Coding transformations of parameter estimates

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

In the present example, X X) is given by Equation 11.14. Other arrays are 

The location of the predicted optimum pH may be found by differentiating the fitted model with respect to pH. Setting the derivative of Equation 11.47 equal to zero gives the location of the stationary point (in this case, a maximum). 

Anticipating a later section on canonical analysis of second-order polynomial models, we will show that the first-order term can be made to equal zero if we code the model using the stationary point as the center of the symmetrical design. For this new system of coding, c, = 10 2/3 and (see Section 8.5). 

in this new system of coding, b = 0 the first-order parameter is zero. 

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