  We use a sample of over 5000 active galactic nuclei (AGN) with extended
morphologies at z<0.8 from the Sloan Digital Sky Survey (SDSS) to study the
ensemble optical variability as a function of rest-frame time lag and AGN
luminosity with the aim of investigating these parameter relationships at lower
luminosities than previously studied. We compare photometry from imaging data
with spectrophotometry obtained weeks to years later in the Sloan g, r, and i
bands. We employ quasar and galaxy eigenspectra fitting to separate the AGN and
host galaxy components. A strong correlation between the variability amplitude
and rest-frame time lag is observed, in agreement with quasar structure
functions but extending to AGN several magnitudes fainter than previously
studied. The structure function slopes for our fainter AGN sample are slightly
shallower than those found in quasars studies. An anticorrelation with
luminosity is clearly detected, with lower luminosity AGN displaying greater
variability amplitudes. We demonstrate for the first time that this
anticorrelation extends to AGN as faint as $M_{AGN_i}\sim-18.5$, with a slight
trend towards shallower slopes at luminosities fainter than
$M_{AGN_i}\sim-20.2$.
