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.
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