12.4 PRINCIPAL COMPONENTS ANALYSIS
So, now that we have identified the multicollinearity among our predictors, what do we do now?
One solution is to apply principal components analysis. Principal components analysis (PCA) seeks to account for the correlation structure of a set of predictor variables, using a smaller set of uncorrelated linear combinations of these variables, called components. The total variability produced by the complete set of m predictors can often be mostly accounted for by a smaller set of k < m components. This means that there is almost as much information in the k components as there is in the original m variables. In addition, the k components are uncorrelated with each other, unlike the original correlated predictors. If desired, the analyst can then replace the original m variables with the k < m components, so that the working data set now consists of n records on k components, rather than n records on m predictors. This...