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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?

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  • $\begingroup$ When you mean that you do not have knowledge on its component, you mean you do not know its functional dependence or whether it depends on a component or not? From what you wrote I would say you know it depends on some components or variables, but not how. $\endgroup$ Commented May 21, 2014 at 15:01
  • $\begingroup$ @pedrofigueira I should revise my statement then, I meant that I didn't know its functional dependence. $\endgroup$
    – 114
    Commented May 21, 2014 at 15:06
  • $\begingroup$ I think what you are trying to do is to control for the different independent variables you know that affect the dependent variable, your performance measure. To control means to remove their influence and effect. Without knowing the type of data you have is quite difficult to answer. Do you have a set of m measurements with n parameters per measurement, for instance? Do you want to test if the variation in performance is entirely due to the parameters or not? I am sorry to insist, but I think the question is not well posed. $\endgroup$ Commented May 21, 2014 at 15:45
  • $\begingroup$ @Pedrofigueira That's okay, I will try to rephrase it so that it is well-posed. What you have said is correct, I am looking to test if the variation in performance is entirely due to the parameters. $\endgroup$
    – 114
    Commented May 21, 2014 at 15:58

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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.

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