In a study relating college grade point average to time spent in various activities, you distribute a survey to several students. The students are asked how many hours they spend each week in four activities: studying, sleeping, working, and leisure. Any activity is put into one of the four categories, so that for each student, the sum of hours in the four actives must be 168.
(i) In the model
GPA = (0 + (1 study + (2 sleep + (3 work + (4 leisure + u,
Does it make sense to hold sleep, work, and leisure fixed, while changing study?
(ii) Explain why this model violates Assumption MLR.3.
(iii) How could you reformulate the model so that its parameters have a useful interpretation and it satisfies Assumption MLR.3?