  State of the art radial-velocity (RV) exoplanet searches are currently
limited by RV signals arising from stellar magnetic activity. We analyze solar
observations acquired over a 3-year period during the decline of Carrington
Cycle 24 to test models of RV variation of Sun-like stars. A purpose-built
solar telescope at the High Accuracy Radial velocity Planet Searcher for the
Northern hemisphere (HARPS-N) provides disk-integrated solar spectra, from
which we extract RVs and $\log{R'_{\rm HK}}$. The Solar Dynamics Observatory
(SDO) provides disk-resolved images of magnetic activity. The Solar Radiation
and Climate Experiment (SORCE) provides near-continuous solar photometry,
analogous to a Kepler light curve. We verify that the SORCE photometry and
HARPS-N $\log{R'_{\rm HK}}$ correlate strongly with the SDO-derived magnetic
filling factor, while the HARPS-N RV variations do not. To explain this
discrepancy, we test existing models of RV variations. We estimate the
contributions of the suppression of convective blueshift and the rotational
imbalance due to brightness inhomogeneities to the observed HARPS-N RVs. We
investigate the time variation of these contributions over several rotation
periods, and how these contributions depend on the area of active regions. We
find that magnetic active regions smaller than $60 \ \rm Mm^2$ do not
significantly suppress convective blueshift. Our area-dependent model reduces
the amplitude of activity-induced RV variations by a factor of two. The present
study highlights the need to identify a proxy that correlates specifically with
large, bright magnetic regions on the surfaces of exoplanet-hosting stars.
