Use a Pareto chart of the standardized effects to compare the relative magnitude and the statistical significance of main, square, and interaction effects.
Minitab plots the standardized effects in the decreasing order of their absolute values. The reference line on the chart indicates which effects are significant. By default, Minitab uses a significance level of 0.05 to draw the reference line.
To determine whether the association between the response and each term in the model is statistically significant, compare the p-value for the term to your significance level to assess the null hypothesis. The null hypothesis is that the term's coefficient is equal to zero, which implies that there is no association between the term and the response. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that an association exists when there is no actual association.
Odds ratios that are greater than 1 indicate that the event is more likely to occur as the predictor increases. Odds ratios that are less than 1 indicate that the event is less likely to occur as the predictor increases.
For categorical predictors, the odds ratio compares the odds of the event occurring at 2 different levels of the predictor. Minitab sets up the comparison by listing the levels in 2 columns, Level A and Level B. Level B is the reference level for the factor. Odds ratios that are greater than 1 indicate that the event is more likely at level A. Odds ratios that are less than 1 indicate that the event is less likely at level A. For information on coding categorical predictors, go to Coding schemes for categorical predictors.
Many of the model summary and goodness-of-fit statistics are affected by how the data are arranged in the worksheet and whether there is one trial per row or multiple trials per row. The Hosmer-Lemeshow test is unaffected by how the data are arranged and is comparable between one trial per row and multiple trials per row. For more information, go to How data formats affect goodness-of-fit in binary logistic regression.
The higher the deviance R^{2}, the better the model fits your data. Deviance R^{2} is always between 0% and 100%.
Deviance R^{2} always increases when you add additional terms to a model. For example, the best 5-term model will always have an R^{2} that is at least as high as the best 4-term model. Therefore, deviance R^{2} is most useful when you compare models of the same size.
The data arrangement affects the deviance R^{2} value. The deviance R^{2} is usually higher for data with multiple trials per row than for data with a single trial per row. Deviance R^{2} values are comparable only between models that use the same data format.
Goodness-of-fit statistics are just one measure of how well the model fits the data. Even when a model has a desirable value, you should check the residual plots and goodness-of-fit tests to assess how well a model fits the data.
Use adjusted deviance R^{2} to compare models that have different numbers of terms. Deviance R^{2} always increases when you add a term to the model. The adjusted deviance R^{2} value incorporates the number of terms in the model to help you choose the correct model.
Use AIC, AICc, and BIC to compare different models. For each statistic, smaller values are desirable. However, the model with the smallest value for a set of predictors does not necessarily fit the data well. Also use goodness-of-fit tests and residual plots to assess how well a model fits the data.
If the deviation is statistically significant, you can try a different link function or change the terms in the model.