In the car package, you can find the Salaries dataset where it records nine-month academic salary for Assistant Professors, Associate Professors and Professors in a college in the U.S. You can find more information about the dataset in R documents. We are interested in which factors are associated with a professor's salary. Since the response salary is right skewed, a log transformation should be applied to salary. (a) Fit a full model to log(salary) using R. For the dummy variable rank, what is the baseline level chosen by R? (2 marks) (b) For the full model in (a), write out the model fitted. Clearly define variables. (3 marks) (c) Suppose we want to compare the expected salaries on the log-scale for two hypo- thetical professors, A and B. Professor A is a male associate professor in the applied department. Professor B is a female professor in the theoretical department. A and B obtained their PhD degree at the same year. However, A has been teaching for 2 years whereas B has been teaching for 5 years. What is the expected log(salary) difference between A and B