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This can be illustrated yet another way

This can be illustrated yet another way - . . . .

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This can be illustrated yet another way. Each circle below represents the  variability in a set of numbers. The area of the circle labeled Y represents  the variability on the Y-axis. The area of the circle labeled X represents  the variability on the X-axis. The intersection of the two circles represents  the covariance while the area in Y remaining in addition to the overlap  represents the variability around the regression line or the variability in Y  not "explained" or accounted for by the variability in X.    There are several types of models for accountable variance. They differ  with respect to what is known, or what information is specified by the  model, and the certainty of their predictions.  It is necessary to experimentally manipulate the relevant variables to  prove that a cause-effect relationship exists. 
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