We present a theory for resonance-tunneling magnetoresistance (MR) in ferromagnetic-insulator-nonmagnetic junctions. The theory sheds light on many of the recent electrical spin injection experiments, suggesting that this MR effect rather than spin accumulation in the nonmagnetic channel corresponds to the electrically detected signal. We quantify the dependence of the tunnel current on the magnetic field by quantum rate equations derived from the Anderson impurity model, with the important addition of impurity spin interactions. Considering the on-site Coulomb correlation, the MR effect is caused by competition between the field, spin interactions, and coupling to the magnetic lead. By extending the theory, we present a basis for operation of novel nanometer-size memories.