Residual stresses can reduce the reliability of plastic injection molding parts. This work is an attempt to model the residual stresses as a function of injection molding parameters. More stress is placed on reducing the number of input factors and to include all possible interactions. For this purpose, two-stage experimentation is suggested: a factor screening stage and Response Surface optimization stage. In screening stage Taguchi 3 level experimental design is used to classify the input parameters as significant and non-significant factors. Eight input variables were classified into 3 non-significant and 5 significant factors using this screening stage. Thus for the Response Surface optimization stage: instead of doing 160 experiments in Central Composite, 56 are only needed after the screening stage in half Central Composite Design. The best subset and regression model fitting tools in addition to model verification using randomly selected input setting were used to select a model for predicting residual stresses with a verified Root Mean Square Error (RSME) of nearly 0.93 MPa.