Distance flown by eagles and their weight
Does distance flown by eagles depend on their weight?
Use this diagram to explain that the marginal relationship between Y and X in a scatterplot may be misleading if the data are observational.
Heavier eagles seem to fly further — Weight and Distance are moderately correlated and a naive biologist might try to explain this in terms of their body mass providing the energy necessary to extend their range.
However click Slice and drag the slider. The data were collected over a year and there is little relationship within any Season — Weight and Distance are uncorrelated conditional on Season.
The marginal relationship was caused by a lurking variable, Season.
The data are artificial.