Mathematics and Statistics Support

# Regression for categorical dependent (outcome) variables

Regression allows the simultaneous testing of relationships between several continuous and binary independent variables with one dependent (outcome) variable. It also enables the prediction of the dependent through the creation of a model (equation). For standard linear multiple regression, the predicted outcome is continuous but this page relates to analysis for categorical outcomes.

### Logistic regression

Dependent (outcome) variable: Binary (two possible outcomes usual event happens or does not happen)
Independent (predictor/explanatory) variable): Any number of continuous or binary variables.
Use: Tests which independent variables are significant predictors of a binary outcome and the estimation of the likelihood of the event occuring given values of the independent variables.
Example: Car insurance companies estimate the likelihood of you crashing based on your answers to a number of questions using a logistic regression model.

### Other types of categorical regression

There are other types of regression when the outcome is not binary such as:
Multinomial regression
Nominal (more than two possible outcomes) dependent

Ordinal regression Ordinal dependent
Note: We only have notes for binary logistic regression which is a fairly standard technique. If you have more than two categories for your dependent variable, consider combining categories so that there are only two categories and using logistic regression rather than using more complex techniques such as multinomial or ordinal regression

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