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Correlation Index


Given a curved regression, the correlation index is defined by

 r_c=(s_(yy^^))/(s_ys_(y^^)),
(1)

where s_y and s_(y^^) are the standard deviations of the data points y and the estimates y^^ given by the regression line (Kenney and Keeping 1962, p. 293). Unfortunately, the quantity s_(yy^^) appears not to be defined by Kenney and Keeping (1962, p. 293). Then

r_c^2=(s_(y^^)^2)/(s_y^2)
(2)
=1-(s_(ey)^2)/(s_y^2),
(3)

where s_(ey)^2 is the variance of the observed ys about the best-fitting curved line (Kenney and Keeping 1962, p. 293).


See also

Correlation Coefficient, Regression

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References

Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, 1962.

Referenced on Wolfram|Alpha

Correlation Index

Cite this as:

Weisstein, Eric W. "Correlation Index." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CorrelationIndex.html

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