When fitting a logistic model, you want to choose a model (link function and predictors) that results in a good fit to your data. You can use goodness-of-fit statistics to compare the fits of different models. A low p-value indicates that the predicted probabilities deviate from the observed probabilities in a way that the binomial distribution does not predict.

By default, Minitab provides three goodness-of-fit tests: Pearson, Deviance, and Hosmer-Lemeshow.

Pearson and Deviance are both types of residuals for logistic models. They are useful measures for evaluating how well the selected model fits the data. The higher the p-value, the better the model fits the data. You may want to check other models and select the one that produces the largest goodness-of-fit p-values (unless one model has special meaning in your discipline).

For the cereal data, both the Pearson and Deviance tests have p-values that are greater than 0.10 indicating that there is insufficient evidence for the model not fitting the data adequately when the a-level is less than or equal to 0.10.