# Binary Logistic Regression

Statistics Solutions provides a data analysis plan template for the binary logistic regression analysis. You can use this template to develop the data analysis section of your dissertation or research proposal.

The template includes research questions stated in statistical language, analysis justification and assumptions of the analysis. Simply edit the blue text to reflect your research information and you will have the data analysis plan for your dissertation or research proposal.

**Data Analysis Plan: Binary Logistic Regression**

Copy and paste the following into a word document to use as your data analysis plan template.

*Research Question:*

Do independent variable 1 and independent variable 2 predict dependent variable?

H_{o}: Independent variable 1 and independent variable 2 do not predict dependent variable.

H_{a}: Independent variable 1 and independent variable 2 predict dependent variable.

*Data Analysis*

To examine the research question, a binary logistic regression will be conducted to assess if the independent variable(s) predict the dependent variable. The binary logistic regression is an appropriate statistical analysis when the purpose of research is to assess if a set of independent variables predict a dichotomous dependent variable (Stevens, 2009). This type of analysis can be used when the independent variables (predictors) are continuous, discrete, or a combination of continuous and discrete. For this research question, the independent variables are independent variable 1, independent variable 2, etc.; the dependent variable is dependent variable and consists of two levels. This analysis permits the evaluation of the odds of membership in one of the two outcome groups based on the combination of predictor variable values. Evaluation of the logistic regression model includes the overall model evaluation and a classification table showing the percentage of correct predictions. The overall model significance for the binary logistic regression will be examined using the χ^{2} omnibus test of model coefficients. The Nagelkerke *R*^{2} will be examined to assess the percent of variance accounted for by the independent variables. Predicted probabilities of an event occurring will be determined by Exp (β).

Binary logistic regression analysis, by design, overcomes many of the restrictive assumptions of linear regressions. For example, linearity, normality and equal variances are not assumed, nor is it assumed that the error term variance is normally distributed. The major assumption is that the outcome variable must be dichotomous. There should be no multicollinearity among the independent variables, there should be no outliers, and there should be a linear relationship between the odds ratio and the independent variable. Linearity with an ordinal or interval independent variable and the odds ratio can be checked by creating a new variable that divides the existing independent variable into categories of equal intervals and conducting the same regression on these newly categorized versions as categorical variables. Linearity is shown if the *B* coefficients increase or decrease in linear steps. Finally, a larger sample is recommended with the maximum likelihood method; using discrete variables requires that there are enough responses in each category.

*Reference*

Statistics Solutions. (2016). Data analysis plan: Binary Logistic Regression [WWW Document]. Retrieved from http://www.statisticssolutions.com/membership-resources/member-profile/data-analysis-plan-templates/binary-logistic-regression/