A professor decides to run an experiment to measure the effect of time pressure on final exam scores. He gives each of the 400 students in her course the same final exam, but some students have 90 minutes to complete the exam, while others have 120 minutes. Each student is randomly assigned one of the examination times, based on the flip of a coin. Let Y; denote the number of points scored on the exam by the ith student (0 (a) Explain what the term ui represents. Why will different students have different values of ui?
(b) Explain why E(ui|X;) = 0 for this regression model.
(c) Are the other assumptions among SLR.1-SLR.4 satisfied? Explain why.
(d) The estimated model is Y; = 49+0.24X;.
i. Based on the estimated model, predict the average score of students given 90 minutes. Repeat for 120 minutes and 150 minutes.
ii. Compute the average predicted gain in score for a student who is given an additional 10 minutes on the exam.

ui in the regression model represents other underlying factors aside the model variables which may affect the final exam score of student. These factor will almost likely vary from student to student and may include factors such as ; rate of assimilation, natural brilliance, psychological factors and so on.

E(ui|X) = 0 ; because ui and Xi are independent.

The estimated model is Y; = 49+0.24X;.

i. Based on the estimated model, predict the average score of students given 90 minutes.

X = 90 minutes

Y; = 49+0.24(90)

Y = 70.6

Repeat for 120 minutes and 150 minutes.

X = 120 minutes

Y; = 49+0.24(120)

Y = 77.8

X = 150 minutes

Y; = 49+0.24(150)

Y = 85

ii. Compute the average predicted gain in score for a student who is given an additional 10 minutes on the exam.

Gain in score for student Given additional 10 minutes :

Gain in score for X = 10

0.24X

= 0.24(10)

= 2.4