<P> The covariance of two aggregated variables depends not only on the covariance of two variables within the same individuals but also on covariances of the variables between different individuals . In other words, correlation of aggregate variables take into account cross sectional effects which are not relevant at the individual level . </P> <P> The problem for correlations entails naturally a problem for regressions on aggregate variables: the correlation fallacy is therefore an important issue for a researcher who wants to measure causal impacts . Start with a regression model where the outcome Y i (\ displaystyle Y_ (i)) is impacted by X i (\ displaystyle X_ (i)) </P> <Dl> <Dd> Y i = α + β X i + u i, (\ displaystyle Y_ (i) = \ alpha + \ beta X_ (i) + u_ (i),) </Dd> <Dd> cov ⁡ (u i, X i) = 0 . (\ displaystyle \ operatorname (cov) (u_ (i), X_ (i)) = 0 .) </Dd> </Dl> <Dd> Y i = α + β X i + u i, (\ displaystyle Y_ (i) = \ alpha + \ beta X_ (i) + u_ (i),) </Dd>

The primary explanation for the occurrence of the ecological fallacy is