  The radial velocity of the Sun as a star is affected by its surface
convection and magnetic activity. The moments of the cross-correlation function
between the solar spectrum and a binary line mask contain information about the
stellar radial velocity and line-profile distortions caused by stellar
activity. As additional indicators, we consider the disc-averaged magnetic flux
and the filling factor of the magnetic regions. Here we show that the
activity-induced radial-velocity fluctuations are reduced when we apply a
kernel regression to these activity indicators. The disc-averaged magnetic flux
proves to be the best activity proxy over a timescale of one month and gives a
standard deviation of the regression residuals of 1.04 m/s, more than a factor
of 2.8 smaller than the standard deviation of the original radial velocity
fluctuations. This result has been achieved thanks to the high-cadence and time
continuity of the observations that simultaneously sample both the radial
velocity and the activity proxies.
