Normal equations State that u _i=0, and _(i=1)^nx_i u _i =0; if they are satisfied by the estimated errors u _i, we can be certain that our assumptions E[u]=0 and E[ux]=0 hold. State that u _i y_i=0, and _(i=1)^nx_i^' x_i u _i =0; if they are satisfied by the estimated errors u _i, we can be certain that our assumptions E[u]=0 and E[ux]=0 hold State that u _i=0, and _(i=1)^nx_i u _i =0. OLS estimator ensures that they always hold. State that u ^' u =0, and X'u =0; it is important to always check if they are satisfied by the data. State that u _i=0, and _(i=1)^nx_i u _i =0; they are satisfied only if there is no heteroscedasticity