It has been known since the work by Claverie et al. (1982) that integrated-sunlight velocities measured with the resonance scattering technique show variations with time scales of weeks to months. The cause can be understood in terms of the effects of solar activity as was pointed out by Edmunds & Gough (1983) and Andersen & Maltby (1983). The latter authors included a model calculation based on sunspot areas which showed good promise of being able to quantitatively reproduce the observed velocity shifts. We discuss in this paper a new modeling effort based on daily magnetograms obtained at the 150-ft tower on Mt. Wilson. This type of database is more quantitative than sunspot area. Similar maps of magnetically sensitive quantities will be measured on a continuous time base as part of several planned helioseismology experiments (from space with the Solar Oscillations Imagery/Michelson Doppler Imager (SOI/MDI) experiment on the Solar and Heliospheric Observatory (SOHO), see Scherrer et al. (1991) or with ground-based networks, see Hill & Leibacher (1991)). We discuss the correlations between various magnetically sensitive quantities and develop a new model for the effects of magnetic field on line profiles and surface brightness. From these correlations we integrate the line profile changes over the solar surface using observed magnetic field strengths measured at lambda 5250.2. The final output is a new model for the effects of magnetic fields on integrated sunlight velocities which we compare with daily offset velocities derived from the International Research on the Interior of the Sun (IRIS)-T instrument at the Observatorio del Teide.