In this work we have studied the density and temperature dependencies of the parameters of the average effective pair potential using linear isotherm regularity (LIR). Such a potential is considered to be the interaction of two nearest neighbor molecules in which all of their longer range interactions are added to it, and also the effect of the medium on the charge distributions of two neighboring molecules is included. We have found that the density dependencies of the parameters of the average effective pair potential are negligible for densities greater than the Boyle density for which the LIR is valid. The parameter sigma, the separation at which the potential is zero, increases with temperature while the depth of the potential well, is an element of, decreases. Furthermore, analytical expressions for is an element of and sigma are obtained in terms of the LIR parameters. Using these parameters for the average effective pair potential, a strong principle of corresponding states is proposed.