2. A survey of students has been conducted thatIseeks to relate academic perform

Question

2. A survey of students has been conducted thatIseeks to relate academic performance (average grade) to time spent at various activities. Students are asked how many hours per week they spend studying, sleeping, working and at leisure. For each student, the sum if the hours spent on the four activities must be 168 (i.e. 7 times 24). In the model, grade = 0 + 1Study + 2sleep + 3work +leisure + (i) Does it make sense to hold sleep, work and leisure fixed while changing study? (i) Explain why this model violates assumption MLR3? (ii) How could you reformulate the model so that: its parameters have a useful 10 10 interpretation; and it satisfies assumption MLR3.

Explanation / Answer

(i) Here in the given model. The basic fact is

study + sleep + work + leisure = 24 hours ....(i)

as there are only 24 hours in a day which can be spend in these 4 activites that means if we hold sleep, work and leisure fixed we will automatically get the results for study time, as there is a relation between all the variables. So, it is not sensible here.

(ii) Yes, this model violates the assumption MLR3 which relates to multicollinearlity between regressor or independent variables, as regressor model varies linearly with each other.

(iii) Here we will put the relation given in (i) , in the model equation.

so grade = 0 + 1 study + 2 sleep + 3  work + 4 leisure + u

so by putting, study = 24 - sleep - work - leisure

grade = 0 + 1 ( 24 - sleep - work - leisure) + 2 sleep + 3  work + 4 leisure + u

grade = (0 + 24 1) + (2  - 1) sleep + (3  - 1) work + (4  - 1) leisure + ui

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