  The kinematics of satellite galaxies reflect the masses of the extended dark
matter haloes in which they orbit, and thus shed light on the mass-luminosity
relation (MLR) of their corresponding central galaxies. In this paper we select
a large sample of centrals and satellites from the Sloan Digital Sky Survey
(SDSS) and measure the kinematics (velocity dispersions) of the satellite
galaxies as a function of the $r$-band luminosity of the central galaxies.
Using the analytical framework presented in Paper I, we use these data to infer
{\it both} the mean and the scatter of the MLR of central galaxies, carefully
taking account of selection effects and biases introduced by the stacking
procedure. As expected, brighter centrals on average reside in more massive
haloes. In addition, we find that the scatter in halo masses for centrals of a
given luminosity, $\sigma_{\log M}$, also increases with increasing luminosity.
As we demonstrate, this is consistent with $\sigma_{\log L}$, which reflects
the scatter in the conditional probability function $P(L_c|M)$, being
independent of halo mass. Our analysis of the satellite kinematics yields
$\sigma_{\log L}=0.16\pm0.04$, in excellent agreement with constraints from
clustering and group catalogues, and with predictions from a semi-analytical
model of galaxy formation. We thus conclude that the amount of stochasticity in
galaxy formation, which is characterized by $\sigma_{\log L}$, is well
constrained, is independent of halo mass, and is in good agreement with current
models of galaxy formation.
