What I know to begin with is that the sum will be 0 if there is a y-intercept b0 , why is that? my book doesnt say and can't figure it out. I also know that an importantant assumption for the OLS estimators to be BlUE is that x and the erros can't be corralated otherwise the estimators would be biased. This correlation assumption may entail problems so we take one step further and we assert that by combining E(u)=0 ( an assumption that the book doesnt explain where it comes from) + E(u|x) - the average value of u doesnt depend on the value of x) , we get E(u)=0=E(u|x). so this assumption is somehow related to that the sum of residuals should be 0. But how do I mathematically prove that?
Sorry if I have been a bit unclear but I am a quite confused, it seems all this topic quite redundant to me , like of the assumptions that jusify the method are infered from the method itself..