We present archival high-resolution X-ray imaging observations of 25 nearby LINERs observed by ACIS on board Chandra. This sample builds on our previously published proprietary and archival X-ray observations and includes the complete set of LINERs with published black hole masses and FIR luminosities that have been observed by Chandra. Of the 82 LINERs observed by Chandra, 41 (50%) display hard nuclear cores consistent with an AGN. The nuclear 2-10 keV luminosities of these AGN-LINERs range from ~2 × 1038 to ~1 × 1044 ergs s-1. Reinforcing our previous work, we find a significant correlation between the Eddington ratio, Lbol/LEdd, and the FIR luminosity, LFIR, as well as the IR brightness ratio, LFIR/LB, in the host galaxy of AGN-LINERs that extends over 7 orders of magnitude in Lbol/LEdd. Combining our AGN-LINER sample with galaxies from other AGN subclasses, we find that this correlation is reinforced in a sample of 129 AGNs, extending over almost 9 orders of magnitude in Lbol/LEdd. Using archival and previously published observations of the 6.2 μm PAH feature from ISO, we find that it is unlikely that dust heating by the AGN dominates the FIR luminosity in our sample of AGNs. Our results may therefore imply a fundamental link between the mass accretion rate (), as measured by the Eddington ratio, and the star formation rate (SFR), as measured by the FIR luminosity. Apart from the overall correlation, we find that the different AGN subclasses occupy distinct regions in the LFIR and Lbol/LEdd plane. Assuming a constant radiative efficiency for accretion, our results may imply a variation in the SFR/ ratio as a function of AGN activity level, a result that may have significant consequences for our understanding of galaxy formation and black hole growth.