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 $cov(x,y)=cov(y,x)$.