Consider a (simple) Poisson regression . Given a sample where , the goal is to derive a 95% confidence interval for given , where is the prediction. Hence, we want to derive a confidence interval for the prediction, not the potential observation, i.e. the dot on the graph below > r=glm(dist~speed,data=cars,family=poisson) > P=predict(r,type="response", + newdata=data.frame(speed=seq(-1,35,by=.2))) > plot(cars,xlim=c(0,31),ylim=c(0,170)) > abline(v=30,lty=2)...