Stepwise addition method regression

Linear models were generated using multiple linear regression analysis techniques. Several methods were utilized to develop models for evaluation, including stepwise addition, backward elimination, and leaps and bounds regression techniques. The models were evaluated with respect to the multiple correlation coefficient (r), the standard error (s), and predictive ability of the model. 

In the steady state case example, because the data were sparse and there were more unknowns than constraining equations, an additional restriction to the linear programming method was needed. This was done by utilizing a mixed integer-programming model such as in a stepwise multiple regression solution. In the multiple regression method, the identification problem was formulated as follows ... 

Step 4 may be redundant if the covariates were tested directly in the nonlinear mixed effects model. If the covariates were screened using some external method, e.g., regression models, then these covariates are included in the model in a forward stepwise manner. Improvement in the goodness of fit in the model is tested using either the LRT or T-test. In addition, reduction in parameter variability is expected as well. Further discussion of this topic will be made later in the chapter. 

---