Linear modeling by stepwise subset selection

It is to be expected that models of higher Rjg can be found using more than five descriptors. Unfortunately, the large descriptor pool will limit our ability to search for best subsets. Therefore we will use the method of stepwise subset selection here, described in Subsection 6.1.4. 

We generate models of n = 1. 20 descriptors. In each step 50 subsets of descriptors are selected, producing best linear models (with respect to Rj ). These are enlarged by one descriptor in all possible ways, again the 50 best models are selected, and so on. The final result is 50 models each of n = 1. 20 descriptors. Although these do not necessarily contain the very best linear model for each particular n, this technique is suitable to obtain good models for reasonable effort. 

For the prediction of PD our choice is the model with the highest B j, an 8-descriptor model  

100 random experiments were performed to select best combinations of 8 out of 98 pseudodescriptors to fit 80 pseudoobservations. As in the procedure used for the real data, the 50-fold stepwise selection procedure was applied instead of unfeasible complete searches. The result is m/irB = 0A5266, stdev = 0.04723. Note the rather high mhrR value resulting from several descriptors to be selected from a large descriptor pool. Nevertheless, the difference between B and mhrR for our best model is 10.8 standard deviations. So the original model fits the data far better than the random models, and it is extremely unlikely that it is based on chance correlations. 

We saw that the PD of propyl acrylates is modeled well using arithmetical and topological descriptors with OLS as the predicting method. Thus, computer-intensive 

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