A GEOMETRIC CHARACTERIZATION OF LINEAR REGRESSION
- 1 March 2003
- journal article
- research article
- Published by Taylor & Francis in Statistics
- Vol. 37 (2) , 101-117
- https://doi.org/10.1080/0223188031000112881
Abstract
It hardly seems an exaggeration to contend that the fitting of straight lines to experimental data permeates all of science. Would it not seem reasonable to expect a purely geometric characterization of such a straight line? Just such a geometrical perspective was provided by Francis Galton in 1886 if only one of the experimental variables contains an error. This was extended by Karl Pearson in 1901 to allow both variables to be subject to measurement error so long as both errors have equal variances. After an intervening century, the present paper extends the Galton/Pearson geometrical characterization of linear regression in terms of the "concentration ellipse" to the case of unequal variances in the experimental data.Keywords
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