I have some trouble understanding the normality assumptions of the linear model. I have found a wealth of information already, but some of it is contradictory and I couldn't find a definite answer to my questions, unfortunately.
1) I found that the residuals need to be normally distributed in order for the OLS to yield optimal results. Does this apply to the residuals in the population (according to Andy Field in his book "Discovering Statistics using SPSS", for example) or to the sampling distribution of the residuals?
2) Given a sufficiently large sample, am I right that we could only assume approximate normality in the sampling distribution of the residuals (CLT) and not the population? That is what confuses me about question 1): If it were the residuals in the population that were relevant, the CLT wouldn't provide an answer (I think).
3) Again in Andy Field's book, it is said that the parameter estimates must have a normal sampling distribution in order to allow significance testing and calculating CIs. In many other sources I looked at, the normality of the residuals is mentioned. Which one is right? I think that the statements might be equivalent concerning deterministic predictors, but couldn't the distribution of the parameter estimates be different than the distribution of the residuals if the predictors were stochastic?