Redundancy in Performance Measures I have a performance rating that correlates positively with a variety of other parameters used individually to evaluate the performance rating of a given operation.  However, I suspect that many of these other parameters are incorporated in the performance rating and that these parameters 'compose' the performance rating, whose composition is not known.  To rephrase, I know nothing about the functional dependence of the performance rating, but do know how these other parameters correlate with both the performance rating and the performance itself (the rating is noisy so these are not necessarily the same).  To define these terms more clearly let me give an example:
Performance Rating: 4.5
Performance: Estimated RPM = 1000
In other words, the rating creates a unit-less way to compare how something is expected to perform.
It turns out that the performance rating predicts performance in a way that is similar to the way specific parameters predict performances, suggesting that these parameters might be components of the rating.  Is there a best way to go about testing whether the reason the performance rating gives similar results is because it is composed of some of these parameters?  That is, is there a way to test whether the predictive capacity of the performance rating is entirely due to these parameters?  Would this just follow a basic regression?
 A: Regression would be a way of tackling it, and it would take the form of a multivariate regression on your parameters. The main advantages are that it would have a unique solution and that is implemented in a large number of software suites; the main disadvantage is that you would have to assume some functional dependence on the parameters. Maybe a multivariate linear regression would be a good way to start exploring your data, but I am not sure it could give a definitive answer to the question you posed.
A rather different approach is to try to understand if the data can be collapsed into a smaller number of dimensions that it has. You could try PCA or factor analysis and conclude if most of the variability can be explained by a smaller number of vectors/components than the parameters + dependent variable you feed it. The main problem will be the interpretation of the principal vectors obtained, but it could certainly shed some light on the degree of correlation among your parameters and between each and the dependent variable.
