Binary logistic regression examines the relationship between one or more predictor variables and a binary response. The logistic equation can be used to examine how the probability of an event changes as the predictor variables change.

The interpretation of the estimated coefficients for categorical predictors is relative to the reference level of the predictor. Positive coefficients indicate that a level of the predictor is more likely to impact the binary response than the reference level. Negative coefficients indicate that a level of the predictor is less likely to impact the binary response than the reference level. Coefficients close to zero indicate that an association between the predictor and binary response may not be important.

For the cereal data,

·    The positive coefficient for ViewAd (1.034) implies that an adult that has viewed the advertisement is more likely to purchase the cereal than an adult that has not viewed the advertisement. Note that the reference level for ViewAd is No.

·    Similarly, the positive coefficient for Children (1.433) implies that an adult with children is more likely to purchase the cereal than an adult without children. Note that the reference level for Children is No.

·    The positive coefficient for Income (0.0137) implies that the greater the household income, the more likely a subject is to purchase the cereal. This statement only applies to the range of household incomes in the sample, that is, incomes less than $75,000. (The relatively large p-value suggests that this association is not important. You would probably exclude this predictor and refit the model.)