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This is a visual representation of a 2-dimensional kd-tree. The tree itself is used to iterpolate a local regression surface. For more information on how image itself was generated, see [1].

The data set used is from Brinkman, N.D.: Ethanol Fuel-A Single-Cylinder Engine Study of Efficiency and Exhaust Emissions. SAE transactions, *90*, 1410-1424. (1981). For more information see also Cleveland, William S: Visualizing Data. Hobart Press, Summit, New Jersey, pages 188-190. (1996).

For more information on how kd-trees are used in local regression, see W. S. Cleveland and C. L. Loader: Smoothing by Local Regression: Principles and Methods, Statistical Theory and Computational Aspects of Smoothing, 10-49, edited by W. Haerdle and M. G. Schimek, Springer, New York, 1996.

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This chart was created with R.