11.9 For the data set described in Problem 11.6, suppose that you obtain the following results for a random intercept model, where πij is the predicted probability of proficiency, AGEc is mean-centered age using the mean age of 50 years, and STAFFc is the mean-centered number of clinic staff using the mean of 15 staff members:

logit πij ij j AG j ( ) = −  . 27 02. . 5 0 ( ) Ec + 5( ) STAFFc +U0

a. Fully interpret the value of the intercept in this model.

b. Is this a random intercept (only) or random slope model? Explain how you determined this.

c. What would be the predicted odds and probability of recovery for a patient who is 65 years old and is treated in a clinic with 20 staff members?