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The regression (or regressive) fallacy is a logical fallacy. It ascribes cause where none exists. The flaw is failing to account for natural fluctuations. It is frequently a special kind of the post hoc fallacy.

Things like stock market prices, golf scores, and chronic back pain can fluctuate naturally and may regress towards the mean. The logical flaw is to make predictions that expect exceptional results to continue as if they were average. (See representativeness heuristic.) People are most likely to take action when variance is at its peak. Then after results become more normal they believe that their action was the cause of the change when in fact it was not causal.

The word ‘regression’ was coined by Sir Francis Galton in a study from 1885 called "Regression Toward Mediocrity in Hereditary Stature”. He showed that the height of children from very short or very tall parents would move towards the average.^{[citation needed]} In fact, in any situation where two variables are less than perfectly correlated, an exceptional score on one variable will not be matched by an equally exceptional score on the other variable. The imperfect correlation between parents and children (height is not entirely heritable) means that children's height will fall somewhere between the average of the parents and the average of the population as whole.

When his pain got worse, he went to a witchdoctor, after which the pain subsided a little. Therefore, he benefited from the witchdoctor's powers.

The pain subsiding a little after it has gotten worse is more easily explained by regression towards the mean^{[citation needed]}. Assuming it was caused by the witchdoctor is fallacious.

The student did exceptionally poorly last semester, so I punished him. He did much better this semester. Clearly, punishment is effective in improving students' grades.

Often exceptional performances are followed by more normal performances, so the change in performance might better be explained by regression towards the mean. Incidentally, tests^{[citation needed]} have shown that people may develop a systematic bias for punishment and against reward because of reasoning analogous to this example of the regression fallacy.

The frequency of accidents on a road fell after a speed camera was installed. Therefore, the speed camera has improved road safety.

Speed cameras are often installed after a road incurs an exceptionally high number of accidents, and this value usually falls (regression to mean) immediately afterwards. Many speed camera proponents attribute this fall in accidents to the speed camera, without observing the overall trend.

On the other hand, dismissing valid explanations can lead to a worse situation. For example:

After the Western Allies invaded Normandy, creating a second major front, German control of Europe waned. Clearly, the combination of the Western Allies and the USSR drove the Germans back.

Given that the counterattacks against Germany occurred only after they had conquered the greatest amount of territory under their control, regression to the mean can explain the retreat of German forces from occupied territories as a purely random fluctuation that would have happened without any intervention on the part of the USSR or the Western Allies.

In essence, mis-application of regression to the mean can reduce all events to a "just so" story, without cause or effect.

• Fallacy files: Regression fallacy