Attributing the change in mean from the regression effect
to some cause. The cause can be almost anything.
A way of lying with statistics.
Let's take a whole bunch of students and give them a test, any test. Now let's take the lowest scorers and give them some "special treatment." Say we give them all red shoelaces. Now we retest them. Lo and behold, their test scores have gone up! New shoes all around!
Of course, the regression effect says that any time you re-measure a group chosen by its low mean (relative to the population as a whole,) their mean will go up (all other things being equal.)
This fallacy is particularly powerful because the regession effect is more pronounced the farther a group is from the mean. So the cause can appear to be "helping those who need it the most."