  We investigate faint radio emission from low- to high-luminosity Active
Galactic Nuclei (AGN) selected from the Sloan Digital Sky Survey (SDSS). Their
radio properties are inferred by co-adding large ensembles of radio image
cut-outs from the FIRST survey, as almost all of the sources are individually
undetected. We correlate the median radio flux densities against a range of
other sample properties, including median values for redshift, [OIII]
luminosity, emission line ratios, and the strength of the 4000A break. We
detect a strong trend for sources that are actively undergoing star-formation
to have excess radio emission beyond the ~10^28 ergs/s/Hz level found for
sources without any discernible star-formation. Furthermore, this additional
radio emission correlates well with the strength of the 4000A break in the
optical spectrum, and may be used to assess the age of the star-forming
component. We examine two subsamples, one containing the systems with emission
line ratios most like star-forming systems, and one with the sources that have
characteristic AGN ratios. This division also separates the mechanism
responsible for the radio emission (star-formation vs. AGN). For both cases we
find a strong, almost identical, correlation between [OIII] and radio
luminosity, with the AGN sample extending toward lower, and the star-formation
sample toward higher luminosities. A clearer separation between the two
subsamples is seen as function of the central velocity dispersion of the host
galaxy. For systems with similar redshifts and velocity dispersions, the
star-formation subsample is brighter than the AGN in the radio by an order of
magnitude. This underlines the notion that the radio emission in star-forming
systems can dominate the emission associated with the AGN.
