General Regression: The REG Procedure

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Introduction to Regression Procedures

General Regression: The REG Procedure

The REG procedure is a general-purpose procedure for regression that

handles multiple regression models
provides nine model-selection methods
allows interactive changes both in the model and in the data used to fit the model
allows linear quality restrictions on parameters
tests linear hypotheses and multivariate hypotheses
produces collinearity diagnostics, influence diagnostics, and partial regression leverage plots
saves estimates, predicted values, residuals, confidence limits, and other diagnostic statistics in output SAS data sets
generates plots of data and of various statistics
"paints" or highlights scatter plots to identify particular observations or groups of observations
uses, optionally, correlations or crossproducts for input

Model-selection Methods in PROC REG

The nine methods of model selection implemented in PROC REG are

NONE: no selection. This method is the default and uses the full model given in the MODEL statement to fit the linear regression.
FORWARD: forward selection. This method starts with no variables in the model and adds variables one by one to the model. At each step, the variable added is the one that maximizes the fit of the model. You can also specify groups of variables to treat as a unit during the selection process. An option enables you to specify the criterion for inclusion.
BACKWARD: backward elimination. This method starts with a full model and eliminates variables one by one from the model. At each step, the variable with the smallest contribution to the model is deleted. You can also specify groups of variables to treat as a unit during the selection process. An option enables you to specify the criterion for exclusion.
STEPWISE: stepwise regression, forward and backward. This method is a modification of the forward-selection method in that variables already in the model do not necessarily stay there. You can also specify groups of variables to treat as a unit during the selection process. Again, options enable you to specify criteria for entry into the model and for remaining in the model.
MAXR: maximum R² improvement. This method tries to find the best one-variable model, the best two-variable model, and so on. The MAXR method differs from the STEPWISE method in that many more models are evaluated with MAXR, which considers all switches before making any switch. The STEPWISE method may remove the "worst" variable without considering what the "best" remaining variable might accomplish, whereas MAXR would consider what the "best" remaining variable might accomplish. Consequently, MAXR typically takes much longer to run than STEPWISE.
MINR: minimum R² improvement. This method closely resembles MAXR, but the switch chosen is the one that produces the smallest increase in R².
RSQUARE: finds a specified number of models having the highest R² in each of a range of model sizes.
CP: finds a specified number of models with the lowest C_p within a range of model sizes.
ADJRSQ: finds a specified number of models having the highest adjusted R² within a range of model sizes.

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