1. Lecture 19 Today: More Chapter 9 Next day: Finish Chapter 9 Assignment: Chapter 9: 17

3. Analysis of Second Order Model Characterizing the stationary point

4. Central Composite Design Cannot fit a second order model to the data we have thus far Central composite design is an efficient design for fitting a second order model Consists of: –first order design (factorial or fractional factorial) (coded -1 or +1) –center points (coded as 0) –axial points (coded ) Have n f, n c, and 2k trials for each type of design respectively

5. Central Composite Design The axial points chosen so that the design is rotatable Good choice of axial points Choice of number of center points

6. Example Center for new first-order design is ( z 1,z 2 )=(85,175) Origin is at ( x 1,x 2 )=(0,0)

7. Example

8. Finding the maximum

9. Response Surface

10. Example

11. Canonical Form of Fitted Model

13. Ridge Systems What if one of the eigen values is close to 0?

14. Ridge Systems