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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.  The plot shown below could possibly be the graph of which model? 2. If you want to test whether type of student modifies the association between hours of sleep per night and daily productivity score, which model should you consider and what is the null hypothesis for this test?

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.  The plot shown below could possibly be the graph of which model? 2. If you want to test whether type of student modifies the association between hours of sleep per night and daily productivity score, which model should you consider and what is the null hypothesis for this test?

MATLAB: An Introduction with Applications
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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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.  The plot shown below could possibly be the graph of which model?

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

3. Suppose you use Model 5 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: Y = -0.5 + 3 (X1) + 1.5 (X2) + 2.5 (X1)(X2).  

Mean Y Model 1: Y = X₁ = 1 X₁ = 0 (a) Model 2: Y = Bo + B₁X₁ + ε Model 3: Y = B₁ Bo + B₂X₂ + ε Model 4: Y = Bo + B₁X₁ + B₂X₂ + ε = Bo Model 5: Y = Bo + B₁X₁ + B₂X₂ + ß3X₁X₂ + ε X₂
Transcribed Image Text:Mean Y Model 1: Y = X₁ = 1 X₁ = 0 (a) Model 2: Y = Bo + B₁X₁ + ε Model 3: Y = B₁ Bo + B₂X₂ + ε Model 4: Y = Bo + B₁X₁ + B₂X₂ + ε = Bo Model 5: Y = Bo + B₁X₁ + B₂X₂ + ß3X₁X₂ + ε X₂
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