My dog hides, bites his rear, and won't come. Is he depressed or sick?

Billion and his little friend are so cute and I bet they are best of friends. It sounds like he is not feeling good and these cues are his way of telling you this, especially the hiding. I wish we could know if our furry friends are depressed but more often these symptoms are linked to some sort of physical ailment and this is their way of conveying it to us. As he is biting his rear end this could be a sign that something is itchy (do you see any fleas as this is a common area for fleas to be?) or painful for him (like his rear end (anal sac issues are sometimes a concern in younger dogs) or his back). As I can see that you are concerned about your little guy I would recommend he be seen by your family vet for an exam. That way he or she can rule out some common problems and get your little guy some help. I hope this helps and thank you for using Petco Pet Education Center, formerly Petcoach!