Is Regression Analysis Really Machine Learning?

That's a broad topic which has been treated many times. Much of what has been written on this topic is good, much is bad. But I find that the stats vs. machine learning argument, at that level, tends to focus on the forest at the cost of completely overlooking the trees. Shah's definitions, which I believe are reflective of many approaches, tend to focus on different ends of the respective spectrums of each of these concepts, treating machine learning as a practical activity and statistics as a theoretical abstraction (and, yes, I'm lumping "statistical modeling" together with "statistics" in this case... at least, for now). The relationship between statistics and machine learning is actually a highly complex one, and merely defining the 2 concepts is not helpful in dissecting this connection.