  We investigate the relationship between black hole accretion and star
formation in a sample of 453 $z\approx0.3$ type 1 active galactic nuclei
(AGNs). We use available CO observations to demonstrate that the combination of
nebular dust extinction and metallicity provides reliable estimates of the
molecular gas mass even for the host galaxies of type 1 AGNs. Consistent with
other similar but significantly smaller samples, we reaffirm the notion that
powerful AGNs have comparable gas content as nearby star-forming galaxies and
that AGN feedback does not deplete the host of cold gas instantaneously. We
demonstrate that while the strong correlation between star formation rate and
black hole accretion rate is in part driven by the mutual dependence of these
parameters on molecular gas mass, the star formation rate and black hole
accretion rate are still weakly correlated after removing the dependence of
star formation rate on molecular gas mass. This, together with a positive
correlation between star formation efficiency and black hole accretion rate,
may be interpreted as evidence for positive AGN feedback.
