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To evaluate the relationship between variables coefficient of correlation and coefficient of determination obtained from regression are used. But what is the procedure if I have 1 Independent variable (IV), let's call it $X$, and multiple dependent variables $Y_1,Y_2,Y_3,Y_4,Y_5$? All my variables are continuous.

I am trying to evaluate the relationship of GPA with the total test score of an entry exam. The dependent variables will be probably strongly correlated and they do measure the same construct: GPA in fist semester, GPA in second semester, GPA for history course, GPA for technical courses.

Which technique can I use in this case?

I was thinking of reverse regression, as every correlation matrix will be symmetric because of $cov(x,y)=cov(y,x)$.

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Turn the model around. Usually you can turn the model around. Then you can also use all sorts of regression and looking at your example, this seems to be satisfying. You can also solve the dependency between the tests with interaction, found from correlation for groupwise variables/ or identified via testing.

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  • $\begingroup$ so you mean to use reverse regression? $\endgroup$ – user1607 Nov 26 '18 at 14:44
  • $\begingroup$ I mean show that your entry exam test score can be correctly modeled by your GPA's. So Exam_Test_Score=GPA_History+GPA_TechCourse+GPA_second_semester+GPA_First_semester + \epsilon. The only thing that changes in this model is the side of \epsilon which is the error residual. If you choose this model, you can still evaluate if it is a reasonable model by R² and you can also implement interaction terms for interdependency of your GPA_i's . To me there is no reason, why you could not evaluate this model, instead of the other way around, math doesn't care for the direction of your equation. $\endgroup$ – Nuke Nov 27 '18 at 21:53
  • $\begingroup$ My bad, did not look up reverse regression. Yeah that's the way to go. $\endgroup$ – Nuke Nov 27 '18 at 21:55

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