  We address the correlations of black hole (BH) mass with four different
host-galaxy properties from eleven existing data sets. To guide theoretical
understanding, we first try to quantify the tightness of the intrinsic
correlations. Given the estimated measurement errors, we evaluate the
probability distribution of the residual variance in excess of that expected
from the measurement errors. Our central result is that the current data sets
do not allow definite conclusions regarding the quality of the true
correlations because the obtained probability distributions for the residual
variance overlap for most quantities. We then consider which of the relations
offer the best inferences of BH mass when there is no direct measurement
available. As with the residual variances, we find that the probability
distribution of expected uncertainty in inferred BH masses overlaps
significantly for most of the relations. Photometric methods would then be
preferred because the data are easier to obtain, as long as bulge-disk
decomposition or detailed modeling of the photometric profile (as in
\citet{graham:01}) do not present problems. Determining which correlation
offers the best inferences requires reducing the uncertainty in the expected
error in the inferred BH masses (the ``error on the error''). This uncertainty
is currently limited by uncertainty in the residual variance for all of the
relations.
