4. In a study relating college grade point average to time spent in various acti

Question

4. 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 four categories, so that for each student, the sum of hours in the four activities must be 168 (total number of hours in a week) In the following model: a. GPA = 0 + |study + 2sleep + 3work + 41eisure + u ke sense to hold sleep, work, and leisure fixed, while changing study? b. Explain why this model violates the No perfect collinearity assumption for unbiasedness. (Hint: Remember perfect collinearity can happen when one independent variable is a linear combination of one or more of the other independent variables)

Explanation / Answer

a. In the given multiple variable model, as it is asked to change the study hours variable while keeping all other variable fixed. THere is no sense to change study hours while keeping other variable fixed.

As study + sleep + work + leisure = 168 hours are fixed here so these variables also are not indpendent of each other. SO, it doesn't make sense.

b. Here one variable like study is a linear combination of other variables Sleep, Work and leaisure .

Study = 168 - (sleep + work + leisure)

So, here as the variables are dependent of each other, then the model violates the No perfect collinearity assumption for unbiasedness.

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