We consider the role of the third dimension in the conductivity of a quasi-two-dimensional electron gas (Q2DEG). If the transverse correlation radius of the scattering potential is smaller than the width of the channel, i.e. the width of the transverse electron density distribution, then virtual scattering to higher levels of the confinement potential becomes important, which causes a broadening of the current flow profile. The resulting conductivity is larger than that obtained from a quasi-classical two-dimensional Boltzmann equation. A magnetic field, parallel to the driving electric field, effectively adds strength to the confining potential. As a result, the width of the current flow profile decreases and a positive longitudinal magnetoresistivity of the Q2DEG is expected.