  Stellar activity is the ultimate source of radial-velocity (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 $\log R'_{\rm HK}$ in detecting RV variations induced by stellar activity
in 15 slowly rotating ($v\sin i \leq 5$ km/s), weakly active ($\log R'_{\rm HK}
\leq -4.95$) solar-like stars observed with the high-resolution spectrograph
HARPS-N. 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), $\Delta V$,
and a new indicator $V_{\rm asy(mod)}$ 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. The considered indicators together with
the KR prove to be useful to detect activity-induced RV variations in $47 \pm
18$ 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 $V_{\rm
asy(mod)}$ are the best indicators, being useful in $27 \pm 13$, $13 \pm 9$,
and $13 \pm 9$ percent of the cases, respectively. The relatively limited
performances of the activity indicators are related to the very low activity
level and $v\sin i$ of the considered stars. For the application of our
approach to sun-like stars, a spectral resolution of at least $10^5$ and highly
stabilized spectrographs are recommended.
