an increase of one unit in Year would result in a 16.7 percentage increase in length of stay? That does not make sense to me, because it is a percentage and not “days”. I supposed it converts to percentages due to the transformation calculation.
Or would I say that an increase of one unit in Year would result in an increase of 16.7 day in the length of stay. And can you help me with the interpretation of the intercept and for a dummy coded variable (
Gender: 1=male; 0=Female)?
LOGLOS = 3.27+0.167(Year) – 0.43(Gender) -.31 (Income) -0.001 (Score) + .576(White).