Why is the the t distribution not suitable in here? Also, just a general question, for binomial the expected probability of component damage is p. It doesnt seem like Y is doing anything here, for the prediction is about p, not Y. Sure, p is used in Y's distribution, but to predict mean Y, you're not directly using mu but n*p.Sorry this is badly framed, but I just want to say it's not very intuitive.
Hello The t-result we use in linear regression comes from assuming normality of the data - which is not something that we assume in general for a GLM. So, we use ML estimator theory. See Section 5.2 of Chapter 13. If you have a look at section 2.3 of the notes, you'll see that a perhaps more intuitive set up is where we consider the response to be the proportion of success rather than the number of successes itself. In this case, a prediction about p perhaps feels more intuitive. Hope that helps Andy
