The results from a regression analysis of data collected on SAT score and current GPA for a random sample of 100 students at a large university are summarized in the partial computer output below. Term Coef SE Coef Constant SAT r=0.431 1.406 0.143 0.001340 0.000114 R² = 0.1862 Assume all conditions for inference were met. Based on the output shown, is there a statistically significant linear relationship between SAT score and current GPA for all students at this university? (A) No, because the estimated slope is very close to 0. (B) No, because the correlation is not close to -1 or 1. (C) No, because R² is quite small. (D) Yes, because the ratio of 1.406 to 0.143 is very large. (E) Yes, because the ratio of 0.001340 to 0.000114 is very large.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
Question

why the correct answer is letter e?

The results from a regression analysis of data collected on SAT score and current GPA for a random
sample of 100 students at a large university are summarized in the partial computer output below.
Term
Coef SE Coef
Constant
SAT
r=0.431
1.406
0.143
0.001340 0.000114
R² = 0.1862
Assume all conditions for inference were met. Based on the output shown, is there a statistically
significant linear relationship between SAT score and current GPA for all students at this university?
(A) No, because the estimated slope is very close to 0.
(B) No, because the correlation is not close to -1 or 1.
(C) No, because R² is quite small.
(D) Yes, because the ratio of 1.406 to 0.143 is very large.
(E) Yes, because the ratio of 0.001340 to 0.000114 is very large.
Transcribed Image Text:The results from a regression analysis of data collected on SAT score and current GPA for a random sample of 100 students at a large university are summarized in the partial computer output below. Term Coef SE Coef Constant SAT r=0.431 1.406 0.143 0.001340 0.000114 R² = 0.1862 Assume all conditions for inference were met. Based on the output shown, is there a statistically significant linear relationship between SAT score and current GPA for all students at this university? (A) No, because the estimated slope is very close to 0. (B) No, because the correlation is not close to -1 or 1. (C) No, because R² is quite small. (D) Yes, because the ratio of 1.406 to 0.143 is very large. (E) Yes, because the ratio of 0.001340 to 0.000114 is very large.
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