When fitting a nominal logistic model, you want to choose a model that fits your data well. 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 multinomial distribution does not predict.

Minitab provides two goodness-of-fit tests: Pearson and Deviance.

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 by considering other predictors, quadratic terms, and/or interaction terms. By including all significant terms, you are more likely to have an acceptable goodness-of-fit p-value.

For the horse racing data, both the Pearson and Deviance tests have p-values (0.771 and 1.000, respectively) that are far greater than 0.05 indicating that there is insufficient evidence for the model not fitting the data adequately.