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Probably it is duplicate (but I could not fine it) or it is a question for MathOverflow. Still I would like to use Mathematica to analyze my data.
In experiment I measure the parameter "P" of the set of objects. This is extremely difficult and pricy. From the other hand I can easily measure the set of parameters "p1,p2,...,p10" of all objects. I know that they somehow correlates with parameter "P", but I do not know how. Is it possible reveal this hidden correlation? Should I use some modification of PrincipalComponents or cluster analysis?

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    $\begingroup$ This may be a question for Cross Validated, the companion site for probability and statistics. Once you have a method in mind, then we can see how to implement that in MMA. $\endgroup$ – MarcoB Jun 9 '16 at 21:17
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If you can build a classifier for your data, e.g.

$$F : \{p^k_1,p^k_2,...,p^k_{10}\} \longrightarrow P_i ,$$

then you can use the approach described in this discussion:

"How can I determine the importance of variables from Classify?".

Should I use some modification of PrincipalComponents or cluster analysis?

The document Importance of variables investigation guide", has much more extensive descriptions, explanations, and code for importance of variables investigation using classifiers, Mosaic plots, Decision trees, Association rules, and Dimension reduction.

If all of your data is numerical you can compare simple variable-to-variable scatter plots as shown in this image for the Fisher Iris Dataset:

enter image description here

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