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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
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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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32. See Table 10.4 for the viscosity regression model
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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
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42. 10.7 Regression Model Diagnostics
Scaled residuals and PRESS
Standardized residual
Studentized residual
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45. Influence Diagnostics
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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:
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