Lyman Alpha Reference Sample: X. Predicting Lyman alpha output from starforming galaxies using multivariate regression

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.