DOE_linear_quad - Predictionvariance

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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
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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
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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
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This note was uploaded on 06/06/2011 for the course EAS 4240 taught by Professor Peterifju during the Spring '08 term at University of Florida.

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DOE_linear_quad - Predictionvariance

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