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 .