Leaps-and-bounds regression

Models can be generated using stepwise addition multiple linear regression as the descriptor selection criterion. Leaps-and-bounds regression [10] and simulated annealing (ANNUN) can be used to find a subset of descriptors that yield a statistically sound model. The best descriptor subset found with multiple linear regression can also be used to build a computational neural network model. The root mean square (rms) errors and the predictive power of the neural network model are usually improved due to the higher number of adjustable parameters and nonlinear behavior of the computational neural network model. 

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. 

An exhaustive search for an optimal variable subset is impossible for this data set because the number of variables is too high. Even an algorithm like leaps-and-bound cannot be applied (Section 4.5.4). Instead, variable selection can be based on a stepwise procedure (Section 4.5.3). Since it is impossible to start with the full model, we start with the empty model (regress the y-variable on a constant), with the scope... 

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