If there was unreacted magnesium left in the solution when you filtered it, the empirical formula of the magnesium oxide would be affected. This is because the mass of magnesium used in the reaction would be overestimated, leading to an incorrect molar ratio between magnesium and oxygen.
Recall that the empirical formula of magnesium oxide is given by the ratio of the number of moles of magnesium to the number of moles of oxygen in the compound. If there is unreacted magnesium left in the reaction mixture, this will increase the mass of the magnesium measured, but not the number of moles of magnesium. As a result, the molar ratio of magnesium to oxygen would be higher than it should be, leading to an empirical formula that contains too much magnesium relative to the amount of oxygen.
For example, if there was unreacted magnesium left in the reaction mixture, the mass of magnesium would be higher than the actual amount that reacted with oxygen, leading to a higher molar ratio of magnesium to oxygen. This would result in an empirical formula that contains more magnesium atoms than the true empirical formula, and consequently, fewer oxygen atoms than the true empirical formula.