Multilevel model , varying intercept and both varying intercept and slope.

The file ProfEvalBeauty.esv (posted in the course web site) contains data from Hamermesh and Parker (2005) on student evaluations of instructors" beauty and teaching quality for several courses at the University of Texas. The teaching evaluations were conducted at the end of the semester, and the beauty judgments were made later, by six students who had not attended the classes and were not aware of the course evaluations. Write a multilevel model to predict course evaluations (the variable course.evaluation) from beauty (beauty.score) allowing the intercept to vary by course category (course. id). Fit the model using Bayesian approach, and interpret the fixed-effects coefficient for beauty.score. How does the variation in average ratings across courses compare to the variation in ratings across evaluators for the same course? b) Write a multilevel model to predict course evaluations from beauty allowing the intercept and coefficient for beauty to vary by course category. Fit the model using Bayesian approach. Compare the results of this model with those of (a). Hint: You may need to increase adapt_delta for MCMC sampling for both (a) and (b)