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Lec 07 - Validation

# Lec 07 - Validation - Validating the Model Given a Model...

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Validating the Model Given a Model for the performance Measure Examine Regression Model Fit if R 2 is large, greater than .75, fit is pretty good Examine Residuals: Y observed - Y predicted random normally distributed Perform validation experiment select optimal levels from model predict performance measure make one or more runs

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compare predicted to observed Router Example Model and Prediction Equations 2 2 Experiment with 4 replicates Model from graphical analysis: Y x x x x N Y = + + + + 23 9 8 4 3 8 4 4 0 1 2 1 2 . . . . ( , ) ε ε σ Calculate Residual ε for each run Y observed -Y predicted 2
Residuals for the Router Experiment Trt mt x 1 x 2 Y obs a Y resid 1 -1 -1 18.2 16.1 2.1 1 -1 -1 18.9 16.1 2.8 1 -1 -1 12.9 16.1 -3.2 1 -1 -1 14.4 16.1 -1.7 2 +1 -1 27.2 24.1 3.1 2 +1 -1 24.0 24.1 -0.1 2 +1 -1 22.4 24.1 -1.7 2 +1 -1 22.5 24.1 -1.6 3 -1 +1 15.9 14.9 1.0 3 -1 +1 14.5 14.9 -0.4 3 -1 +1 15.1 14.9 0.2 3 -1 +1 14.2 14.9 -0.7 4 +1 +1 41.0 40.5 0.5 4 +1 +1 43.9 40.5 3.4 4 +1 +1 36.3 40.5 -4.2 4 +1 +1 39.9 40.5 -0.6 residual = y observed - y predicted Y Y x x x x predicted = = + + + . . . . 23 9 8 4 3 8 4 4 1 2 1 2 3

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What to Look For in the Residuals
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Lec 07 - Validation - Validating the Model Given a Model...

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