In a study relating college grade point average to time spent in various activities, 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 activities must be 168. The regression model is given by
GPA = β_{0} + β_{1}study + β_{2}sleep + β_{3 }work + β_{4 }leisure +u
a) Does it make sense to hold sleep, work, and leisure fixed while changing study? Why or why not?
b) Explain why this model violates the assumption of no perfect collinearity.
c) How could you reformulate the model so that its parameters have a useful interpretation and it satisfies the no perfect collinearity assumption?