# 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.