We used a large, homogeneous sample of 4178 z <= 0.8 Seyfert 1 galaxies and QSOs selected from the Sloan Digital Sky Survey to investigate the strength of Fe II emission and its correlation with other emission lines and physical parameters of active galactic nuclei. We find that the strongest correlations of almost all the emission-line intensity ratios and equivalent widths (EWs) are with the Eddington ratio (L/L Edd), rather than with the continuum luminosity at 5100 A (L 5100) or black hole mass (M BH); the only exception is the EW of ultraviolet Fe II emission, which does not correlate at all with broad-line width, L 5100, M BH, or L/L Edd. By contrast, the intensity ratios of both the ultraviolet and optical Fe II emission to Mg II Delta *l2800 correlate quite strongly with L/L Edd. Interestingly, among all the emission lines in the near-UV and optical studied in this paper (including Mg II Delta *l2800, H Delta *b, and O III Delta *l5007), the EW of narrow optical Fe II emission has the strongest correlation with L/L Edd. We hypothesize that the variation of the emission-line strength in active galaxies is regulated by L/L Edd because it governs the global distribution of the hydrogen column density of the clouds gravitationally bound in the line-emitting region, as well as its overall gas supply. The systematic dependence on L/L Edd must be corrected when using the Fe II/Mg II intensity ratio as a measure of the Fe/Mg abundance ratio to study the history of chemical evolution in QSO environments.