The model summary table contains statistics that you can use to select a model. The table includes three statistics:

·    Deviance R-Sq is typically thought of as the proportion of the deviance in the data that the model explains. The larger the deviance R, the better the model fits the data.

·    Deviance R-Sq(adj) is a modified deviance R that has been adjusted for the number of terms in the model. The typical interpretation is the same as for Deviance R2. Use the adjusted statistic to compare models with different numbers of predictors.

·    Akaike Information Criterion (AIC) is the most useful statistic of the three statistics that compare models. However, AIC has no typical interpretation by itself like the R2 statistics do. The smaller the AIC, the better the model fits the data.

Use these statistics to compare different models. High R2 values and low AIC values do not guarantee that a model fits the data well. Use the goodness-of-fit tests in addition to the model summary to assess how well a model fits the data.

For the cereal data, deviance R2 is 12.66%, adjusted deviance R2 is 9.25%, and AIC is 84.77. Higher values of the R2 statistics or a lower value of AIC for another model suggests that a different set of predictors does a better job.