I have many dependent variables I want to measure (change in volume measurements over time) and want to look at how medication effects those changes. I want to look at:

1). Is there a statistically significant relationship between taking a drug in class A on volume change

2) Is there a statistically significant difference in the effect of taking a drug in class A versus class B on volume change

3) Is there a statistically significant difference between taking a certain drug in class A versus another drug in that same class on volume change?

Because the number of dependent variables is quite high, I am unsure of how I can test for linearity. Further, I am pretty sure I would find linearity with some, but not all, of the DV/IV combinations. I had originally planned on running multiple regression, but now am not sure if that's the right choice.

If someone can offer input or point me in the right direction, I would greatly appreciate it. Thank you!