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Statistics LibreTexts

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.

cereal3D.jpg

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.

cereal3D2.jpg

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.

cereal3D3.jpg

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.

randu1.jpg.png

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.

randu2.jog.png

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.