MANE 6313

Week 13, Module G

Student Learning Outcome

• Select an appropriate experimental design with one or more factors,
• Select an appropriate model with one or more factors,
• Evaluate statistical analyses of experimental designs,
• Assess the model adequacy of any experimental design, and
• Interpret model results.

Module Learning Outcome

Compute stationary point for Box-Behnken example.

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Stationary Points

• Stationary points are points where \(\frac{\partial\hat{y}}{\partial x_1}=\frac{\partial\hat{y}}{\partial x_2}=\cdots=\frac{\partial\hat{y}}{x_k}=0\)
• There are three types of stationary points: maximum response, minimum response, and saddle point.
• Note that stationary points are not optimal points, but could be optimal points
• Second derivative information is needed to determine if a stationary point is an optimal point,
• Contour plots and 3D plots can also be used to determine type of stationary point

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Box-Benkhen Fitted Model

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Box-Behnken Contour Image

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Stationary Points by Hand

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Stationary Points from rsm()

• Check rsm() output
• Confirm graphically