I was wondering why the sum of the residuals of a simple regression line must always equal zero. It simply blows my mind that it could always be true. Please help me wrap my mind around this concept.

I was wondering why the sum of the residuals of a simple regression line must always equal zero. It simply blows my mind that it could always be true. Please help me wrap my mind around this concept.

Uh... That's pretty much one of the only terms that doesn't evaluate to 0. \(\sum(x_i - \bar{x})\) is 0 though so when you multiply r(sy/sx) by 0 you get 0.