Suppose the government would like to investigate the relationship between the engine size of sedans and the miles per gallon (MPG) they get. The accompanying table shows the engine size in cubic liters and rated miles per gallon for a selection of sedans. Complete parts a through e below. a. Calculate the sample covariance. Engine Size versus MPG (Round to three decimal places as needed.) b. Calculate the sample correlation coefficient. Car Engine Size MPG 2.1 27 2.3 31 (Round to three decimal places as needed.) 2.3 25 4. 3.4 20 c. Describe the relationship between x and y. Select the correct choice below. 3 2 29 O A. There is a perfect negative linear relationship between the two variables. 2.4 23 O B. There is no linear relationship between the two variables. 1.9 28 OC. There is a perfect positive linear relationship between the two variables. O D. There is a negative linear relationship between the two variables. O E. There is a positive linear relationship between the two variables. Print Done d. Which do you think is more valuable in expressing the relationship between MPG and engine size-the covariance or the correlation coefficient? Explain. O A. The covariance, because it is a measure of the relationship between MPG and engine size. O B. The correlation coefficient, because the covariance is useful in describing the direction of the relationship but not the strength of the relationship. O C. The covariance, because the correlation coefficient is useful in describing the direction of the relationship but not the strength of the relationship. O D. The correlation coefficient, because the covariance describes nothing about the relationship between MPG and engine size.
Suppose the government would like to investigate the relationship between the engine size of sedans and the miles per gallon (MPG) they get. The accompanying table shows the engine size in cubic liters and rated miles per gallon for a selection of sedans. Complete parts a through e below. a. Calculate the sample covariance. Engine Size versus MPG (Round to three decimal places as needed.) b. Calculate the sample correlation coefficient. Car Engine Size MPG 2.1 27 2.3 31 (Round to three decimal places as needed.) 2.3 25 4. 3.4 20 c. Describe the relationship between x and y. Select the correct choice below. 3 2 29 O A. There is a perfect negative linear relationship between the two variables. 2.4 23 O B. There is no linear relationship between the two variables. 1.9 28 OC. There is a perfect positive linear relationship between the two variables. O D. There is a negative linear relationship between the two variables. O E. There is a positive linear relationship between the two variables. Print Done d. Which do you think is more valuable in expressing the relationship between MPG and engine size-the covariance or the correlation coefficient? Explain. O A. The covariance, because it is a measure of the relationship between MPG and engine size. O B. The correlation coefficient, because the covariance is useful in describing the direction of the relationship but not the strength of the relationship. O C. The covariance, because the correlation coefficient is useful in describing the direction of the relationship but not the strength of the relationship. O D. The correlation coefficient, because the covariance describes nothing about the relationship between MPG and engine size.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Transcribed Image Text:Suppose the government would like to investigate the relationship between the engine size of sedans and the miles per gallon (MPG) they get. The accompanying table shows the engine size in cubic liters and rated miles per gallon for a
selection of sedans. Complete parts a through e below.
.....
a. Calculate the sample covariance.
Engine Size versus MPG
Sxy =U
(Round to three decimal places as needed.)
b. Calculate the sample correlation coefficient.
Car
Engine Size
MPG
1
2.1
27
xy =D
(Round to three decimal places as needed.)
2.3
31
3
2.3
25
4
3.4
20
c. Describe the relationship between x and y. Select the correct choice below.
22
29
O A. There is a perfect negative linear relationship between the two variables.
7
2.4
23
O B. There is no linear relationship between the two variables.
8
1.9
28
OC. There is a perfect positive linear relationship between the two variables.
D. There is a negative linear relationship between the two variables.
O E. There is a positive linear relationship between the two variables.
Print
Done
d. Which do you think is more valuable in expressing the relationship between MPG and engine size-the covariance or the correlation coefficient? Explain.
OA.
The covariance, because it is a measure of the relationship between MPG and engine size.
O B
The correlation coefficient, because the covariance is useful in describing the direction of the relationship but not the strength of the relationship.
O c. The covariance, because the correlation coefficient is useful in describing the direction of the relationship but not the strength of the relationship.
O D. The correlation coefficient, because the covariance describes nothing about the relationship between MPG and engine size.
e. What conclusion can you reach about the relationship between MPG and engine size?
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