Jolliffe I. Principal Component Analysis (2ed., Springer, 2002)(518s)

198 8. Principal Components in Regression Analysisrecomputing the PCs as suggested by Mansfield et al. (1977), indicatedthat only 12, and possibly fewer, variables need to be retained. R 2 for the12-variable subset given by this method is 0.862, and it only drops to 0.847for the 8-variable subset, compared with 0.874 for the full model and 0.851using the first 20 PCs in the regression. Other variable selection methods,described by Jolliffe (1972) and in Section 6.3, were also tried, but these didnot produce quite such good results as the Mansfield et al. (1977) method.This is not surprising since, as noted in the previous example, they are notspecifically tailored for variable selection in the context of regression. However,they did confirm that only eight to ten variables are really necessaryin order to provide an adequate prediction of ‘income’ for these data.