Our analysis on the two magnitude-limited samples of LINERs suggests a correlation between L _ { { FIR } } / L _ { { B } } or f ( 25µm ) /f ( 60µm ) , and Hubble-type index at > 99.99 % significance level . As L _ { { FIR } } / L _ { { B } } and f ( 25µm ) /f ( 60µm ) are considered as the indicators of star-formation activity and AGN activity , respectively , our result suggests that LINERs with higher AGN activity may have a lower star-formation contribution . The ones with highest AGN activity and lowest star-formation contributions are ellipticals . All well-studied LINER 1s belong to this group . On the other hand , LINERs with higher star-formation activity present lower AGN contributions . We find all well-studied LINER 2s in this parameter space . Most of LINERs having inner ring structures belong to this group . Statistics with other indicators of star-formation or AGN activity ( nulear mass-to-light ratio at H band , and the ratio of X-ray-to-UV power ) provide further evidence for such a trend . We have seen that along with the evolution of galaxies from late-type spirals to early-type ones , and up to ellipticals , the intensity of AGN activity increases with decreasing star-formation contributions , The above analyses may suggest a possible connection between the host galaxies and nuclear activities , and it might also indicate a possible evolutionary connection between AGN and starburst in LINERs .