We present a statistical study of a large, homogeneously analyzed sample of narrow-line Seyfert 1 (NLS1) galaxies, accompanied by a comparison sample of broad-line Seyfert 1 (BLS1) galaxies. Optical emission-line and continuum properties are subjected to correlation analyses, in order to identify the main drivers of the correlation space of active galactic nuclei (AGNs), and of NLS1 galaxies in particular. For the first time, we have established the density of the narrow-line region as a key parameter in Eigenvector 1 space, as important as the Eddington ratio L/L_Edd_. This is important because it links the properties of the central engine with the properties of the host galaxy, i.e., the interstellar medium (ISM). We also confirm previously found correlations involving the line width of H{beta} and the strength of the Fe II and [O III]{lambda}5007 emission lines, and we confirm the important role played by L/L_Edd_ in driving the properties of NLS1 galaxies. A spatial correlation analysis shows that large-scale environments of the BLS1 and NLS1 galaxies of our sample are similar. If mergers are rare in our sample, accretion-driven winds, on the one hand, or bar-driven inflows, on the other hand, may account for the strong dependence of Eigenvector 1 on ISM density.