For Poisson regression, Minitab shows two types of regression equations. The first equation relates the number of events 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 Poisson Model.
Use the equations to examine the relationship between the response and the predictor variables.
For example, a model to predict whether a resin part has a defect contains these terms:
- Size of Screw
The first equation shows the relationship between the number of events and the transformed response because of the natural log link function.
The second equations show how the size of the screw and the temperature are related to the transformed response. When the size of the screw is large, the coefficient for temperature is about −0.003. When the size of the screw is small, the coefficient is about −0.0005. For these equations, the higher the temperature the fewer defects occur. However, temperature has a stronger effect on the number of defects when the size of the screw is large.
Poisson Regression Analysis: Discoloration De versus Temperature, Size of Screw
Discoloration Defects = exp(Y')
large Y' = 4.649 - 0.003285 Temperature
small Y' = 4.105 - 0.000481 Temperature
If your model is nonhierarchical and you standardized the continuous predictors, 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?.