Results for the expanded model

Fitting the expanded (parabolic) model to the data in Equation 11.16 gives the parameter estimates 

Source Degrees of freedom Sum of squares Mean square 

The parabolic relationship between reaction rate and uncoded pH is obtained by 

In the present example, (A A ) is given by Equation 10.14. 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 10.47 equal to zero gives the location of the stationary point (in this case, a maximum). 

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