The correlation between the magnitude of the Debye-Waller anomaly and the temperature dependence of the relaxation time and viscosity of glass-forming liquids (i.e., their fragility) is investigated using the coupling model of relaxation. The correlation is shown to be a natural consequence of the relationship between the noncooperative and intermolecularly cooperative relaxation times of the model. Specifically, the deviation of the mean squared displacement from a linear temperature dependency increases as the fragility (in the Angell sense) of the glass-forming liquid increases because more fragile glasses exhibit substantially more short-time, noncooperative relaxation. This latter fact arises from their shorter noncooperative relaxation times, as deduced from the coupling model.