A professor wants to investigate the relationship between the grades students obtain in their midterm exam (X;) and the grades they obtain (Y;) in the final exam. The professor collects data from 60 randomly chosen students. The estimated OLS regression is: V₁ = 45 +0.74X;, where ŷ, denotes the predicted value of the grades obtained in the final exam by the 1th individual and X; denotes the grades obtained in the midterm exam. From the sample data he makes the following calculations: ^2 where u¡ is the square of the residual for the ith observation. 60 Σ (X; -X)² = 230.48, i=1 60 Σ (X-X)²=471.87, i=1 He wants to test whether the grades obtained in the midterm exam have any effect on the grades obtained in the final exam or not. Which of the following are the null and the alternative hypotheses of the test the professor wishes to conduct? OA. Ho B₁ =0 vs. H₁: ß₁ #0. OB. Ho B₁ =0.74 vs. H₁: ß₁ # 0.74. OC. Ho: B₁ 0 vs. H₁: ß₁ = 0. D. Ho B₁ 0.74 vs. H₁: ß₁ = 0.74. If B₁ is the estimated slope coefficient, then the value of standard error of the estimated slope (SE (B₁)) is (Round your answer to four decimal places.)
A professor wants to investigate the relationship between the grades students obtain in their midterm exam (X;) and the grades they obtain (Y;) in the final exam. The professor collects data from 60 randomly chosen students. The estimated OLS regression is: V₁ = 45 +0.74X;, where ŷ, denotes the predicted value of the grades obtained in the final exam by the 1th individual and X; denotes the grades obtained in the midterm exam. From the sample data he makes the following calculations: ^2 where u¡ is the square of the residual for the ith observation. 60 Σ (X; -X)² = 230.48, i=1 60 Σ (X-X)²=471.87, i=1 He wants to test whether the grades obtained in the midterm exam have any effect on the grades obtained in the final exam or not. Which of the following are the null and the alternative hypotheses of the test the professor wishes to conduct? OA. Ho B₁ =0 vs. H₁: ß₁ #0. OB. Ho B₁ =0.74 vs. H₁: ß₁ # 0.74. OC. Ho: B₁ 0 vs. H₁: ß₁ = 0. D. Ho B₁ 0.74 vs. H₁: ß₁ = 0.74. If B₁ is the estimated slope coefficient, then the value of standard error of the estimated slope (SE (B₁)) is (Round your answer to four decimal places.)
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
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Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...
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Transcribed Image Text:A professor wants to investigate the relationship between the grades students obtain in their midterm exam (X;) and the grades they obtain (Y;) in the final exam.
The professor collects data from 60 randomly chosen students. The estimated OLS regression is:
V₁ = 45 +0.74X;,
where ŷ, denotes the predicted value of the grades obtained in the final exam by the 1th individual and X; denotes the grades obtained in the midterm exam.
From the sample data he makes the following calculations:
^2
where
u¡
is the square of the residual for the ith observation.
60
Σ (X; -X)² = 230.48,
i=1
60
Σ (X-X)²=471.87,
i=1
He wants to test whether the grades obtained in the midterm exam have any effect on the grades obtained in the final exam or not.
Which of the following are the null and the alternative hypotheses of the test the professor wishes to conduct?
OA. Ho B₁ =0 vs. H₁: ß₁ #0.
OB. Ho B₁ =0.74 vs. H₁: ß₁ # 0.74.
OC. Ho: B₁ 0 vs. H₁: ß₁ = 0.
D. Ho B₁ 0.74 vs. H₁: ß₁ = 0.74.
If B₁ is the estimated slope coefficient, then the value of standard error of the estimated slope (SE (B₁)) is
(Round your answer to four decimal places.)
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