We consider the line shapes of single molecules in low temperature glasses due to dipole-dipole interaction between the molecules and other particles of the system. Motivated by computer simulations, we employ a simplified formula for the absorption lines and derive an analytic expression for the distribution of the variance of such absorption lines. The simplest version of this distribution-derived for pointlike particles without cutoff of the interaction at small distances-already accounts for the qualitative features of width histograms measured experimentally or gained by computer simulation. We further analyze the effect of the minimal approach distance between the chromophore and the perturbing particles and employ an approximate relation between the variance and the full width at half maximum of the absorption lines. We find that the main characteristics of the histogram of widths stem from the (homogeneous) distribution of interactions in space and do not reflect the distribution of the internal parameters of the underlying model.