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...

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Estimating a proportion at first looks elementary. Hail to aymptotics, right? Well, initially it might seem efficient to iuse the fact that . In other words the classical confidence interval relies on the inversion of Wald’s test. A function to ease the computation is the following (not really needed!). waldci<- function(x,n,level){ phat<-sum(x)/n results<-phat + c(-1,1)*qnorm(1-level/2)*sqrt(phat*(1-phat)/n) print(results) } An exact confidence interval is