  We present a study of the global properties of Joguet's sample of 65 Seyfert
2 galaxies. We use the population synthesis models of our Paper II to derive
`pure' emission-line spectra, and thus explore the statistical properties of
the nuclear nebular components and their relation to the stellar populations.
We find that the emission line clouds suffer substantially more extinction than
the starlight, and confirm the correlations between stellar and nebular
velocity dispersions and between emission line luminosity and velocity
dispersions. Nuclear luminosities correlate with stellar velocity dispersions.
Removing the contribution of young stars to the optical continuum produces a
tighter and steeper relation, $L \propto \sigma_\star^4$, consistent with the
Faber-Jackson law. Emission line ratios indicative of the gas excitation such
as [OIII]/H$\beta$ and [OIII]/[OII] are statistically smaller for Seyferts with
significant star-formation, implying that ionization by massive stars is
responsible for a substantial, and sometimes even a dominant, fraction of the
H$\beta$ and [OII] fluxes. We use our models to constrain the maximum fraction
of the ionizing power that can be generated by a hidden AGN. We correlate this
fraction with classical indicators of AGN photo-ionization: X-ray luminosity
and nebular excitation, but find no significant correlations. Thus, while there
is a strong contribution of starbursts to the excitation of the nuclear nebular
emission in low-luminosity Seyferts, the contribution of the hidden AGN remains
elusive even in hard X-rays. (abridged)
