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.
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
Box-Benkhen Fitted Model¶
Box-Behnken Contour Image¶
Stationary Points by Hand¶
Stationary Points from rsm()¶
- Check rsm() output
- Confirm graphically
