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 can not 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 .