I am attending a data analysis class and some of my well-rooted ideas are being shaken. Namely, the idea that the error (epsilon), as well as any other sort of variance, applies only (so I thought) to a group (a sample or whole population). Now, we're being taught that one of the regression assumptions is that the variance is "the same for all individuals". This is somehow shocking to me. I always thought that it was the variance in Y accross all values of X that was assumed to be constant.
I had a chat with the prof, who told me that when we do a regression, we assume our model to be true. And I think that's the tricky part. To me, the error term (epsilon) always meant something like "whatever elements we don't know and that might affect our outcome variable, plus some measurement error". In the way the class is taught, there's no such thing as "other stuff"; our model is assumed to be true and complete. This means that all residual variation has to be thought of as a product of measurement error (thus, measuring an individual 20 times would be expected to produce the same variance as measuring 20 individuals one time).
I feel something's wrong somewhere, I'd like to have some expert opinion on this... Is there some room for interpretation as to what the error term is, conceptually speaking?