  A comprehensive toolkit is developed for regression analysis of directional
data based on a flexible class of angular Gaussian distributions. Informative
testing procedures for isotropy and covariate effects on the directional
response are proposed. Moreover, a prediction region that achieves the smallest
volume in a class of ellipsoidal prediction regions of the same coverage
probability is constructed. The efficacy of these inference procedures is
demonstrated in simulation experiments. Finally, this new toolkit is used to
analyze directional data originating from a hydrology study and a
bioinformatics application.
