8.3 3D Plots

Just as two-dimensional scatter plots show the data in two dimensions, 3D plots show data in three dimensions. Figure 1 shows a 3D scatter plot of the fat, non-sugar carbohydrates, and calories from a variety of cereal types.

Three-dimensional scatterplot of breakfast cereals with axes Carbohydrates (10 to 55), Fat (0 to 10) and Calories (50 to 250), drawn as a wireframe box with dropped gridlines to each point. Most cereals cluster at low fat with carbohydrates between about 20 and 30 and calories between about 100 and 150; a few high-calorie points sit near the top of the box. — Figure 1. A 3D scatter plot showing fat, non-sugar carbohydrates, and calories from a variety of cereal types.

Many statistical packages allow you to rotate the axes interactively to view the data from a different vantage point. Figure 2 is an example.

The same three cereal variables plotted in three dimensions but with the box rotated to a different vantage point, so Fat now runs up the left-hand axis and Calories along the top. The cluster of low-fat cereals now reads as a dense flat sheet near the bottom, and the spread in calories is easier to see than in the first orientation. — Figure 2. An alternative 3D scatter plot showing fat, non-sugar carbohydrates, and calories.

A fourth dimension can be represented as long as it is represented as a nominal variable. Figure 3 represents the different manufacturers by using different colors.

The same rotated cereal plot with a fourth, nominal variable added: each point is colored by manufacturer (red, blue, green and orange). The colors are interleaved through the main low-fat cluster rather than separating into distinct blocks. — Figure 3. The different manufacturers are color coded.

Interactively rotating 3D plots can sometimes reveal aspects of the data not otherwise apparent. Figure 4 shows data from a pseudo random number generator. Figure 4 does not show anything systematic and the random number generator appears to generate data with properties similar to those of true random numbers.

Three-dimensional scatterplot of 400 X, Y, Z triples from a pseudo random number generator, shown inside a wireframe cube. From this vantage point the points look evenly and formlessly scattered throughout the cube — nothing systematic is visible, so the generator appears to behave like a true random source. — Figure 4. A 3D scatter plot showing 400 values of X, Y, and Z from a pseudo random number generator.

Figure 5 shows a different perspective on these data. Clearly they were not generated by a random process.

The same 400 pseudo-random triples viewed from a different angle. The points are no longer formless: they lie on a series of evenly spaced parallel diagonal planes running across the cube, with empty space between them. Rotating the plot exposes the lattice structure that the first view concealed — these values were not generated by a random process. — Figure 5. A different perspective on the 3D scatter plot showing 400 values of X, Y, and Z from a pseudo random number generator.

Figures 4 and 5 are reproduced with permission from R snippets by Bogumil Kaminski.

Adapted from Online Statistics Education: A Multimedia Course of Study (onlinestatbook.com), Project Leader: David M. Lane, Rice University. Developed with NSF support. The original work is in the public domain; it is cited here at the authors' request. Changes were made: reformatted as an accessible XYZ web edition with native MathML. License: Public-Domain.