# Interpreting estimates from generalized models in R [duplicate]

I'm using R to run some generalized linear models (GLM) and I want to interpret the estimates.

If I use a GLM assuming Gaussian distribution with identity link, interpretation is easy: if the estimate for factor $x$ is $y$ then an increase of 1 of factor $x$ (if all other factors remain constant) will be estimated to result in a change in the response variable by $y$ units.

Now, if I run a GLM assuming Poisson distribution with log link, in the example above, will the response variable be expected to change by $y$ units, or by $\exp(y)$ units?

note: I'm getting the estimates from summary(model object)

## marked as duplicate by gung♦, Nick Cox, Peter Flom♦Mar 6 '14 at 17:03

For a unit change in $x$ you expect the response to change by a factor of $\exp(y)$. So say $\exp(y)=1.5$, then a unit change in $x$ is associated with a $(1.5-1)\times 100\% = 50\%$ increase in the response.