  The inter-band correlations between optical/UV and X-ray luminosities of
active galactic nuclei (AGN) are important for understanding the disc-coronal
connection, as well as using AGN as standard candles for cosmology. It is
conventional to measure the X-ray luminosity at rest frame 2 keV and compare to
the UV luminosity at the rest-frame 2500 \AA, but the wavelength-dependence was
never well explored. In this work, we adopt a well-defined sample of 1169
unobscured quasars in the redshift range 0.13 - 4.51, and apply the
direct-correlation method to explore how the correlation with the 2 keV
luminosity changes at different optical/UV wavelengths, from 1280 - 5550 \AA\
where the spectral quality is high. We find that the luminosity at all UV
continuum wavelengths correlates with the X-ray luminosity similarly to that at
2500 \AA, and that these correlations are better than at the optical
wavelengths. Strong self-correlation is also found in the broadband optical/UV
continuum, supporting the scenario that it is dominated by the disc emission.
Correlations of various emission lines are also investigated (e.g. C IV, C
III], Mg II, H$\beta$, [O III]$\lambda\lambda 4959/5007$), including the
Baldwin effect and correlations involving line-widths. We find the forms of
these line correlations are different, and they are also different from their
underlying continua, suggesting various complexities in the line-generation
process. We discuss these results in the disc-wind scenario. Our study confirms
that the rest-frame 2500 \AA\ is a good wavelength to represent the optical/UV
continual properties of quasars, and shows the advantages of the
direct-correlation method.
