For glass-forming substances, we show that the ratio $E_{\beta }{/RT}_g$ can be predicted quantitatively from the coupling model. Here $E_{\beta }$ is the glassy state activation enthalpy of the Johari-Goldstein β relaxation, $T_g$ is the glass transition temperature of the α relaxation, and R is the gas constant. The calculated value is in good agreement with the experimental value in many glass formers. The results locate the origin of this cross correlation between $E_{\beta }$ of the Johari-Goldstein β relaxation and $T_g$ of the α relaxation, although there are some notable exceptions to this cross correlation.