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.

Sales of ice cream

The scatterplot below describes sales of ice cream cones from a beach kiosk during 30 days one summer. Sales and the midday temperature were recorded each day. The cones are sold for $2.10 each.

Since the ice cream cones were all sold for the same price, sales can be expressed in units or in dollar revenue (2.1 times the number of cones sold). The midday temperatures can similarly be expressed in degrees Celsius or Fahrenheit.

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.