We reinvestigate the relationship between the characteristic broad-line region size ( R _ { BLR } ) and the Balmer emission-line , X-ray , UV , and optical continuum luminosities .
Our study makes use of the best available determinations of R _ { BLR } for a large number of active galactic nuclei ( AGNs ) from Peterson et al .
Using their determinations of R _ { BLR } for a large sample of AGNs and two different regression methods , we investigate the robustness of our correlation results as a function of data sub-sample and regression technique .
Though small systematic differences were found depending on the method of analysis , our results are generally consistent .
Assuming a power-law relation R _ { BLR } \propto L ^ { \alpha } , we find the mean best-fitting \alpha is about 0.67 \pm 0.05 for the optical continuum and the broad H \beta luminosity , about 0.56 \pm 0.05 for the UV continuum luminosity , and about 0.70 \pm 0.14 for the X-ray luminosity .
We also find an intrinsic scatter of \sim 40 % in these relations .
The disagreement of our results with the theoretical expected slope of 0.5 indicates that the simple assumption of all AGNs having on average same ionization parameter , BLR density , column density , and ionizing spectral energy distribution , is not valid and there is likely some evolution of a few of these characteristics along the luminosity scale .