Let rij be the element in the current swept matrix associated with Xi and Xj.
Variables are entered or removed one at a time. Xk is eligible for entry if it is an independent variable not currently in the model with rkk ≥ 1 (tolerance with a default of 0.0001) and also for each variable Xj that is currently in the model,
To remove highly correlated predictors from a regression equation, Minitab does the following steps:
- Minitab performs the SWEEP method on the correlation matrix, R, treating X1 … Xp as if they are random variables.
- For any continuous predictor, Minitab compares the element rkk with the tolerance; rkk ≥ tolerance, where k = 1 to p.
- For each variable Xj currently in the model, Minitab checks that (rjj – rjk * (rkj / rkk)) * tolerance ≤ 1.
Where rkk, rjk, rjj are the corresponding diagonal and off diagonal elements for Xj and Xk variables after k step SWEEP operations.
- Otherwise, the predictor fails the test and is removed from the model.
The default tolerance value is 8.8e–12.
You can use the TOLERANCE subcommand with the REGRESS session command to force Minitab to keep a predictor in the model that is highly correlated with a different predictor. However, lowering the tolerance can be dangerous, possibly producing numerically inaccurate results.