We investigate the activity-induced signals related to rotation and magnetic cycles in late-type stars (FGKM) and analyse the Ca II H&K, the H α and the radial velocity time series of 55 stars using the spectra from the HARPS public data base and the light curves provided by the All Sky Automated Survey. We search for short-term and long-term periodic signals in the time series of activity indicators as well as in the photometric light curves. Radial velocity data sets are then analysed to determine the presence of activity-induced signals. We measure a radial velocity signal induced by rotational modulation of stellar surface features in 37 stars, from late-F-type to mid-M-type stars. We report an empirical relationship, with some degree of spectral type dependency, between the mean level of chromospheric emission measured by the log _{10}(R^' }_{HK}) and the measured radial velocity semi-amplitude. We also report a relationship between the semi-amplitude of the chromospheric measured signal and the semi-amplitude of the radial velocity-induced signal, which strongly depends on the spectral type. We find that for a given strength of chromospheric activity (i.e. a given rotation period), M-type stars tend to induce larger rotation-related radial velocity signals than G- and K-type stars.