Aims. Stellar activity is the ultimate source of radial-velocity (hereinafter RV) noise in the search for Earth-mass planets orbiting late-type main-sequence stars. We analyse the performance of four different indicators and the chromospheric index log R^′_HK in detecting RV variations induced by stellar activity in 15 slowly rotating (υ sin i ≤ 5 km s⁻¹), weakly active (log R^′_HK ≤ −4.95) solar-like stars observed with the high-resolution spectrograph High Accuracy Radial velocity Planet Searcher for the Northern hemisphere (HARPS-N). Methods. We consider indicators of the asymmetry of the cross-correlation function (CCF) between the stellar spectrum and the binary weighted line mask used to compute the RV, that is the bisector inverse span (BIS), ΔV, and a new indicator V_asy(mod) together with the full width at half maximum (FWHM) of the CCF. We present methods to evaluate the uncertainties of the CCF indicators and apply a kernel regression (KR) between the RV, the time, and each of the indicators to study their capability of reproducing the RV variations induced by stellar activity. Results. The considered indicators together with the KR prove to be useful to detect activity-induced RV variations in ~47 ± 18 percent of the stars over a two-year time span when a significance (two-sided p-value) threshold of one percent is adopted. In those cases, KR reduces the standard deviation of the RV time series by a factor of approximately two. The BIS, the FWHM, and the newly introduced V_asy(mod) are the best indicators, being useful in 27 ± 13, 13 ± 9, and 13 ± 9 percent of the cases, respectively. The relatively limited performances of the activity indicators are related to the very low activity level and υ sin i of the considered stars. For the application of our approach to sun-like stars, a spectral resolution allowing λ/Δλ ≥ 10⁵ and highly stabilized spectrographs are recommended.