line flux can be easily determined by Equation (3), within observed wavelength range from 4840Å to 5030Å. Then, uncertainty of the line flux is determined by uncertainty in spectral flux provided by the AGNWATCH project, and uncertainty of the line width is determined by the bootstrap method. Here, we do not show all the observed spectra of NGC5548, but only show one spectrum as an example in the top-right panel of Figure \[fj\_ngc5548\]. The measured line parameters and corresponding uncertainties of the broad H$\beta$ of NGC5548 are listed in Table 2.

Figure \[fj\_ngc5548\] shows the correlation between the line width and the line flux of the broad H$\beta$ for NGC5548. The linear correlation coefficient is about -0.83 with $P_{null}\sim0$. The best fitted results with the considerations of the uncertainties of the parameters in both coordinates can be written as $$\log(\frac{flux(H\beta)}{10^{-14}{\rm erg/s/cm^2}})\propto(-4.25\pm0.11)\times\log(\frac{\sigma(H\beta)}{{\rm \AA}})$$ It is clear there is one strong negative correlation for NGC5548, which is well consistent with the expected result under the Virialization assumption: $L(H\beta_B)\propto\sigma(H\beta_B)^{-4}$. Undoubtfully, the negative correlation is well consistent with the negative correlation between the size of BLR and the line width found in Bentz et al. (2006), Denney et al. (2010) and Peterson et al. 