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 $M_{AGN_i}sim-20.2$.
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