Three or more variables

We previously described the relationship between two numerical variables, X and Y.

In many applications, more than two measurements are made from each individual and the additional variables may throw light on the relationship.

Body fat of AIS athletes

Data were collected from a sample of 202 elite athletes who were in training at the Australian Institute of Sport. Two of the measurements from each athlete were:

Body fat
The percentage body fat of individuals is difficult to measure. Accurate measurements were obtained from the AIS athletes by an underwater weighing technique.
Body mass index (BMI)
The body mass index of an individual is defined as the individual's weight (kg) divided by the squared height (metres). BMI is often used as an indicator of obesity — an adult with BMI of 30 or above is usually classified as obese.

The scatterplot below shows the relationship between Body fat and BMI. The relationship is not particularly strong, throwing doubt on the use of BMI as a predictor of body fat for athletes such as these.

Several other measurements were also made from each individual, as shown in the table below the scatterplot.

Click on any cross on the scatterplot to see the additional information that is available from that athlete.

The extra variables might help us to understand the relationship between body fat and BMI. It may help us to predict body fat more accurately.