I am running a GLM regression from the Poisson family. My dependent variable is the number of train accidents per month, and I define as offset variable the total number of train routes for that month. How could I interpret the coefficients of the independent variables? If I find a coefficient of 3.6 for one of my independent variables would it be correct to interpret as an increase of one unit of the independent variable leads to 3.6 times increase of the train accident probability? I am thinking that as the offset variable receives a coefficient equal to 1 I can form from the left side train accidents/ total train routes that is the probability of train accident. Thank you very much for help.