  Our former study on the empirical relations between the Fourier parameters of
the light curves of the fundamental mode RR Lyrae stars and their basic stellar
parameters has been extended to considerably larger data sets. The most
significant contribution to the absolute magnitude M_v comes from the period P
and from the first Fourier amplitude A_1, but there are statistically
significant contributions also from additional higher order components, most
importantly from A_3 and in a lesser degree from the Fourier phase phi_51. When
different colors are combined in reddening-free quantities, we obtain basically
period-luminosity-color relations. Due to the log T_eff (B-V, log g, [Fe/H])
relation from stellar atmosphere models, we would expect some dependence also
on phi_31. Unfortunately, the data are still not extensive and accurate enough
to decipher clearly the small effect of this Fourier phase. However, with the
aid of more accurate multicolor data on field variables, we show that this
Fourier phase should be present either in V-I or in B-V or in both. From the
standard deviations of the various regressions, an upper limit can be obtained
on the overall inhomogeneity of the reddening in the individual clusters. This
yields sigma_E(B-V)}< 0.012 mag, which also implies an average minimum
observational error of sigma_V > 0.018 mag.
