Interpret GLM coefficients can be tricky, especially if you want to do that in a similar way like OLS. I personally prefer calculating the expected outcomes and plot the results, but if you’re really into that odds ratio stuffs. Here’s someway to do that.

In poisson regression, the regression coefficients are interpreted as the difference between the log of expected counts, where formally, this can be written as

Let do the exponential transformation:

The last equation can be interpreted as the percentage increase of the count number.

To give you a working example, let first run a poisson regression on an arbitrary R dataset. I use Zelig here, results are the same for glm function.

library(Zelig)
#1000 random poisson numbers, lambda = 0.1
y <- rpois(1000, 0.1)
#1000 random standard normal numbers
x <- rnorm(1000, 0, 1)
#combine them
mydata <- as.data.frame(cbind(x, y))
z.out <- zelig(y ~ x, model = "poisson", data = mydata)
summary(z.out)

The out puts are

Coefficients:
            Estimate Std. Error z value Pr(>|z|)
(Intercept) -2.44355    0.10740 -22.751   <2e-16
x            0.07271    0.10871   0.669    0.504

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 433.20  on 999  degrees of freedom
Residual deviance: 432.75  on 998  degrees of freedom
AIC: 606.59

We can then use the function exp(0.07271) - 1 to calculate the percentage changes. The results are

exp(0.07271) - 1
[1] 0.07541862

Basically means one unit increase of x increase the number of y by 7 percent.