Question

2. . In a study relating college grade point average (GPA) 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 activities must be 168. Based on the study, you set an econometric model: GPA P+study+B,sleep+,work+B,leisure+ a. Does this model satisfy all the Gauss-Markov assumptions? Briefly Explain b. Why must the sum of hours in hours? the four activities be 168 c. How could you reformulate the model to satisfy all the assumptions and to have a useful interpretation?

Answer 1

a)

No. By definition, study + sleep + work + leisure = 168. Therefore, if we change study, we must change at least one of the other categories so that the sum is still 168.

b)

From part (i), we can write, say, study as a perfect linear function of the other independent variables:

study = 168 − sleep − work − leisure.

study + sleep + work + leisure = 168

This holds for every observation. Hence, It must be the sum of hours in the four activities be 168 hours.

c)

Simply drop one of the independent variables, say leisure:

GPA = β0 + β1 study + β2 sleep + β3 work + u.

Now, for example, β1 is interpreted as the change in GPA when study increases by one hour, where sleep, work, and u are all held fixed. If we are holding sleep and work fixed but increasing study by one hour, then we must be reducing leisure by one hour. The other slope parameters have a similar interpretation.