Context :

Aims : The availability of large amounts of multiwavelength data allows us to perform an extensive statistical analysis to look for correlations between different parameters of AGN .
The physical implications of these correlations , when considered within the framework of current AGN models , can be enlightening in the resolution of the problems and the open issues which still characterise this class of sources .

Methods : We presented CAIXA , a Catalogue of AGN in the XMM- Newton Archive , in a companion paper .
It consists of radio-quiet X-ray unobscured sources , which cover a range in X-ray luminosities between L _ { \mathrm { 2 - 10 keV } } = 2.0 \times 10 ^ { 41 } and 3.9 \times 10 ^ { 46 } erg s ^ { -1 } , and in redshift from z=0.002 to z=4.520 .
Here , a systematic search for correlations between the X-ray spectral properties and the multiwavelength data was performed for the sources in CAIXA .
All the significant ( > 99.9 \% confidence level ) correlations are discussed along with their physical implications on current models of AGN .

Results : Two main correlations are discussed in this paper : a ) a very strong anti-correlation between the FWHM of the H \beta optical line and the ratio between the soft and the hard X-ray luminosity .
Although similar anti-correlations between optical line width and X-ray spectral steepness have already been discussed in the literature ( see e.g. , Laor et al .
1994 , Boller et al .
1996 , Brandt et al .
1997 ) , we consider the formulation we present in this paper is more fundamental , as it links model-independent quantities .
Coupled with a strong anti-correlation between the V to hard X-ray flux ratio and the H \beta FHWM , it supports scenarios for the origin of the soft excess in AGN , which require strong suppression of the hard X-ray emission ; b ) a strong ( and expected ) correlation between the X-ray luminosity and the black hole mass .
Its slope , flatter than 1 , is consistent with Eddington ratio-dependent bolometric corrections , such as that recently proposed by Vasudevan & Fabian ( 2009 ) .
Moreover , we critically review through various statistical tests the role that distance biases play in the strong radio to X-ray luminosity correlation found in CAIXA and elsewhere ; we conclude that only complete , unbiased samples ( such as that recently published by Behar & Laor , 2008 ) should be used to draw observational constraints on the origin of radio emission in radio-quiet AGN .

Conclusions :