We have conducted bivariate and multivariate statistical analysis of data measuring the luminosity and interstellar medium of the Einstein sample of early-type galaxies (presented by Fabbiano, Kim, and Trinchieri 1992). We find a strong nonlinear correlation between L(B) and L(X), with a power-law slope of 1.8 +/- 0.1, steepening to 2.0 +/- 0.2 if we do not consider the Local Group dwarf galaxies M32 and NGC 205. Considering only galaxies with log L(X) less than or equal to 40.5, we instead find a slope of 1.0 +/- 0.2 (with or without the Local Group dwarfs). Although E and SO galaxies have consistent slopes for their L(B)-L(X) relationships, the mean values of the distribution functions of both L(X) and L(X)/L(B) for the SO galaxies are lower than those for the E galaxies at the 2.8 sigma and 3.5 sigma levels, respectively. We find clear evidence for a correlation between L(X) and the X-ray color C-21, defined by Kim, Fabbiano, and Trinchieri (1992b), which indicates that X-ray luminosity is correlated with the spectral shape below 1 keV in the sense that low-L(X) systems have relatively large contributions from a soft component compared with high-L(X) systems. We find evidence from our analysis of the 12 mu m IRAS data for our sample that our SO sample has excess 12 mu m emission compared with the E sample, scaled by their optical luminosities. This may be due to emission from dust heated in star-forming regions in SO disks. This interpretation is reinforced by the existence of a strong L(12)-L(100) correlation for our SO sample that is not found for the E galaxies, and by an analysis of optical-IR colors. We find steep slopes for power-law relationships between radio luminosity and optical, X-ray, and far-IR (FIR) properties. This last point argues that the presence of an FIR-emitting interstellar medium (ISM) in early-type galaxies is coupled to their ability to generate nonthermal radio continuum, as previously argued by, e.g., Walsh et al. (1989). We also find that, for a given L(100), galaxies with larger L(X)/L(B) tend to be stronger nonthermal radio sources, as originally suggested by Kim and Fabbiano (1990). We note that, while L(B) is most strongly correlated with L(6), the total radio luminosity, both L(X) and L(X)/L(B) are more strongly correlated with L(6co), the core radio luminosity. These points support the argument (proposed by Fabbiano, Gioia, and Trinchieri 1989) that radio cores in early-type galaxies are fueled by the hot ISM.
