t Reader DO Lecture 6 to view.pdf 172 A survey of students has been conducted th

Question

t Reader DO Lecture 6 to view.pdf 172 A survey of students has been conducted that seeks 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 + |study + 2sleep + 3work + Paleisure + () Does it make sense to hold sleep, work and leisure fixed while changing study? (ii) Explain why this model violates assumption MLR3? (i) How could you reformulate the model so that: its parameters have a 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)

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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