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Sometimes R2 > r2 yx1 + r2 yx2 : Correlated Variables Are Not Always Redundant

David Hamilton
The American Statistician
Vol. 41, No. 2 (May, 1987), pp. 129-132
DOI: 10.2307/2684224
Stable URL: http://www.jstor.org/stable/2684224
Page Count: 4
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Sometimes R2 > r2
yx1
 + r2
yx2
: Correlated Variables Are Not Always Redundant
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Abstract

An extreme example of regression on two variables is presented in which there is almost no correlation between y and x1 and y and x2, yet the coefficient of determination is 1. This example illustrates the often counter-intuitive nature of multivariate relationships and is also relevant to discussions on multicollinearity and variable selection techniques.

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