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   / Home / LernStats / Correlation / The Coefficient of Determination


LernStats
(Chapter 5 - Page 9 / 9)

The Coefficient of Determination

»I would like to point out, that the correlation coefficint should not be mistaken as a percentage. r = 0.80 for example, does not mean that the values of both variables are equal in 80 of 100 cases.

For r 2 this would make sense. r 2 is often referenced as ´Coefficient of Determination´ (E. WEBER 1963, S. 270 ff). This measure describes in which way the variance of one variable is determined by the variance of the other variable.

A r = 0.80 leads to r 2 = 0.64 this makes it possible to state that 64% of the variance of both variables are determined.«
(CLAUSS/EBNER, 1970, S. 112).

A correlation r, htat looks good at first glance often looks weaker after computing r 2.

e.g.:

r = 0.30 => r 2 = 0.09,

with less than 10% common variance and over 90% unknown parts or specific variance.

Remark: The Coefficient of Determination should only be calculated with product-moment coefficient of correlation or its derivatives.



 
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