Applied Statistics PhD Comprehensive Question #2

PhD students in the Dept. of Statistics at the University of Toronto normally write three comprehensive exams at the end of their first year, in Probability, Theoretical Statistics, and Applied Statistics. Below is a question I set for the 2007 exam in Applied Statistics. It may be an interesting exercise for others too. It should in theory be doable by someone with just a good introductory undergraduate course in statistics, including multiple regression. However, many PhD students had difficulty with it, so I wouldn’t say it’s easy.

The question is here. I’ll post my answer in a week or so.

My previous post with a question from the 2008 exam is here.

Update: Here is the post with the answers.