We investigate the relations between the observed emission-line strengths, widths, and continuum properties of a sample of 41 low-redshift (z < 1) quasars for which contemporaneous IR/soft X-ray spectral energy distributions are available. This includes investigating correlations between optical and UV lines with both the luminosity and the shape of the quasars' continuum, as well as correlations between the various lines. The sample is heterogeneous, primarily selected on the existence of good-quality Einstein X-ray data, and includes Is radio-loud and 23 radio-quiet quasars. We find anticorrelations between the equivalent width and various UV luminosities (the Baldwin effect) for the Ly alpha and H beta lines and a marginal anticorrelation for C III]. Exclusion of narrow-line, low-luminosity active galactic nuclei reveals a significant Baldwin effect for the C rv and C III] lines. A significant anticorrelation of EW(C IV) with alpha(ox) is also present. We find no correlations between any lines and the X-ray luminosity or X-ray slope. The Fe II optical multiplet shows no simple relationship with luminosity or continuum slope; however, there is a tendency for objects with flat X-ray spectra and/or strong X-ray luminosities to have weak Fe II. Our data do not favor a model in which changes in continuum shape (due to, e.g., a decreasing ionization parameter) cause the Baldwin effect. The data can instead be explained by an accretion disk (AD) model in which limb darkening and the projected surface area of an optically thick, geometrically thin disk combine to cause a viewing-angle-dependent UV luminosity and a more isotropic X-ray luminosity. The scatter in our correlations is larger than that expected from this AD model, suggesting the presence of dust, which reddens both the continuum and the broad emission lines. The C Iv and C mi lines show flatter slopes and larger scatter in the line-continuum relations than predicted by the AD+dusty torus model. This may be due to a significant contribution from collisional excitation that is not directly related to the ionizing continuum.
