  Gaussian process regression is a widespread tool used to mitigate stellar
correlated noise in radial velocity time series. It is particularly useful to
search for and determine the properties of signals induced by small-size,
low-mass planets ($R_p<4R_{\rm \oplus}$, $m_p<10M_{\rm \oplus}$). By using
extensive simulations based on a quasi-periodic representation of the stellar
activity component, we investigate the ability in retrieving the planetary
parameters in 16 different realistic scenarios. We analyse systems composed by
one planet and host stars having different levels of activity, focusing on the
challenging case represented by low-mass planets, with Doppler semi-amplitudes
in the range 1-3 $m s^{-1}$. We consider many different configurations for the
quasi-periodic stellar activity component, as well as different combinations of
the observing epochs. We use commonly-employed analysis tools to search for and
characterize the planetary signals in the datasets. The goal of our
injection-recovery statistical analysis is twofold. First, we focus on the
problem of planet mass determination. Then, we analyse in a statistical way
periodograms obtained with three different algorithms, in order to explore some
of their general properties, as the completeness and reliability in retrieving
the injected planetary and stellar activity signals with low false alarm
probabilities. This work is intended to provide some understanding of the
biases introduced in the planet parameters inferred from the analysis of radial
velocity time series that contain correlated signals due to stellar activity.
It also aims to motivate the use and encourage the improvement of extensive
simulations for planning spectroscopic follow-up observations.
