We investigate faint radio emission from low-to high-luminosity active galactic nuclei (AGNs) selected from the Sloan Digital Sky Survey. 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, [O iii] luminosity, emission-line ratios, and the strength of the 4000 8 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 À1 Hz À1 level found for sources without any discernible star formation. Furthermore, this additional radio emission correlates well with the strength of the 4000 8 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. AGNs). For both cases we find a strong, almost identical correlation between [O iii] 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 at similar redshifts and values of , 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.