The determining the appropriate dosage of coagulant is very important, because dosage of coagulant in the coagulation process for wastewater affects removing the amount of pollutants, cost, and producing sludge amount. Accordingly, in this study, in order to determine the optimal PAC dosage in the coagulation process, CCD (Central composite design) was used to proceed experimental design, and the quadratic regression models were constructed between independent variables (pH, influent turbidity, PAC dosage) and each response variable (Total coliform, E.coli, PSD (Particle size distribution) (< $10{\mu}m$), TP, $PO_4$-P, and $COD_{cr}$) by the RSM (Response surface methodology). Also, Considering the various response variables, the optimum PAC dosage and range were derived. As a result, in order to maximize the removal rate of total coliform and E.coli, the values of independent variables are the pH 6-7, the influent turbidity 100-200 NTU, and the PAC dosage 0.07-0.09 ml/L. For maximizing the removal rate of TP, $PO_4$-P, $COD_{cr}$, and PSD(< $10{\mu}m$), it is required for the pH 9, the influent turbidity 200-250 NTU, and the PAC dosage 0.05-0.065 ml/L. In the case of multiple independent variables, when the desirable removal rate for total coliform, E.coli, TP, and $PO_4$-P is 90-100 % and that for $COD_{cr}$ and PSD(< $10{\mu}m$) is 50-100 %, the required PAC dosage is 0.05-0.07 ml/L in the pH 9 and influent turbidity 200-250 NTU. Thus, if the influent turbidity is high, adjusting pH is more effective way in terms of cost since a small amount of PAC dosage is required.