A Ten-Experiment Example

Enzymes are large biological molecules that act as catalysts for chemical reactions in living organisms. As catalysts, they allow chemical reactions to proceed at a rapid rate, a rate much faster than would occur if the enzymes were not present. The action of an enzyme is often represented as 

The reasons for the effect of pH on the catalytic properties of enzymes are numerous and will not be discussed here. For most enzymes, however, there is a pH at which they are optimally effective changing the pH to lower (more acidic) levels or to higher (more basic) levels will decrease the overall rate at which the associated chemical reaction occurs. In the region of the optimum pH, the reaction rate vs. pH response surface can usually be approximated reasonably well by a second-order, parabolic relationship. 

We assume a limited budget that allows resources for only ten experiments. How can these experiments be distributed among factor combinations (design points) and replicates At what levels of pH should the experiments be carried out How can the results be interpreted  

Let us assume that we are primarily interested in estimating the optimum pH for a particular enzyme catalyzed reaction. We might also be interested in determining if a parabolic relationship provides a significantly better fit than is provided by a straight line relationship over the domain of pH studied. If it does provide a better 

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Response Surfaces. 3. Basic Statistics. 4. One Experiment. 5. Two Experiments. 6. Hypothesis Testing. 7. The Variance-Covariance Matrix. 8. Three Experiments. 9. Analysis of Variance (ANOVA) for Linear Models. 10. A Ten-Experiment Example. 11. Approximating a Region of a Multifactor Response Surface. 12. Additional Multifactor Concepts and Experimental Designs. Append- ices Matrix Algebra. Critical Values of t. Critical Values of F, a = 0.05. Index. 

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