HI Content and Optical Properties of Field Galaxies from the ALFALFA
  Survey. II. Multivariate Analysis of a Galaxy Sample in Low Density
  Environments
  This is the second paper of two reporting results from a study of the HI
content and stellar properties of nearby galaxies detected by the Arecibo
Legacy Fast ALFA blind 21-cm line survey and the Sloan Digital Sky Survey in a
2160 deg^2 region covered by both surveys. We apply strategies of multivariate
data analysis to a complete HI flux-limited subset of 1624 objects extracted
from the control sample of HI emitters assembled by Toribio et al. (2011a) in
order to: i) investigate the correlation structure of the space defined by an
extensive set of observables describing gas-rich systems; ii) identify the
intrinsic parameters that best define their HI content; and iii) explore the
scaling relations arising from the joint distributions of the quantities most
strongly correlated with the HI mass. The principal component analysis
performed over a set of five galaxy properties reveals that they are strongly
interrelated, supporting previous claims that nearby HI emitters show a high
degree of correlation. The best predictors for the expected value of MHI are
the diameter of the stellar disk, D25r, followed by the total luminosity (both
in the r-band), and the maximum rotation speed, while morphological proxies
such as color show only a moderately strong correlation with the gaseous
content attenuated by observational error. The simplest and most accurate
prescription is log(MHI/Msun)= 8.72 + 1.25*log(D25r/kpc). We find a slope of
$-8.2 \pm 0.5$ for the relation between optical magnitude and log rotation
speed, in good agreement with Tully-Fisher studies, and a log slope of $1.55
\pm 0.06$ for the HI mass-optical galaxy size relation. Given the homogeneity
of the measurements and the completeness of our dataset, the latter outcome
suggests that the constancy of the average (hybrid) HI surface density
advocated by some authors for the spiral population is a crude approximation.
