The correlation coefficient understates the strength of nonlinear relationships. Transformation of one or both variables may linearise the relationship — the higher correlation coefficient is more descriptive of the strength of the relationship. Drag the red lines on the axes to apply power transformations — the arrow keys can be used to fine-tune the transformation.
In the first example, r = -0.907 understates strength of relationship. A log transformation of the response linearises the relationship and gives a more descriptive value, r = -0.994.
In the second example, log transformations of both variables gives a reasonably linear relationship. Ask which mammals now seem most unusual.
Transforming to remove skewness in the marginal distributions usually helps with linearity too.
The first data set shows the numbers of a marine bacterium surviving exposure to 200 kilovolt X-rays for periods ranging from t=1 to t=15 intervals of 6 minutes.
The second data set contains the lifespan (in years) and metabolic rate (measured by oxygen intake per gram of weight) of a selection of mammals.