Question 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 his course the same final exam, but some students have 90 minutes to complete the exam while others have 120 minutes. Each students 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 (X₂ = 90 or 120), and consider the regression model Yi = 3o+ BiXi tui. (1) Explain what the term u; represents. Why will different students have different values of ui? (2) Explain why E(u₁|X₁) = 0 for this regression model. (3) The Least Squares Assumptions Y = Bo + BiXi+ui, i = 1 …, ng
Question 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 his course the same final exam, but some students have 90 minutes to complete the exam while others have 120 minutes. Each students 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 (X₂ = 90 or 120), and consider the regression model Yi = 3o+ BiXi tui. (1) Explain what the term u; represents. Why will different students have different values of ui? (2) Explain why E(u₁|X₁) = 0 for this regression model. (3) The Least Squares Assumptions Y = Bo + BiXi+ui, i = 1 …, ng
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Question 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 his course the same final exam, but
some students have 90 minutes to complete the exam while others have 120 minutes.
Each students 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 + BiXitu.
(1) Explain what the term u, represents. Why will different students have different values
of ui?
(2) Explain why E(u₁|X₁) = 0 for this regression model.
(3) The Least Squares Assumptions
Yi Bo + B₁Xi + Ui, i = 1,..., n,
where
I The error term u, has conditional mean zero given X₂: E(ui Xi) = 0;
II (X₁, Yi), i
1,, n, are independent and identically distributed (i.i.d.) draws
from their joint distribution; and
III Large outliers are unlikely: X, and Y; have nonzero finite fourth moments.
=
Are the above assumptions satisfied? Explain.
(4) The estimated regression is Ỹ; =49+0.24X.
MMAT5330 Econometric Principles and Data Analysis
(a) Compute the estimated regression's prediction for the average score of students
given 90 minutes to complete the exam. Repeat for 120 minutes and 150 minutes.
(b) Compute the estimated gain in score for a student who is given an additional 10
minutes on the exam.
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