But, still, the smaller the percentage of slaves and slaveowners, the less likely it was that a state would join the rebellion. That's a pretty good wholesale indicator, though of course, it can't account for everything.
You can not make the statement "The Southern states seceded over slavery" and give a clear picture of the whole.
So far as I can make out, historians tend to avoid blanket statements like that, and look at the actual details of the conflict. Nonetheless, it is quite clear that without slavery and the perceived threat to it, there woud have been no secession and no war.
It's not a black and white answer. Very few things are.
Undoubtedly. In history few things happen because of one and only one reason, but the connection between slavery and secession in starting the Civil War is clearer than the reasons for many other conflicts.
...or it could just be a spurious correlation that hasn't been demonstrated under reputable statistical scrutiny.