The regression equation is an algebraic representation of the regression line and is used to describe the relationship between the response and predictor variables. The form of the regression equation with respect to the probability of an event depends on the link function. Use the equation to predict the probability of an event.

Minitab provides a separate regression equation for each level of each categorical predictor in the model. When Minitab calculates probabilities, the results of the linear equation is the input into the equation for the probability.

For the cereal data, there are four equations because there are 2 categorical levels with 2 levels. Because there is no interaction in the model, the coefficient for income is the same in all four equations.

In the absence of interactions, you can evaluate the relative probabilities of the groups with a comparison of the constant values in the equation. For example, customers who did not have children and did not view the ad have the most negative constant (-3.016). This group is least likely to buy the cereal.