## Sunday, June 1, 2014

### Excel R Square Tests: Nagelkerke, Cox and Snell, and Log-Linear Ratio in Excel 2010 and Excel 2013

This is one of the following seven articles on Logistic Regression in Excel

Logistic Regression Overview

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

Likelihood Ratio Is Better Than Wald Statistic To Determine if the Variable Coefficients Are Significant For Excel 2010 and Excel 2013

Excel Classification Table: Logistic Regression’s Percentage Correct of Predicted Results in Excel 2010 and Excel 2013

Hosmer- Lemeshow Test in Excel – Logistic Regression Goodness-of-Fit Test 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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