The REG Procedure
- Overview
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Getting Started
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Syntax
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DetailsMissing ValuesInput Data SetsOutput Data SetsInteractive AnalysisModel-Selection MethodsCriteria Used in Model-Selection MethodsLimitations in Model-Selection MethodsParameter Estimates and Associated StatisticsPredicted and Residual ValuesModels of Less Than Full RankCollinearity DiagnosticsModel Fit and Diagnostic StatisticsInfluence StatisticsReweighting Observations in an AnalysisTesting for HeteroscedasticityTesting for Lack of FitMultivariate TestsAutocorrelation in Time Series DataComputations for Ridge Regression and IPC AnalysisConstruction of Q-Q and P-P PlotsComputational MethodsComputer Resources in Regression AnalysisDisplayed OutputPlot Options Superseded by ODS GraphicsODS Table NamesODS Graphics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).