Uncoded models

Equation 14.9 gives the empirical model of the response surface for the data in Table 14.4 when the factors are in coded form. Convert the equation to its uncoded form. 

Table 14.5 lists the uncoded factor levels, coded factor levels, and responses for a 2 factorial design. Determine the coded and uncoded empirical model for the response surface based on equation 14.10. 

To transform the coded empirical model into its uncoded form, it is necessary to replace A, B, and C with the following relationships... 

The parabolic relationship between reaction rate and uncoded pH is obtained by expansion of the coded model. 

Full second-order polynomial models used with central composite experimental designs are very powerful tools for approximating the true behavior of many systems. However, the interpretation of the large number of estimated parameters in multifactor systems is not always straightforward. As an example, the parameter estimates of the coded and uncoded models in the previous section are quite different, even though the two models describe essentially the same response surface (see Equations 12.63 and 12.64). It is difficult to see this similarity by simple inspection of the two equations. Fortunately, canonical analysis is a mathematical technique that can be applied to full second-order polynomial models to reveal the essential features of the response surface and allow a simpler understanding of the factor effects and their interactions. 

Acknowledgements. This research was supported in part by the Leverhulme Trust via project UnCoDe ( Uncertainty and confidence in safety arguments effect on expert decision makers ) and by the SeSaMo project ( Security and Safety Modelling ), supported by the Artemis JU, and the United Kingdom... 

---