regression models are empirical as opposed to mechanistic models

Design & Analysis of Experiments 8E 2012 Montgomery

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Regression models are empirical as opposed to mechanistic modelsRegression modeling is often performed on undesigned or unplanned dataRegression modeling is also used extensively to build models to data from designed experiments


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L is minimized by taking derivatives with respect to the model parameters and equating to zero


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Taking the derivatives and equating to zero results in:


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Mean square error


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The test uses an ANOVA approach. The regression or model sum of squares is

See Table 10.4 for the viscosity regression model


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See Table 10.4 for the viscosity regression model


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Prediction intervals are useful when running conformation experimentsIf the new observation falls within the prediction interval that is some evidence that the model is reliable


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10.7 Regression Model DiagnosticsScaled residuals and PRESS

Standardized residual

Studentized residual


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Influence Diagnostics


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10.8 Testing for Lack of FitVery important test in both general regression modeling and in analysis of a designed experimentDoes 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:


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regression models are empirical as opposed to mechanistic models

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