Question

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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 activities must be 168

Answer 1

i.)

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.

ii.)

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

independent variables: \(\quad\) study \(=168-\) sleep \(-\) work \(-\) leisure, This holds for every

observation, so MLR. 3 violated

iii.)

Simply drop one of the independent variables, say leisure:

$$ G P A=\beta_{0}+\beta_{1} \text { study }+\beta_{2} \text { sleep }+\beta_{3} \text { work }+\mathrm{ei} $$

Now, for example, \(\beta_{1}\) is interpreted as the change in \(G P A\) 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.