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Aug 4, 2010 at 22:23 comment added Abhijit Yes, this is true, but for general regression problems (as opposed to anova or designed problems), X really isn't fixed but are observations from the underlying process. However, for the Poisson case, the point still holds, since mixtures of Poissons aren't necessarily Poisson.
Aug 4, 2010 at 15:28 comment added user28 Your last point about regression would only be true if X is random. If X is fixed then Y would also be a normal. no?
Aug 4, 2010 at 15:24 history answered Abhijit CC BY-SA 2.5