EXAMPLE 17.4 Parameter Estimates for Tipping Behavior

CASE 17.1 For the tipping example, we found the log odds for servers wearing red,

and for servers wearing a different color,

To find estimates and of the model parameters and we match the two model equations in Example 17.3 with the corresponding data equations. Because

the estimate of the intercept is simply the logs odds ) for servers wearing a different color,

Similarly, the estimated slope is the difference between the log(odds) for servers wearing red and the log(odds) for servers wearing a different color,

The fitted logistic regression model is