This project is based on dataset lssal.dta that contains data on median starting salaries of graduates of 156 US law schools in 1985. The variables in the data set are defined as follows: RANK law school ranking (rank=1 is the top ranked school, rank=2 is the second-ranked, etc.) SALARY median starting salary, $/year COST law school cost, $/year LSAT median LSAT score GPA median college GPA LIBVOL number of volumes in library, 1000s FACULTY number of faculty AGE age of law school, years CLSIZE size of entering class NORTH dummy=1 if law school in north SOUTH dummy=1 if law school in south EAST dummy=1 if law school in east WEST dummy=1 if law school in west Notes: 1) Use the dataset lssal.dta provided with the assignment. 2) The dataset has missing observations for some variables. 3) Show your work. PRINT OUT the commands and output for all the operations you are using to answer the questions. 4) You can (and should) use built-in tests whenever possible. That is, use the test command to test simple and complex hypotheses after regressions. 5) Pay close attention to interpreting variable RANK. A higher value of RANK means lower-ranked school. For example, a school with RANK=5 is ranked higher than a school with RANK=10. 6) Pay close attention to logs in the models and interpret accordingly. 1. Consider the following model: log(SALARY) = 0 + 1 LSAT + 2 GPA + 3 log(LIBVOL) + 4 RANK + u. (a) [1p] Use the data file to create the necessary variables, estimate the model, and interpret the results. (b) [1p] Based on the results in (a), would you say it is better, in terms of starting salary, to attend a higher ranked law school? How much is a difference in ranking of 10 worth in terms of predicted starting salary?

(c) [2p] Test if the features of the incoming class of students---LSAT and GPA---are individually and jointly significant for explaining SALARY. (d) [2p] Add the size of the entering class (CLSIZE) and the size of the faculty (FACULTY) to the model. Test their joint significance. Should they have been added? 2. Suppose the research question is how law school ranking affects a graduates starting salary. (a) [2p] Consider the model in problem 1. Does it adequately address the question, given the limitations of the dataset? Explain why or why not. (b) [2p] Use any of the available variables in the dataset to construct the best alternative model you can come up with. Justify your choice. Provide the results for your new model and explain the differences (if any) between the results produced by your model and by the initial model.