ABSTRACT The radial velocity (RV) 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 RV 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 time-scale of one month and gives a standard deviation of the regression residuals of 1.04 m s−1, more than a factor of 2.8 smaller than the standard deviation of the original RV fluctuations. This result has been achieved thanks to the high-cadence and time continuity of the observations that simultaneously sample both the RV and the activity proxies.