At Stage 3, we proceeded with the resulting sets of non-collinear Xn regressors and tested whether all of them yield low-redundant regression models. According to Johnsson [83], Zhou and Jiang [84], Evans [85], and Qi et al. [86], when regression analysis involves a significant quantity of data, regression models can be tested for redundancy without checking all sets of independent variables. As shown by Gupta [87], Hosmer et al. [88], and Sullivan and Wilson [89], this can be done by applying the stepwise regression technique. Among the stepwise regression variations, the best subsets approach (BSA) has gained particularly widespread acceptance in contemporary studies on multicollinearity [10,90,91] and prediction of interactions between variables in large arrays [92,93,94].

The BSA approach is based on the adjustment of R2 values in individual Y–X multitudes to account for the number of regressors and the sample size [82,95]. Due to the fact that at Stage 3 we compared non-collinear sets of Xn variables with different numbers of regressors, the application of adjusted R2 instead of R2 was preferable. The goal was to identify the dataset with the largest adjusted R2, which was then used at Stage 4 for regression analysis. According to Ermakov et al. [96], Nikolov and Stoimenova [97], and Alshqaq and Abuzaid [98], such a goal can be achieved by using a criterion of Mallows’ Cp statistic. Following the results of Hansen [99], Irurozki et al. [100], Liao and Zou [101], Feng et al. [102], and Aydin and Yilmaz [103], we utilized the Cp criterion to measure the differences between the models constructed at Stage 2 and optimal (or true) models that best explain the correlations. The closer the Cp is to the number of variables in a dataset, the more accurate the model would be (only random differences from the optimal model might occur) [10]. Thus, Stage 3 resulted in identifying the sets of variables where Cp was close to or below (k + 1) (where k is the number of regressors).

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