PROC REG internally uses a SWEEP operator to compute the regression coefficients, X'X inverse, and the error sum of squares. PROC REG performs a sequential sweep. That is, it always begins by sweeping the second column of (y X)'(y X), that is the first column corresponding to the first X column. Then it sweeps the next column if the pivot is not zero (if the that column is not a linear function of the preceding column). Then it sweeps the next column if the pivot is not zero (if that column is not a linear combination of preceding columns). ... and so on ....
In contrast, a procedure like TRANSREG does nonsequential sweeps, finding the best column to sweep first, then the second best, and so on. The TRANSREG approach tends to be more accurate, but in linear models, you might prefer sequential sweeps to get Type I sums of squares.
... View more
