## Sunday, June 1, 2014

### R Square For Logistic Regression Overview

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

# R Square For Logistic Regression Overview

A reliable goodness-of-fit calculation is essential for any model. The measures of goodness-of-fit for linear regression are R Square and the related Adjusted R Square. These metrics calculated the percentage of total variance can be explained by the combined variance of the input variables since variances can added.

R Square is calculated for binary logistic regression in a different way. R Square in this case is based upon the difference in predictive ability of the logistic regression equation with and without the independent variables. This is sometimes referred to as pseudo R Square.

## R Square For Logistic Regression With Excel Solver Overview

### Step 1) Calculate the Maximum Log-Likelihood for Full Model

The Maximum Log-Likelihood Function, MLL, is calculated for the full model. This has already been done by the Excel Solver in order to determine the constants b0, b1, b2, …, bk that create the most accurate P(X) equation. MLL for the full model is designated as MLLm. This has already been calculated to be the following:

MLLm = Maximum Log-Likelihood for Full Model

MLLm = -6.6545

### Step 2) Calculate the Maximum Log-Likelihood for the Model With No Explanatory Variables

Calculating the Maximum Lob-Likelihood Function for the model with no explanatory variables is done by setting all constants (Solver Decision Variables) except b0 to zero before calculating the MLL.

The Maximum Log-Likelihood for the model with no explanatory variables (b1 = b2 = … = bk = 0) designated as MLL0.

The constant b0 is the Y Intercept of regression equation. This is the only constant that will be included in the calculation of MLL0. The other constants, b1, b2, …, bk, are the coefficients of the input variables X1, X2, … , Xk. Setting the constants b1, b2, …, bk to zero removes all explanatory variables X1, X2, … , Xk. The terms b1*X1, b2*X2, …, bk*Xk will now all equal to zero in the Logit (and therefore the logistic equation P(X)) no matter what the values of the input variables X1, X2, … , Xk are.

Constants b1 and b2 are set to zero as follows before running the Excel Solver to calculate MLL0: (Click On Image To See a Larger Version)

Below is the Solver dialogue box to calculate MLL0. Note that there is only one Solver Decision Variable (b0 in cell C2) that will be adjusted to find MLL0. (Click On Image To See a Larger Version)

Running the Solver produced the following MLL0: (Click On Image To See a Larger Version)

MLL0 = Maximum Log-Likelihood for Model With Only Intercept and No Explanatory Variables (b1 = b2 = … = bk = 0)

MLL0 = MLLb1=b2= ... =bk=0 = -13.8629

Calculating MML for the full model produced the following:

MLLm = Maximum Log-Likelihood for Full Model

MLLm = -6.6545

The three different ways to calculate R Square for logistic regression as performed in Excel in the following blog article. These three methods are Nagelkerke, Cox and Snell, and the Log-Linear Ratio.

Excel Master Series Blog Directory

Statistical Topics and Articles In Each Topic

• Histograms in Excel
• Bar Chart in Excel
• Combinations & Permutations in Excel
• Normal Distribution in Excel
• t-Distribution in Excel
• Binomial Distribution in Excel
• z-Tests in Excel
• t-Tests in Excel
• Hypothesis Tests of Proportion in Excel
• Chi-Square Independence Tests in Excel
• Chi-Square Goodness-Of-Fit Tests in Excel
• F Tests in Excel
• Correlation in Excel
• Pearson Correlation in Excel
• Spearman Correlation in Excel
• Confidence Intervals in Excel
• Simple Linear Regression in Excel
• Multiple Linear Regression in Excel
• Logistic Regression in Excel
• Single-Factor ANOVA in Excel
• Two-Factor ANOVA With Replication in Excel
• Two-Factor ANOVA Without Replication in Excel
• Randomized Block Design ANOVA in Excel
• Repeated-Measures ANOVA in Excel
• ANCOVA in Excel
• Normality Testing in Excel
• Nonparametric Testing in Excel
• Post Hoc Testing in Excel
• Creating Interactive Graphs of Statistical Distributions in Excel
• Solving Problems With Other Distributions in Excel
• Optimization With Excel Solver
• Chi-Square Population Variance Test in Excel
• Analyzing Data With Pivot Tables and Pivot Charts
• SEO Functions in Excel
• Time Series Analysis in Excel
• VLOOKUP

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