Strength of a relationship
We explained earlier that the strength of the relationship between two variables is very important and this section introduces a numerical summary. This should not depend on the units in which we measure the two variables.
Warping of wood
The scatterplot below describes the warping (measured as a bending angle) of 3 metre lengths of wood which have been left for 1 week at various temperatures.
The pop-up menus allow temperatures to be expressed in degrees Celsius or Fahrenheit. The angles can similarly be expressed in degrees or radians.
Whatever the units, the relationship between the two variables has the same form (and strength).
We therefore start by defining units-free versions of the two variables and will summarise the strength of the relationship in terms of them.