“Regression fallacy” in this context could be a special form of causation fallacy (which is also called Post hoc ergo propter hoc). Let me first remind you of what Regression itself is. Regression in statistics is : if you just look at the extremes of one spectrum (e.g in “people’s height”, just looking at the tallest or the shortest people) and measure the correlation of that factor with another variable (the “heights of their children”), you see the regression towards the mean (average); meaning that the children’s height is closer to average than their parents. It is true that height of parents is positively correlated with heights of their children. BUT if you just look at the VERY high or VERY short parents, their children are not THAT tall, or THAT short, but they are still tall or short but closer to the average height that what you expect.

Regression fallacy is when you ASSUME special occasions to be the AVERAGE condition. In the example that I had (having antibiotics for a simple viral common cold), your average state is when you are healthy. In other words having cold or being ill is and extreme condition in the context of your general well-being (most of the time you are healthy; just occasionally you get sick). So there is a high chance that you get back to your normal healthy state without doing anything (unless you get a really bad disease that will kill or disable you with no treatment; we are not talking about this now). One type of logical error that people may commit is that they THINK that their current state (being ill) is their average; and it does not change unless they do something for it. Someone gets medications, someone go to the homeopath, magician, or whatever. While doing this, the disease takes it course and the person get better (getting back to the ACTUAL average). Then he wrongfully thinks that the medication made him better, and the vicious cycle (false belief –> wrong action –> false belief –> …) continues.