Class StepwiseRegression builds a multiple linear regression model using forward selection, backward selection, or forward stepwise (with a backward glance) selection.

Levels of priority can be assigned to the candidate independent variables using Levels. All variables with a priority level of 1 must enter the model before variables with a priority level of 2. Similarly, variables with a level of 2 must enter before variables with a level of 3, etc. Variables also can be forced into the model using Force. Note that specifying "force" without also specifying levels of priority will result in all variables being forced into the model.

Typically, the intercept is forced into all models and is not a candidate variable. In this case, a sum-of-squares and crossproducts matrix for the independent and dependent variables corrected for the mean is required. Other possibilities are as follows:

1. The intercept is not in the model. A raw (uncorrected) sum-of-squares and crossproducts matrix for the independent and dependent variables is required as input in cov. Argument nObservations must be set to one greater than the number of observations.
2. An intercept is a candidate variable. A raw (uncorrected) sum-of-squares and crossproducts matrix for the constant regressor (=1), independent and dependent variables are required for cov. In this case, cov contains one additional row and column corresponding to the constant regressor. This row/column contains the sum-of-squares and crossproducts of the constant regressor with the independent and dependent variables. The remaining elements in cov are the same as in the previous case. Argument nObservations must be set to one greater than the number of observations.

The stepwise regression algorithm is due to Efroymson (1960). StepwiseRegression uses sweeps of the covariance matrix (input in cov, if the covariance matrix is specified, or generated internally) to move variables in and out of the model (Hemmerle 1967, Chapter 3). The SWEEP operator discussed in Goodnight (1979) is used. A description of the stepwise algorithm is also given by Kennedy and Gentle (1980, pp. 335-340). The advantage of stepwise model building over all possible regression (SelectionRegression) is that it is less demanding computationally when the number of candidate independent variables is very large. However, there is no guarantee that the model selected will be the best model (highest ) for any subset size of independent variables.