Mediation model with linear regression In my master thesis I have drawn a few hypotheses. I have answered them all with linear regression. In these linear regressions, I took control variables into account. 
My question is: do I have to run a mediation analysis? Or is it also possible to report the regressions of all relations separately (for example: X -> Y, X -> M, M -> Y and A -> Y)?
Here is how my model look like:

My main hypothesis is about the relation between X and Y. 
I hope my question is clear.
Thank you in advance! 
 A: You can run regression models separately, if you follow the Baron-Kenny approach. As far as I know, there are two general approaches to test for mediation: (1) path models (and, SEM, of course) and (2) the Baron-and-Kenny approach (see item (a)). I use Mplus to run my mediation models which is very handy (+ bootstrapped standard errors). 
Unfortunately, you did not tell us what software package you are using to do your analysis. You have a couple of options:
(a) You might be interested in D Kenny's website on mediation . He gives a very clear description how to proceed in order to test for a mediation effect (see "Baron and Kenny Steps"). 
(b) If you happen to use Stata or R for your analysis, you could check out the ATA website on Stata Frequently Asked Questions (search for 'mediation') or the R package mediation. If you use SPSS, you will like this website. Kenny's website also offers a couple of tips for different software packages, e.g. how to get bootstrapped standard errors in SPSS or SAS.
A: Whether you control for A depends on what you are trying to accomplish. Including A in the model will increase your R-squared.
But if A is uncorrelated with X or M (as your diagram indicates) then inclusion/non-Inclusion of A will not affect coefficients or p-values for X or M.
