Fitting Second-order Models to Mixed Two-level and Four-level Factorial Designs: Is There an Easier Procedure?

Fitting response surface models is usually carried out using statistical packages to solve complicated equations in order to produce the estimates of the model coefficients. This paper proposes a new procedure for fitting response surface models to mixed two-level and four-level factorial designs. New and easier formulae are suggested to calculate the linear, quadratic and the interaction coefficients for mixed two-level and four-level factorial designs regardless of the number of factors included in the experiment. The results of the proposed procedure are in agreement with the results of least squares method. This paper could motivate researchers to study the possibility of applying a fixed formula to all factorial designs.