Dynamic displays
A standard scatterplot is a static display that can be presented on paper as effectively as on a computer screen. In contrast, our next display for data with three variables is a dynamic display that can only be used on a computer — the information in the display is conveyed by movement.
Scatterplots can be extended to 3 dimensions
To display a data set with three numerical variables, imagine a clear plastic cube with axes on its three dimensions (height, width and depth) for the three variables. The three axes could be used to locate a small sphere in the plastic for each individual. The plastic cube would be a 3-dimensional scatterplot.
Although a computer screen is only 2-dimensional, it can display a projection of such a 3-dimensional scatterplot. Rotating such a display with the mouse gives a good feel for the shape of the underlying 3-dimensional scatter of points.
Body fat
The data below arise from a detailed study of 252 men which was intended to provide an estimate of an individual's body fat percentage from measurements that could easily be made with a tape measure, callipers and scales. (Accurate determination of body fat involves submersion in water!)
We only consider here the percentage body fat, weight and height of the individuals.
Position the mouse in centre of the scatterplot — depending on your software, the pointer may change into a hand or there may be a target pink circle. Then drag with the mouse. (It may help to imagine that the mouse is holding the surface of a sphere that surrounds the scatterplot and is using that to do the rotation.) Clicking the Spin button starts the plot spinning by itself.
You may click the buttons under the display to change to one of 4 pre-set rotations.
After a little rotation, you should get a good feel for the shape of the scatter. Have you seen the outlier?
Three-dimensional scatterplots are an interesting (and occasionally useful) way to display data. They are however much overrated as an analysis technique and simpler displays are usually more effective for extracting information from multivariate data.