Multiple regression of GRB luminosity on light–curve properties

Statistical relations between the luminosity L of gamma–ray burster (GRBs) and several of their other observable properties have been discovered. Four of these properties are considered here: the spectral lag; a measure of the light–curve variability; peak energy and the minimum light–curve rise time. Data are taken from a tabulation by Schaefer. Log–log regression of L on various combinations of the four light–curve properties, as well as redshift, is considered, using conventional multiple linear regression, and multiple errors–in–variables regression. Several cases are found in which the regression coefficients of more than one luminosity indicators are significant. In particular, the simultaneous regression of luminosity on peak energy, spectral lag, minimum rise time and redshift is meaningful.