A note on a General Definition of the Coefficient of Determination

thumbnail of NoteonCoeffofdetermination Original by N.J.D Nagelkerke, Biometrika, 1991, 2 pages 

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  • The use of R2, the coefficient of determination, also called the multiple correlation coefficient, is well established in classical regression analysis (Rao,1973)
  • R2 is the square of the Pearson correlation between x and the coefficient score of the model p(), that is the derivative with respect to Beta of log{p(y¦Beta.x+lambda)} at Beta=0
  • For discrete models does not go all the way to 1.
  • Max(R2)=1-exp{2n-1l(0)}=1-L(0)2/n
  • Nagelkerke rescales R2 so that it’s maximum is 1 such that R2 = R2 /max(R2)
  • Just cosmetics.