  We present new near infrared spectroscopic measurements of the H_beta region
for a sample of 29 luminous high redshift quasars. We have measured the width
of H_beta in those sources, and added archival H_beta width measurements, to
create a sample of 92 active galactic nuclei (AGNs) for which H_beta width and
rest-frame UV measurements of N V \lambda 1240 and C IV \lambda 1549
emission-lines are available. Our sample spans six orders of magnitude in
luminosity and includes 31 radio-loud AGNs. It also includes 10 narrow-line
Seyfert 1 galaxies and one broad absorption-line quasar. We find that
metallicity, indicated by the N V/C IV line ratio, is primarily correlated with
accretion rate, which is a function of luminosity and H_beta line-width. This
may imply an intimate relation between starburst, responsible for the metal
enrichment of the nuclear gas, and AGN fueling, represented by the accretion
rate. The correlation of metallicity with luminosity, or black hole (BH) mass,
is weaker in contrast with recent results which were based on measurements of
the width of C IV. We argue that using C IV as a proxy to H_beta in estimating
M_BH might be problematic and lead to spurious BH mass and accretion rate
estimates in individual sources. We discuss the potential implications of our
new result in the framework of the starburst-AGN connection and theories of BH
growth.
