This paper aims to investigate influence of design parameters on partial gear ratios of a coxial helical gearbox. In order to minimize the direct material cost of gearbox, a cost function has been derived with ten design parameters and subjected to partial gear ratio or the second-stage gear ratio (u2). Thus, the change of the second-stage gear ratio impacts on the minimal direct material cost of gearbox. Therefore, this study has been done to figure out the relation between the second-stage gear ratio and nine other independent design parameters. The central composite design method has been used for planning experimental simulations in which each parameter has three values at low, middle and high levels. Results show that almost design parameters and their interactions have strong influence on the response such as total ratio gearbox ratio (ug), price per kilogram of gear material (Cg.m), price per kilogram of shaft material (Cs.m,), allowable contact stress of stage 2 (AS2) and (Cg.m* Cs.m). The contributions of the coefficient of wheel face width of stage 1 (Xba1, Xba2) and their interactions with other factors on the response are negligible. In addition, a regression model of u2 has been developed with high confidence to be further applied in reality