  Understanding the production and escape of Lyman $\alpha$ (Ly$\alpha$)
radiation from star-forming galaxies is a long standing problem in
astrophysics. The ability to predict the Ly$\alpha$ luminosity of galaxies
would open up new ways of exploring the Epoch of Reionization (EoR), and to
estimate Ly$\alpha$ emission from galaxies in cosmological simulations where
radiative transfer calculations cannot be done. We apply multivariate
regression methods to the Lyman Alpha Reference Sample dataset to obtain a
relation between the galaxy properties and the emitted Ly$\alpha$. The derived
relation predicts the Ly$\alpha$ luminosity of our galaxy sample to good
accuracy, regardless of whether we consider only direct observables
(root-mean-square (RMS) dispersion around the relation of $\sim 0.19$ dex) or
derived physical quantities (RMS $\sim 0.27$ dex). We confirm the predictive
ability on a separate sample of compact star-forming galaxies and find that the
prediction works well, but that aperture effects on measured Ly$\alpha$
luminosity may be important, depending on the redshift of the galaxy. We apply
statistical feature selection techniques to determine an order of importance of
the variables in our dataset, enabling future observations to be optimized for
predictive ability. When using physical variables, we are able to determine
that the most important predictive parameters are, in order, star formation
rate, dust extinction, compactness and the gas covering fraction. We discuss
the application of our results in terms of studying the EoR and intensity
mapping experiments.
