No, the order of the rows (observations) does not determine any of the regression results. Can you reproduce this result? Have you started over and made sure that the only change is the order of the rows? You did not exclude rows in one case but not the other?
Example: Big Class data table, Bivariate platform, regress :weight by :height with simple linear regression, plot residuals.
Original row order.
Randomly re-ordered rows.