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In statistics, a spurious relationship (not to be confused with spurious correlation) 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 "common response variable", "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: : Where A is present, B is observed. (A causes B.) : Where B is present, A is observed. (B causes A.) : OR : Where C is present, both A ''and'' B are observed. (C causes both A and B.) In the last case there is a spurious relationship 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". A spurious relationship should not be confused with a spurious regression, which refers to a regression that shows significant results due to the presence of a unit root in both variables. == General example == An example of a spurious relationship can be illuminated by examining a city's ice cream sales. These sales are highest when the rate of drownings in city swimming pools is highest. To allege that ice cream sales cause drowning, or vice versa, would be to imply a spurious relationship between the two. In reality, a heat wave may have caused both. The heat wave is an example of a hidden or unseen variable, also known as a confounding variable. Another popular example is a series of Dutch statistics showing a positive correlation between the number of storks nesting in a series of springs and the number of human babies born at that time. Of course there was no causal connection; they were correlated with each other only because they were correlated with the weather nine months before the observations. However Höfer et al. (2004) showed the correlation to be stronger than just weather variations as he could show in post reunification Germany that, while the number of clinical deliveries was not linked with the rise in stork population, out of hospital deliveries correlated with the stork population. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Spurious relationship」の詳細全文を読む スポンサード リンク
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