I have a scenario where I am collecting a bunch of attributes/demographics about a person. Examining the scatterplot Matrix, it seems that there is not much correlation between various attributes for these 2000 data points. But because they all belong to the same person, they're not independent in the true sense of the term. In such scenarios, is it fair to treat them as independent regressors? (For my data points, I may not find any aliases)

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    $\begingroup$ There is no assumption in multiple regression that regressors should be independent! $\endgroup$ – kjetil b halvorsen Oct 7 '15 at 16:48
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    $\begingroup$ @Kjetil is perfectly right, so the short answer is "no, but it's irrelevant." However, examining a scatterplot matrix--although always a good idea--gives only a small part of the story of the linear relationships among the regressors. It is possible for the regressors to be collinear without exhibiting much, if any, noticeable linear relationships in the scatterplot matrix.That can create estimation problems. If you have many attributes, use tools such as VIF, COVRATIO, PCA, etc. to identify, diagnose, and (if necessary) correct near-collinearity. $\endgroup$ – whuber Oct 7 '15 at 17:10
  • $\begingroup$ Can you please provide the (or your) definition of "independence in the true sense of the word"? It appears that you say that "if a vector of attributes relate to the same person, then these attributes cannot be independent". Why? The concept of "Independence" in the context of probability theory/Statistics has a specific meaning, which does not coincide with the meaning this word may take in everyday language, or in the context of other sciences. $\endgroup$ – Alecos Papadopoulos Oct 7 '15 at 17:16
  • $\begingroup$ Thanks everyone! @Alecos my concern is they're all attributes of one person. So, they're related in some way (may be theoretically), but say in my data sample (supposed to be simple random) I don't find a relationship. Should I consider for all practical purposes, the x variables to be independent? $\endgroup$ – rk567 Oct 7 '15 at 21:05

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