This is one of the following seven articles on Logistic Regression in Excel
Logistic Regression in 7 Steps in Excel 2010 and Excel 2013
R Square For Logistic Regression Overview
Excel R Square Tests: Nagelkerke, Cox and Snell, and Log-Linear Ratio in Excel 2010 and Excel 2013
Excel R Square Tests:
Nagelkerke, Cox and
Snell, and Log-Linear Ratio
There are three different measures of R Square that are commonly quoted for binary logistic regression. They are the Log-Linear Ratio R Square, the Cox and Snell R Square, and the Nagelkerke R Square.
The Nagelkerke R Square is generally the larger value of the three and is the preferred metric of the three. The Nagelkerke R Square is preferred over the Cox and Snell R Square because the Cox and Snell R Square has the limitation that it cannot achieve the value of 1.0 as R Square in linear regression can. The Nagelkerke R Square overcomes that limitation.
The calculations of each of the three R Square methods are shown as follows:
MLLm = -6.6545
MLL0 = -13.8629
n = 20
Log-Linear Ratio R Square =
R Square L
R Square L = 1 – MLLm/MLL0 = 0.5199
Cox and Snell R Square =
R Square CS
R Square CS = 1 – exp[(-2) * (MLLm - MLL0 ) / n ] = 0.5137
Nagelkerke R Square =
R Square N
R Square N = [ R Square CS ] / [ 1 – exp( 2 * MLL0 / n ) ] = 0.6849
These R Square calculations, particularly the preferred Nagelkerke R Square of 0.6849, indicate that the logistic regression equation, P(X) for the full model, has reasonably good predictive power.
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