Consider the following variables:Y=daily productivity score (measured in points)X1=0 if undergraduate student,1 if graduate studentX2=hours of sleep per night1. If you want to test whether type of student modifies the association between hours of sleep per night and daily productivity score, which model (from attached image) should you consider and what is the null hypothesis for this test?A. Use Model 3 and test H0: β2=0B. Use Model 5 and test H0: β3=0C. Use Model 5 and test H0: β1=0D. Use Model 5 and test H0: β2=0E. Use Model 2 and test H0: β1=0 2. Suppose that you decide to use Model 5 (from pocture attached) to describe the relationship between type of student, hours of sleep per night, and daily productivity score. You use the method of least squares to obtain the following:Y= -0.5 + 3(X1) + 1.5(X2) + 2.5(X1X2)What is the estimated slope relating hours of sleep per night and daily productivity score among undergraduate students? A. 2B. None of theseC. 0.5D. 1.5E. 2.5 Mean YX₁ = 1X₁ = 0(a)X2 Model 5: Y = B₁ + B₁X₁ + B₂X₂ + B3X₁X₂ + εModel 3: Y = ß0 + ß₂X₂ + εEModel 1: Y = BoModel 2: Y = Bo + ß₁X₁ + εModel 4: Y = Bo + B₁X₁ + B₂X₂ + εF217#20F3$000000F4X₁ = 00/F5(a)O G+2

Solution: Let Y be the daily productivity score (measured in points), X1 =0 if undergraduate student, 1 if graduate student and X2 be the hours of sleep per night.The different models are 1. Here, it is needed to test whether there is an association between hours of sleep per night and daily productivity score. This means model should contain interaction effect. Thus, the correct model should be used is This is model 5. From the above model the coefficient of interaction term is β3. Then, the null hypothesis for this test is Thus, the correct option is B.2. From the given information, the regression equation is Then, the estimated slope relating hours of sleep per night and daily productivity score among undergraduate students is Thus, the correct option is D.

Answered: Consider the following variables:…

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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Question

Consider the following variables:

Y=daily productivity score (measured in points)

X₁=0 if undergraduate student,1 if graduate student

X₂=hours of sleep per night

1. If you want to test whether type of student modifies the association between hours of sleep per night and daily productivity score, which model (from attached image) should you consider and what is the null hypothesis for this test?

A. Use Model 3 and test H₀: β₂=0

B. Use Model 5 and test H₀: β₃=0

C. Use Model 5 and test H₀: β₁=0

D. Use Model 5 and test H₀: β₂=0

E. Use Model 2 and test H₀: β₁=0

2. Suppose that you decide to use Model 5 (from pocture attached) to describe the relationship between type of student, hours of sleep per night, and daily productivity score. You use the method of least squares to obtain the following:

Y= -0.5 + 3(X1) + 1.5(X2) + 2.5(X1X2)

What is the estimated slope relating hours of sleep per night and daily productivity score among undergraduate students?

A. 2

B. None of these

C. 0.5

D. 1.5

E. 2.5