  Using a sample of over 25000 spectroscopically confirmed quasars from the
Sloan Digital Sky Survey, we show how quasar variability in the rest frame
optical/UV regime depends upon rest frame time lag, luminosity, rest
wavelength, redshift, the presence of radio and X-ray emission, and the
presence of broad absorption line systems. The time dependence of variability
(the structure function) is well-fit by a single power law on timescales from
days to years. There is an anti-correlation of variability amplitude with rest
wavelength, and quasars are systematically bluer when brighter at all
redshifts. There is a strong anti-correlation of variability with quasar
luminosity. There is also a significant positive correlation of variability
amplitude with redshift, indicating evolution of the quasar population or the
variability mechanism. We parameterize all of these relationships. Quasars with
RASS X-ray detections are significantly more variable (at optical/UV
wavelengths) than those without, and radio loud quasars are marginally more
variable than their radio weak counterparts. We find no significant difference
in the variability of quasars with and without broad absorption line troughs.
Models involving multiple discrete events or gravitational microlensing are
unlikely by themselves to account for the data. So-called accretion disk
instability models are promising, but more quantitative predictions are needed.
