The lower critical solution temperature (LCST) behavior of a linear poly(N-isopropylacrylamide) (PNIPA) in water is thought to result from the polymer-polymer attractive interaction. This polymer-polymer attraction is modeled by a temperature-dependent Yukawa attractive potential, with Yukawa parameters determined by fitting the theoretical phase diagram for a pure Yukawa fluid to the experimental lower consolute boundary for a PNIPA-water solution. The predicted coexistence curve for the PNIPA-water mixtures in the temperature-polymer volume fraction plane is reasonably close to the experimental cloud point data for the PNIPA-water system.