My question may sound trivial but here it goes:

When doing a sample regression by the ordinary least squares method, does the sum (nonsquared! ) of the residuals have to be equal to zero??

Here's what I know. If we have numerous "y observations" per x, one important assumption is that the residuals conditional on a given X follow an identical distribution usually with mean 0 (which also suggests that the sum of the residuals is 0)

i.e

Σ e_ij= 0 where j is the iterating term and where

e_ij = (Yj - Y(estimated)) for a given X_i

However when we do a sample regression we usually have one Y observation per X. With the ordinary least squares method we try to :

min Σ (e_i)^2

Does this however mean that the sum of the residuals will be equal to 0?

i.e

Σ e_i = 0 ??

Thanks