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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. 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

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

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
ChapterP: Prerequisites
SectionP.6: Analyzing Graphs Of Functions
Problem 6ECP: Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
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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. 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
Mean Y X₁ = 1 X₁ = 0 (a) X2
Transcribed Image Text:Mean Y X₁ = 1 X₁ = 0 (a) X2
Model 5: Y = B₁ + B₁X₁ + B₂X₂ + B3X₁X₂ + ε Model 3: Y = ß0 + ß₂X₂ + ε E Model 1: Y = Bo Model 2: Y = Bo + ß₁X₁ + ε Model 4: Y = Bo + B₁X₁ + B₂X₂ + ε F2 17 # 20 F3 $ 000 000 F4 X₁ = 0 0/ F5 (a) O G +2
Transcribed Image Text:Model 5: Y = B₁ + B₁X₁ + B₂X₂ + B3X₁X₂ + ε Model 3: Y = ß0 + ß₂X₂ + ε E Model 1: Y = Bo Model 2: Y = Bo + ß₁X₁ + ε Model 4: Y = Bo + B₁X₁ + B₂X₂ + ε F2 17 # 20 F3 $ 000 000 F4 X₁ = 0 0/ F5 (a) O G +2
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Suppose that the investigators want to control for whether a subject is over 60 years old in the logistic model from part (g) above. Let the variable Over60 = 1 if a subject is over 60 and 0 otherwise. They fit a logistic model with both Finasteride and Over60 as the predictors and obtain the following: Coefficients: (Intercept) Finasteride Over60 Estimate -1.88067 -0.34736 1.32285 Std. Error 0.05075 0.05355 0.05589 z value -37.059 -6.486 23.670 Pr(>|z|) < 2e-16 8.79e-11 < 2e-16 *** Estimated odds ratio associated with the coefficient for the Over60 predictor: *** *** What is the interpretation of the estimated odds ratio associated with the coefficient for the Over60 predictor? times those The odds of developing cancer among those 60 years old and older are aged under 60 years, adjusting for Finasteride treatment group, using a 5% significance level.
Transcribed Image Text:Suppose that the investigators want to control for whether a subject is over 60 years old in the logistic model from part (g) above. Let the variable Over60 = 1 if a subject is over 60 and 0 otherwise. They fit a logistic model with both Finasteride and Over60 as the predictors and obtain the following: Coefficients: (Intercept) Finasteride Over60 Estimate -1.88067 -0.34736 1.32285 Std. Error 0.05075 0.05355 0.05589 z value -37.059 -6.486 23.670 Pr(>|z|) < 2e-16 8.79e-11 < 2e-16 *** Estimated odds ratio associated with the coefficient for the Over60 predictor: *** *** What is the interpretation of the estimated odds ratio associated with the coefficient for the Over60 predictor? times those The odds of developing cancer among those 60 years old and older are aged under 60 years, adjusting for Finasteride treatment group, using a 5% significance level.
Suppose that you decide to fit a logistic regression model using these data. Let Y = 1 if a subject develops cancer and 0 otherwise. Let Finasteride = 1 if a subject received Finasteride and O if they received placebo. The estimated logistic model is logit (P(Y = 1)) = −1.131 + ß * Finasteride What is the value of ? -0.123 -0.329 -0.331 -0.358 -0.347 €
Transcribed Image Text:Suppose that you decide to fit a logistic regression model using these data. Let Y = 1 if a subject develops cancer and 0 otherwise. Let Finasteride = 1 if a subject received Finasteride and O if they received placebo. The estimated logistic model is logit (P(Y = 1)) = −1.131 + ß * Finasteride What is the value of ? -0.123 -0.329 -0.331 -0.358 -0.347 €
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