The REG Procedure
- Overview
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Getting Started
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Syntax
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Details
Missing Values Input Data Sets Output Data Sets Interactive Analysis Model-Selection Methods Criteria Used in Model-Selection Methods Limitations in Model-Selection Methods Parameter Estimates and Associated Statistics Predicted and Residual Values Models of Less Than Full Rank Collinearity Diagnostics Model Fit and Diagnostic Statistics Influence Statistics Reweighting Observations in an Analysis Testing for Heteroscedasticity Testing for Lack of Fit Multivariate Tests Autocorrelation in Time Series Data Computations for Ridge Regression and IPC Analysis Construction of Q-Q and P-P Plots Computational Methods Computer Resources in Regression Analysis Displayed Output ODS Table Names ODS Graphics
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Examples
- References
| Testing for Lack of Fit |
The test for lack of fit compares the variation around the model with "pure" variation within replicated observations. This measures the adequacy of the specified model. In particular, if there are 
replicated observations 
of the response all at the same values 
of the regressors, then you can predict the true response at either by using the predicted value 
based on the model or by using the mean 
of the replicated values. The test for lack of fit decomposes the residual error into a component due to the variation of the replications around their mean value (the "pure" error) and a component due to the variation of the mean values around the model prediction (the "bias" error):
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If the model is adequate, then both components estimate the nominal level of error; however, if the bias component of error is much larger than the pure error, then this constitutes evidence that there is significant lack of fit.
If some observations in your design are replicated, you can test for lack of fit by specifying the LACKFIT option in the MODEL statement (see Example 76.6). Note that, since all other tests use total error rather than pure error, you might want to hand-calculate the tests with respect to pure error if the lack of fit is significant. On the other hand, significant lack of fit indicates that the specified model is inadequate, so if this is a problem you can also try to refine the model.