New England University maintains a data warehouse that stores information about students, courses, and instructors. Members of the university's Board of Trustees are very much interested in students' academic performance as well as instructors' teaching effectiveness. For example, they may like to know:

• The average grades for different courses taught by different instructors.
• The grade distribution for a particular course in a particular semester (e.g., a newly offered MBA course).
• The average ratings of teaching effectiveness for instructors at different ranks (e.g., Lecturer, Assistant Professor, Full Professor, etc.).
• The correlation between students' grades and their ratings for instructors' teaching effectiveness.

Note that each undergraduate student must declare his/her major and up to two minors by the end of the junior year. A graduate student may have a major (e.g., MBA) and a minor or concentration (e.g., IT).  Some courses (e.g., undergraduate GB courses) may be "co-offered" by several departments. An instructor may be affiliated with more than one department.

1. Draw the two star schemas and specify all relevant attributes.

2. Identify conformed dimensions.

3. Identify any slowly changing dimensions and the attributes whose values may change from time to time.

4. Draw a lattice hierarchy for each dimension that has more than one level.