Poisson model offset

I'm using the dataset road (in the MASS package) that concerns the annual deaths in road accidents for some of the US states. It includes:

• deaths: number of deaths;
• drivers: number of drivers (in 10,000s);
• popden: population density in people per square mile;
• rural: length of rural roads, in 1000s of miles.
• temp: average daily maximum temperature in January.
• fuel: fuel consumption in 10,000,000 US gallons per year.

I have part of the R

• See the answer below for an explanation for why one uses an offset. But notice that in this case the offset is log(drivers*10000) because you specified it as such in the model. – HorseOfTheYear Nov 4 '15 at 20:43
• Can you clarify what it is about the log(drivers*1000) that is confusing to you? Are you wondering why the log is taken? Or why drivers is being used as an offset? Or why it's multiplied by 10k? – gung Nov 4 '15 at 20:47
• Sorry I must have accidentally got rid of it – user3443632 Nov 4 '15 at 20:55

With a log-link the linear model is for the log of the conditional mean of the Poisson ($\log(\mu)=\eta=X\beta$). The GLM offset applies on the scale of the linear predictors (in the model it's essentially another predictor which has its coefficient set to 1).