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The REG Procedure |
The mechanism that PROC REG uses to check for singularity involves the diagonal (pivot) elements of X'X 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 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).
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