  We present the measurements and modelling of the small-to-intermediate scale
(0.1--25 Mpc/h) projected and three-dimensional (3D) redshift-space two-point
correlation functions (2PCFs) of local galaxies in the Sloan Digital Sky Survey
(SDSS) Data Release 7. We find a clear dependence of galaxy clustering on
luminosity in both projected and redshift spaces, generally being stronger for
more luminous samples. The measurements are successfully interpreted within the
halo occupation distribution (HOD) framework with central and satellite
velocity bias parameters to describe galaxy kinematics inside haloes and to
model redshift-space distortion (RSD) effects. In agreement with previous
studies, we find that more luminous galaxies reside in more massive haloes.
Including the redshift-space 2PCFs helps tighten the HOD constraints. Moreover,
we find that luminous central galaxies are not at rest at the halo centres,
with the velocity dispersion about 30% that of the dark matter. Such a relative
motion may reflect the consequence of galaxy and halo mergers, and we find that
central galaxies in lower mass haloes tend to be more relaxed with respect to
their host haloes. The motion of satellite galaxies in luminous samples is
consistent with their following that of the dark matter. For faint samples,
satellites tends to have slower motion, with velocity dispersion inside haloes
about 85% that of the dark matter. We discuss possible applications of the
velocity bias constraints on studying galaxy evolution and cosmology. In the
appendix, we characterize the distribution of galaxy redshift measurement
errors, which is well described by a Gaussian-convolved double exponential
distribution.
