Correlations Introductory Overview - Nonlinear Relations between Variables

Another potential source of problems with the linear (Pearson r) correlation is the shape of the relation. As mentioned before, Pearson r measures a relation between two variables only to the extent to which it is linear; deviations from linearity will increase the total sum of squared distances from the regression line even if they represent a "true" and very close relationship between two variables. The possibility of such non-linear relationships is another reason why examining scatterplots is a necessary step in evaluating every correlation. For example, the following graph demonstrates an extremely strong correlation between the two variables that is not well described by the linear function.