This preview shows pages 1–4. Sign up to view the full content.

Prediction variance Recall that standard error (square root of prediction variance is   1 () ˆ mT T m y sX X xx We start with simple design domain: Box Simplest design of experiments: full factorial design For a linear polynomial, this means all vertices Standard error is then ˆ Maximum error at vertices 1 ˆ n 22 2 12 2 1 .... 2 yn n sx x x  Why do we get this result? 2 y n s

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
esigns for linear RS Designs for linear RS aditionally use only two levels Traditionally use only two levels Orthogonal design when X T X is diagonal ll factorial design is orthogonal not so easy Full factorial design is orthogonal, not so easy to produce other orthogonal designs with less oints. points. Stability: Small variation of prediction variance domain is also desirable property in domain is also desirable property
ample .2.2 Example 4.2.2 ompare an orthogonal array based on equilateral Compare an orthogonal array based on equilateral triangle to right triangle at vertices (both are saturated)      32 ,1 2, ,1 2,0 , 2  For linear polynomial y=b 1 +b 2 x 1 +b 3 x 2 get 2 1 - 2 3 1 3 0 0 r right triangle we obtained 2 0 1 2 1 - 2 3 - 1 X 0 3 0 0 0 3 T XX  For right triangle we obtained

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.