  We present a compendium of disk galaxy scaling relations and a detailed
characterization of their intrinsic scatter. Observed scaling relations are
typically characterized by their slope, intercept, and scatter; however, these
parameters are a mixture of observational errors and astrophysical processes.
We introduce a novel Bayesian framework for computing the intrinsic scatter of
scaling relations that accounts for nonlinear error propagation and covariant
uncertainties. Bayesian intrinsic scatters are ~25percent more accurate than
those obtained with a first-order classical method, which systematically
underestimates the true intrinsic scatter. Structural galaxy scaling relations
based on velocity (V23.5), size (R23.5), luminosity (L23.5), colour (g-z),
central stellar surface density (Sigma1), stellar mass (M*), dynamical mass
(Mdyn), stellar angular momentum (j*), and dynamical angular momentum (jdyn),
are examined to demonstrate the power and importance of the Bayesian formalism.
Our analysis is based on a diverse selection of over 1000 late-type galaxies
from the Photometry and Rotation Curve Observations from Extragalactic Surveys
compilation with deep optical photometry and extended rotation curves. We
determine the tightest relation for each parameter by intrinsic orthogonal
scatter, finding M*-V23.5, R23.5-j*, and L23.5-jdyn to be especially tight. The
scatter of the R23.5-L23.5, V23.5-(g-z), and R23.5-jdyn relations is mostly
intrinsic, making them ideal for galaxy formation and evolutionary studies. Our
code to compute the Bayesian intrinsic scatter of any scaling relation is also
presented. We quantify the correlated nature of many uncertainties in galaxy
scaling relations and scrutinize the uncertain nature of disk inclination
corrections and their effect on scatter estimates.
