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.

Metabolic rate of turkeys

The scatterplot below describes the metabolic rate (CO2 production in litres per hour) and body weight (kilograms) of 13 wild turkeys.

The pop-up menus allow body weight to be expressed in either kilograms or pounds. The metabolic rates can similarly be shown as either litres per hour or litres per minute.

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.