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 = -0.80 understates strength of relationship. A log transformation of the response linearises the relationship and gives a more descriptive value, r = -0.90.
In the second example, log transformations of both variables result in 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 price and age of second hand Mazda cars that were advertised for sale in the Melbourne Age newspaper on 8 February 1992.
The second data set contains the Gross Domestic Product (GDP in US$billion) and population (million) in the all countries of the world in 1995.