  The subsurface properties of active regions prior to their appearance at the
solar surface may shed light on the process of active region formation.
Helioseismic holography has been applied to samples taken from two populations
of regions on the Sun (pre-emergence and without emergence), each sample having
over 100 members, that were selected to minimize systematic bias, as described
in Paper I (Leka et al., 2012). Paper II (Birch et al., 2012) showed that there
are statistically significant signatures in the average helioseismic properties
that precede the formation of an active region. This paper describes a more
detailed analysis of the samples of pre-emergence regions and regions without
emergence, based on discriminant analysis. The property that is best able to
distinguish the populations is found to be the surface magnetic field, even a
day before the emergence time. However, after accounting for the correlations
between the surface field and the quantities derived from helioseismology,
there is still evidence of a helioseismic precursor to active region emergence
that is present for at least a day prior to emergence.
