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 his 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 ≤ Y; ≤ 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 Yi=bo+ BiXi + U, E (u) = = 0 Which of the following are true about the unobservable u;? (Check all that apply) ☐ A. u; will be zero for all students because time spent studying is likely the only factor that affects exam performance. "B. u; represents factors other than time that influence the student's performance on the exam. C. All students will necessarily have the same value of u; because they are part of the same population. D. Different students will have different values of u; because they have unobserved individual specific traits that affect exam performance. The Least Squares Assumptions Y=Bo+B₁X; +u, i = 1,..., n where 1. The error term u; has conditional mean zero given X;: E (u;|X;) = = 0; 2. (X,Y), i = 1,..., n, are independent and identically distributed (i.i.d.) draws from their joint distribution; and 3. Large outliers are unlikely: X; and Y; have nonzero finite fourth moments. Assuming this year's class is a typical representation of the same class in other years, are OLS assumption (2) and (3) satisfied? A. Both OLS assumption #2 and OLS assumption #3 are satisfied. ○ B. Only OLS assumption #2 is satisfied. C. Only OLS assumption #3 is satisfied. D. Neither OLS assumption #2 nor OLS assumption #3 is satisfied. The estimated regression is V=47 +0.29X, Compute the estimated regression's prediction for the average score of students given 92, 123, or 154 minutes to complete the exam. Given 92 minutes, the estimated regression's prediction for the average score of students is 73.68 Given 123 minutes, the estimated regression's prediction for the average score of students is 82.67 Given 154 minutes, the estimated regression's prediction for the average score of students is 91.66 (Round your responses to two decimal places.)
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 his 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 ≤ Y; ≤ 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 Yi=bo+ BiXi + U, E (u) = = 0 Which of the following are true about the unobservable u;? (Check all that apply) ☐ A. u; will be zero for all students because time spent studying is likely the only factor that affects exam performance. "B. u; represents factors other than time that influence the student's performance on the exam. C. All students will necessarily have the same value of u; because they are part of the same population. D. Different students will have different values of u; because they have unobserved individual specific traits that affect exam performance. The Least Squares Assumptions Y=Bo+B₁X; +u, i = 1,..., n where 1. The error term u; has conditional mean zero given X;: E (u;|X;) = = 0; 2. (X,Y), i = 1,..., n, are independent and identically distributed (i.i.d.) draws from their joint distribution; and 3. Large outliers are unlikely: X; and Y; have nonzero finite fourth moments. Assuming this year's class is a typical representation of the same class in other years, are OLS assumption (2) and (3) satisfied? A. Both OLS assumption #2 and OLS assumption #3 are satisfied. ○ B. Only OLS assumption #2 is satisfied. C. Only OLS assumption #3 is satisfied. D. Neither OLS assumption #2 nor OLS assumption #3 is satisfied. The estimated regression is V=47 +0.29X, Compute the estimated regression's prediction for the average score of students given 92, 123, or 154 minutes to complete the exam. Given 92 minutes, the estimated regression's prediction for the average score of students is 73.68 Given 123 minutes, the estimated regression's prediction for the average score of students is 82.67 Given 154 minutes, the estimated regression's prediction for the average score of students is 91.66 (Round your responses to two decimal places.)
Chapter2: Mathematics For Microeconomics
Section: Chapter Questions
Problem 2.15P
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Transcribed Image Text: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 his 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 ≤ Y; ≤ 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
Yi=bo+ BiXi + U, E (u) =
= 0
Which of the following are true about the unobservable u;? (Check all that apply)
☐ A. u; will be zero for all students because time spent studying is likely the only factor that affects exam performance.
"B. u; represents factors other than time that influence the student's performance on the exam.
C. All students will necessarily have the same value of u; because they are part of the same population.
D. Different students will have different values of u; because they have unobserved individual specific traits that affect exam performance.
The Least Squares Assumptions
Y=Bo+B₁X; +u, i = 1,..., n where
1. The error term u; has conditional mean zero given X;: E (u;|X;) =
= 0;
2. (X,Y), i = 1,..., n, are independent and identically distributed (i.i.d.) draws from their joint distribution; and
3. Large outliers are unlikely: X; and Y; have nonzero finite fourth moments.
Assuming this year's class is a typical representation of the same class in other years, are OLS assumption (2) and (3) satisfied?
A. Both OLS assumption #2 and OLS assumption #3 are satisfied.
○ B. Only OLS assumption #2 is satisfied.
C. Only OLS assumption #3 is satisfied.
D. Neither OLS assumption #2 nor OLS assumption #3 is satisfied.
Transcribed Image Text:The estimated regression is
V=47 +0.29X,
Compute the estimated regression's prediction for the average score of students given 92, 123, or 154 minutes to complete the exam.
Given 92 minutes, the estimated regression's prediction for the average score of students is 73.68
Given 123 minutes, the estimated regression's prediction for the average score of students is 82.67
Given 154 minutes, the estimated regression's prediction for the average score of students is 91.66
(Round your responses to two decimal places.)
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