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Visualizing Higher-Dimensional Data with 3D Scatterplots

This Demonstration visualizes some four-dimensional data using three-dimensional scatterplots. The data is a random sample of 38 automobiles with four variables: mileage (gallons per mile), weight, displacement, and number of cylinders. There are four possible distinct combinations of interest (mileage-weight-displacement, mileage-weight-cylinders, etc.). Drag to rotate the plot. How does mileage depend on the other variables? Do you think the relationship is approximately linear?

DETAILS

The data is given in [1]. The method given here is reasonable for dimensions, but as increases, the number of combinations of variables rapidly increases and so other methods are needed. In [2] methods are discussed for projecting high-dimensional data into three dimensions and then using a 3D scatterplot along with dynamic graphics methods for brushing and linking.
References
[1] B. Abraham and J. Ledholter, Introduction to Regression Modeling, Belmont, CA: Brooks/Cole, 2006.
[2] D. Cook and D. F. Swayne, Interactive and Dynamic Graphics for Data Analysis, New York: Springer, 2007.

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