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 Vasy(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 Vasy(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. Based on observations made with the Italian Telescopio Nazionale Galileo (TNG) operated on the island of La Palma by the Fundación Galileo Galilei of the INAF (Istituto Nazionale di Astrofisica) at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias.The IDL macro to compute the line profile indicators is also available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/616/A155