12.8 VALIDATION OF THE PRINCIPAL COMPONENTS
As with any other data science method, the results of the PCA should be validated, using the test data set. Figure 12.11 shows the proportions of variance explained by all five components, with percentages not much different from the training set results in Figure 12.8. The four rotated components for the test set, shown in Figure 12.12, are similar to those for the training set from Figure 12.10b.
![No alt text required.](https://static.packt-cdn.com/products/9781119526810/graphics/images/c12f011.gif)
Figure 12.11 Proportions of variance explained from R for the test data set.
![No alt text required.](https://static.packt-cdn.com/products/9781119526810/graphics/images/c12f012.gif)
Figure 12.12 Component weights from R for the test data set.
So, did PCA alleviate our multicollinearity problem? We can check by examining
- The correlations among the four components.
- The predictor VIF for the regression of the response on the components.
The correlation matrix for the principal components is shown in Figure 12.13. All correlations are zero, meaning that the components are uncorrelated. Finally, we obtain the VIFs for the regression of Sales per...