For binary logistic regression, Minitab shows two types of regression equations. The first equation relates the probability of the event to the transformed response. The form of the first equation depends on the link function.
The second equation relates the predictors to the transformed response. If the model contains both continuous and categorical predictors, the second equation can be separated for each combination of categories. For more information on how to choose the number of equations to display, go to Select the results to display for Fit Binary Logistic Model.
Use the equations to examine the relationship between the response and the predictor variables.
For example, a model to predict whether a customer buys a product has these terms:
- Customer's income
- Whether a customer has children
- Interaction between the two predictors
The first equation shows the relationship between the probability and the transformed response because of the logit link function.
The second equations show how income and whether a customer has children relate to the transformed response. When the customer does not have children, the coefficient for income is about 0.04. When the customer has children, the coefficient is about 0.02. For these equations, the more income a customer has, the more likely they are to buy the product. However, income has a stronger effect on whether the customer buys the product when the customer does not have children.
Binary Logistic Regression: Bought versus Income, Children
Regression Equation in Uncoded Units
P(1) = exp(Y')/(1 + exp(Y'))
No Y' = -3.549 + 0.04296 Income
Yes Y' = -1.076 + 0.01565 Income
If your model is nonhierarchical and you standardized the continuous predictors, then the regression equation is in coded units. For more information, see the section on Coded Coefficients. For more information about hierarchy, go to What are hierarchical models?.