We investigate the relation between X-ray nuclear emission, optical emission line, radio luminosity and black hole mass for a sample of 47 Seyfert galaxies. The sample, which has been selected from the Palomar optical spectroscopic survey of nearby galaxies (Ho, Filippenko & Sargent 1997), covers a wide range of nuclear powers, from L(2-10 keV) = 1e43 erg/s down to very low luminosities (L(2-10 keV) = 1e38 erg/s). X-ray luminosities have been corrected taking into account the likely candidate Compton thick sources, which are a high fraction (> 30%) among type 2 Seyferts in our sample. Strong linear correlations between 2-10 keV and [OIII], H(alpha), radio luminosities have been found, showing the same slopes as quasars and luminous Seyfert galaxies, independently from the level of nuclear activity displayed by the sources. Moreover, despite the wide range of Eddington ratios (L/L(Edd)) tested here (six orders of magnitude, from 0.1 down to = 1e-7), no correlation is found between the X-ray, optical emission lines, radio luminosities and the black hole mass. Results will be discussed within theoretical models involving radiatively inefficient accretion, jet emission and standard accretion disks to verify if these Seyfert nuclei are simply a scaled-down version of luminous AGN or if different physical processes are responsible for their emission.