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
| Computational Methods |
The REG procedure first composes a crossproducts matrix. The matrix can be calculated from input data, reformed from an input correlation matrix, or read in from an SSCP data set. For each model, the procedure selects the appropriate crossproducts from the main matrix. The normal equations formed from the crossproducts are solved by using a sweep algorithm (Goodnight 1979). The method is accurate for data that are reasonably scaled and not too collinear.
The mechanism that PROC REG uses to check for singularity involves the diagonal (pivot) elements of 
as it is being swept. If a pivot is less than SINGULAR*CSS, then a singularity is declared and the pivot is not swept (where CSS is the corrected sum of squares for the regressor and SINGULAR is machine dependent but is approximately 1E
7 on most machines or reset in the PROC REG statement).
The sweep algorithm is also used in many places in the model-selection methods. The RSQUARE method uses the leaps-and-bounds algorithm by Furnival and Wilson (1974).