Design & Analysis of Experiments 7E 2009 Montgomery

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Presentation transcript:

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Regression models are empirical as opposed to mechanistic models Regression modeling is often performed on undesigned or unplanned data Regression modeling is also used extensively to build models to data from designed experiments Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery L is minimized by taking derivatives with respect to the model parameters and equating to zero Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Taking the derivatives and equating to zero results in: Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Mean square error Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery The test uses an ANOVA approach. The regression or model sum of squares is See Table 10.4 for the viscosity regression model Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

See Table 10.4 for the viscosity regression model Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Prediction intervals are useful when running conformation experiments If the new observation falls within the prediction interval that is some evidence that the model is reliable Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

10.7 Regression Model Diagnostics Scaled residuals and PRESS Standardized residual Studentized residual Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Influence Diagnostics Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery 10.8 Testing for Lack of Fit Very important test in both general regression modeling and in analysis of a designed experiment Does the chosen model adequately fit the data, or should higher-order terms be considered? A statistical test can be performed provided that the error term can be decomposed into the two components shown below: Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery

Design & Analysis of Experiments 7E 2009 Montgomery Chapter 10 Design & Analysis of Experiments 7E 2009 Montgomery