Question

2. (Based on Stock & Watson "Introduction to Econometrics 6th ed., Exercise 4.5.) 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 student (0 S Y S 100), let X, denote the amount of time that the student has to complete the exam (X, = 90 or 120), and consider the regression model: (a) Explain what the term u represents. Why will different students have different values of u,? (b) Explain why E(u,IX.) = 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

Answer 1

Date: ----8/5/2019 Answer. Consider the experiment provided in the exercise; to measure the effect of time pressure on exam scores, the information from the exercise is written below 1. 400 students take the same exam. 2. Some students have 90 minutes to complete the exam. 3. Some students have 120 minutes to complete the exam. 5. Dependent variable is written below Y, Points scored by the ith student, 0sY, s100 6. Independent variable is written below X,Time to complete the exam by the i student, X, 90 or 120 7. The regression model is Y-Д +AX, +1,

The term u, represents other factors that have an effect on an individual student's exam score. For, example, studying time vary with students, and varying aptitude capability possessed by different students

b. Due to random assignment of X,, u, is independent of X, Since, u, represents deviations from the average value, so E(u,)-0. Also, since uand x are independent, then:

C. The assumption that (X..Х),i = 1, , n are independent and identically distributed draws from their joint distribution is true if this year's students are viewed as random draws from the population of students that take this class.

The assumption that, large outliers are unlikely: X,and Yhave non zero finite fourth moments is true because of the restricted values of Y,0s Y S 100, and X90 or 120, it is expected that outliers are unlikely to occur

i. The computation of the prediction for the average score of students given 90 minutes to complete the exam is as shown below Y, = 49 + 0.24 × 90 170.6 The computation of the prediction for the average score of students given 120 minutes to complete the exam is as shown below Y, 49 + 0.24x1 20 = 77.8 The computation of the prediction for the average score of students given 150 minutes to complete the exam is as shown below Y 490.24x150 185

ii. The computation of the estimated gain in score for a student who is given an additional 10 minutes on the exam is calculated as follows Y = 0.24X, =0.24x10 = 2.4