To study the effect of three independent variables (X1, X2, and X3) with five levels on the dependent variably (Y), it is required to perform 125 experiments. Using fractional factorial design based on design of experiments, only 25 experiments were selected. 25 experiments will be performed to predict a second order quadratic model to describe the effect of independent variables (X1, X2, and X3) in terms of linear and quadratic effects, and their interactions.

Could this model be used to predict the values of dependent variable (Y) at different values of independent variables (X1, X2, and X3) to draw the Interaction plots as

· the effect of X1 on Y at fixed values of X2 and X3

· the effect of X2 on Y at fixed values of X1 and X3

Or I must perform 125 experiments based on full factorial design to draw the Interaction plots?