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Definition:

Regression analysis is used for explaining or modeling the relationship between a single variable Y, called the response, output or dependent variable, and one or more predictor, input, independent or explanatory variables, X1 .... Xp.

from this book https://cran.r-project.org/doc/contrib/Faraway-PRA.pdf

What does independent variables mean in the definition?

Considering Xs to be random variables,does it mean that P(Xi|Xj) = P(Xi). BUt this would be very constrainted for anyone trying to use regression analysis as inputs tend to be dependent in most of the cases.

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    $\begingroup$ "Independent variable" is just one of the many names used for the right-hand side variables (just re-read the quoted passage!). The term is meant to illustrate that the modeled dependence goes from right to left (the value of Y "depends" on the value of the Xs). No, the Xs are not assumed to be pairwise independent. $\endgroup$ – Andreas Dzemski Feb 21 '18 at 13:11
  • $\begingroup$ can someone close this question...i dont have enough rep to do that i guess $\endgroup$ – claudius Feb 21 '18 at 13:13
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    $\begingroup$ You can delete your own question that doesn't have an upvoted answer. Voting to close etc. not needed here. You should see a box for doing that. $\endgroup$ – Nick Cox Feb 21 '18 at 14:34
  • $\begingroup$ Many threads on this site deal with independent variables. I will redirect this thread to the (current) top hit on a search for "independent variable". $\endgroup$ – whuber Feb 21 '18 at 16:06