Using Power Transformations in Response Surface Methodology

Response Surface Methodology (RSM) has succeeded in different scientific areas, such as engineering, pharmaceutics, agriculture, and living and chemical experiments, where linear or quadratic models describe one or more explanatory variables that influence the response variable. When linear and quadratic models fail to represent data using RSM adequately, an alternative technique must be used, which involves choosing the appropriate transformations applied to either the response variable or the explanatory variables. A Tukey transformation and Box-Cox method are applied to the response variable in this article to improve the model's adequacy. A previously performed biological experiment is presented, and RSM is applied with power transformations without iterating the experiment. A parameter in the transformed response surface models is also estimated using the maximum likelihood and Draper and Smith methods.