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# 8.3: 3D Plots

Skills to Develop

• Describe a $$3D$$ Plot
• Give an example of the value of a $$3D$$ plot

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

Figure $$\PageIndex{1}$$: 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 $$\PageIndex{2}$$ is an example.

Figure $$\PageIndex{2}$$: 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 $$\PageIndex{3}$$ represents the different manufacturers by using different colors.

Figure $$\PageIndex{3}$$: The different manufacturers are color coded

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

Figure $$\PageIndex{4}$$: A $$3D$$ scatter plot showing $$400$$ values of $$X$$, $$Y$$, and $$Z$$ from a pseudo random number generator

Figure $$\PageIndex{5}$$ shows a different perspective on these data. Clearly they were not generated by a random process.

Figure $$\PageIndex{5}$$: A different perspective on the $$3D$$ scatter plot showing $$400$$ values of $$X$$, $$Y$$, and $$Z$$ from a pseudo random number generator.

Figures $$\PageIndex{4}$$ and $$\PageIndex{5}$$ are reproduced with permission from R snippets by Bogumil Kaminski.

### Contributor

• Online Statistics Education: A Multimedia Course of Study (http://onlinestatbook.com/). Project Leader: David M. Lane, Rice University.