  In this manuscript, we check the well-known correlation between \oiii
luminosity and continuum luminosity (\loiiicon) for AGN by a large sample of
1982 SDSS QSOs with $z<0.8$ and with high quality spectra. The strong
correlation of \loiiicon can be found, similar as previous results for AGN.
Moreover, among the 1982 QSOs, there are 708 QSOs with the [O~{\sc
iii}]$\lambda$5007\AA\ described by two components: one core component plus one
extended component. Based on the luminosity from the core components ($L_{\rm
[O~\textsc{iii}],~narrow}$) and from the extended components ($L_{\rm
[O~\textsc{iii}],~ext}$), we confirm that the correlation of $L_{{\rm
[O~\textsc{iii}],~ext}}~-~L_{{\rm 5100\textsc{\AA}}}$ is more stronger and
tighter than the correlations on the total \oiii luminosity and on the
luminosity of the core components of the \oiii lines. Therefore, the luminosity
of the extended components should be better applied to trace AGN intrinsic
luminosity. Meanwhile, we have found strong line width correlation and line
luminosity correlation between the core components and the extended components,
indicating the extended components of the \oiii lines should be not due to
commonly considered radial flows in the common \oiii line clouds. And virial
effects due to gravity of central black holes naturally lead to the wider
extended components from regions more nearer to central black holes. Finally,
we can say that the reported correlation of $L_{{\rm
[O~\textsc{iii}],~narrow}}~-~L_{{\rm 5100\textsc{\AA}}}$ on the core components
of the \oiii lines should be more better to estimate AGN intrinsic luminosity
in Type-2 narrow line AGN, because of totally/partly obscured extended
components.
