This paper deals with development of regression models for prediction of compressive strength of concrete. The compressive strength of concrete is predicted using four variables, namely, water-binder ratio, fine aggregate-binder ratio, coarse aggregate-binder ratio and binder content. Linear regression models have been developed for variations in fly ash replacements (0 and 15 percent), Zones of aggregates (A, B and C) and curing ages (28, 56 and 91 days). An effort has also been made to modify the linear models using a two step approach. First step is to develop quadratic models (termed as full models) by identifying the suitable combinations of the four variables described above. The second step is to select the best minimal subset of the predictors in full models using Mallow’s Cp statistic. The proposed quadratic regression models yielded coefficient of determination R2 > 0.99 in almost every case except for concrete with Zones A and B of aggregates without fly ash for 91 days curing period and for concrete with Zone C of aggregates without fly ash for 56 days curing period.