In statistics, a spurious relationship (or, sometimes, spurious correlation or spurious regression) is a mathematical relationship in which two events or variables have no direct causal connection, yet it may be wrongly inferred that they do, due to either coincidence or the presence of a certain third, unseen factor (referred to as a "confounding factor" or "lurking variable"). Suppose there is found to be a correlation between A and B. Aside from coincidence, there are three possible relationships:
- A causes B,
- B causes A,
- OR
- C causes both A and B.
In the last case there is a spurious correlation between A and B. In a regression model where A is regressed on B but C is actually the true causal factor for A, this misleading choice of independent variable (B instead of C) is called specification error.
Because correlation can arise from the presence of a lurking variable rather than from direct causation, it is often said that "Correlation does not imply causation".
Read more about Spurious Relationship: General Example, Detecting Spurious Relationships
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