Should PCA or correlations be examined first in the context of correlated predictors in regression? I'm looking for clarification: Do we have to run correlation analysis before carrying out principal component analysis (PCA), or is this implicitly subsumed under PCA framework? 
I am on my way to write a research plan:


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*Isolate predictors with high collinear relationship to the process.

*Run PCA to convert correlated predictors to uncorrelated principal component variables.


I am wondering if correlation analysis has to be done separately on the dataset in order to choose highly correlated predictors before applying PCA.
 A: Both examination of a correlation matrix and a principal components analysis will provide useful information about the linear relationships between your predictors. 
In broad terms:


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*The correlation matrix will highlight bivariate relationships. It can detect  pairs of variables with particularly high correlations where from a regression context you might want to remove one of the two or create a composite of the two.

*PCA will highlight multivariate relationships (e.g., sets of highly intercorrelated variables; the degree to which the set of variables can be effectively modelled by a smaller number of composites). It can be useful in informing the creation of composites of the variables.


Also, in broad terms there are differences based on  whether you are taking a theoretical or a predictive orientation to your regression problem. If you have a more theoretical orientation, conceptual reasons may influence when and how you create composites and which if any correlated predictors you drop from an analysis. If you have a predictive orientation, you will be more concerned with maximising prediction, albeit preferably some form of out-of-sample prediction. If you have a theoretical orientation, then you are more likely going to be building arguments from an overall examination of the correlation matrix and the PCA analysis.
