  Black hole accretion is widely thought to influence star formation in
galaxies, but the empirical evidence for a physical correlation between star
formation rate (SFR) and the properties of active galactic nuclei (AGNs)
remains highly controversial. We take advantage of a recently developed SFR
estimator based on the [O II] $\lambda3727$ and [O III] $\lambda5007$ emission
lines to investigate the SFRs of the host galaxies of more than 5,800 type 1
and 7,600 type 2 AGNs with $z < 0.35$. After matching in luminosity and
redshift, we find that type 1 and type 2 AGNs have a similar distribution of
internal reddening, which is significant and corresponds to $\sim
10^9\,M_\odot$ of cold molecular gas. In spite of their comparable gas content,
type 2 AGNs, independent of stellar mass, Eddington ratio, redshift or
molecular gas mass, exhibit intrinsically stronger star formation activity than
type 1 AGNs, in apparent disagreement with the conventional AGN unified model.
We observe a tight, linear relation between AGN luminosity (accretion rate) and
SFR, one that becomes more significant toward smaller physical scales,
suggesting that the link between the AGN and star formation occurs in the
central kpc-scale region. This, along with a correlation between SFR and
Eddington ratio in the regime of super-Eddington accretion, can be interpreted
as evidence that star formation is impacted by positive feedback from the AGN.
