8.3: 3D Plots

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Learning Objectives

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.

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.

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