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A regression fallacy is a logical fallacy that occurs when an extreme value of some randomly varying event (something exceptional) is accepted as the normal value, and so when the value regresses to the mean, this change is believed to have been caused by some other event.
- "Approximately 3,000 people were killed in the U.S. due to terrorism in 2001. There were twelve such deaths in 2002. This shows that techniques to prevent terrorism were massively improved after 2001."
This is fallacious. Historically, deaths due to terrorism in the U.S. are rare events, and therefore, after a major spike in the statistics, it is to be expected that there is a regression toward the mean: that the next year's figures would be more like the historical norm.
In general, moving from a mere statistical correlation (or negative correlation) to proof of cause and effect is tricky. In the above example, anti-terrorist measures may indeed have played a role in preventing major attacks in 2002, but the statistics alone are only very weak evidence for this.