Procedure Stepwise regression analysis

Justification of the choice of independent variables. All reasonable parameters must be validated by an appropriate statistical procedure (e.g., by stepwise regression analysis). The best equation is normally the one with the lowest standard deviation, all terms being significant (indicated by the 95% confidence intervals or by a sequential F test). Alternatively, the equation with the highest overall F value may be selected as the best model (nowadays crossvalidation and/or F-scrambling are recommended as validation tools). 

Five parameters in the data-set were found to be unchanged for all 35 compounds and removed from the matrix. These parameters are H-DO for positions II, IV and V and H-AC for positions IV and V. After the redundant elements had been removed, the resulting [35x47] matrix was correlated to the vector of the biological activity. To perform the linear stepwise regression analysis, the STEPWISE procedure of the SAS statistical package ( ) and BASIC programs were used. 

The analysis of a supersaturated design is usually conducted by using some type of sequential model-fitting procedure, such as stepwise regression. Abraham et al. (1999) and Holcomb et al. (2003) have studied the performance of analysis methods for supersaturated designs. Techniques such as stepwise model fitting and all-possible-regressions type methods may not always produce consistent and reliable results. Holcomb et al. (2003) showed that the performance of an analysis technique in terms of its type I and type II error rate can depend on several factors,... 

As with multiple regression analysis, the most commonly used selection procedures involve stepwise methods with the F-test being applied at each stage to provide a measure of the value of the variable to be added, or removed, in the discriminant function. The procedure is discussed in detail in Chapter 6. 

Eqs. 93 and 94 may be considered as extensions of eqs. 90—92. In contrast to these equations, the bilinear model is generally applicable to the quantitative description of a wide variety of nonlinear lipophilicity-activity relationships. In addition to the parameters that are calculated by linear regression analysis, it contains a nonlinear parameter p, which must be estimated by a stepwise iteration procedure [440, 441]. It should be noted that, due to this nonlinear term, the confidence intervals of a, b, and c refer to the linear regression using the best estimate of the nonlinear term. The additional parameter P is considered in the calculation of the standard deviation s and the F value via the number of degrees of freedom (compare chapter 5.1). The term a in eq. 93 is the slope of the left linear part of the lipophilicity-activity relationship, the value (a — b) corresponds to the negative slope on the right side. 

If the aim of data analysis is to build a model for the prediction of y-values then the correlation between a feature and y is a good criterion for feature selection widely used in regression analysis are stepwise selection procedures. ... 

For reasons of comparability the statistical procedures, as well as the set of confounders, were identical to our previous study (Winneke et al, 1985). As before a forced stepwise multiple-regression analysis with the lead exposure... 

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