MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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The data in the table to the right are based on the results of a survey comparing the commute time of adults to their score on a​ well-being test. Complete parts​ (a) through​ (d) below.
 
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Click the icon to view the table of critical values of the correlation coefficient.
 
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Part 1
Commute Time
​(in minutes)
Well-Being
Score
 
3
69.8
 
14
68.7
 
25
67.5
 
34
67.2
 
53
66.7
 
65
65.5
 
104
63.9
 
 
 
 

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Part 1
​(a) Which variable is likely the explanatory variable and which is the response​ variable?
 
 
A.
The explanatory variable is commute time and the response variable is the​ well-being score because commute time affects the​ well-being score.
 
B.
The explanatory variable is the​ well-being score and the response variable is commute time because commute time affects the​ well-being score.
 
C.
The explanatory variable is the​ well-being score and the response variable is commute time because​ well-being score affects the commute time.
 
D.
The explanatory variable is commute time and the response variable is the​ well-being score because​ well-being score affects the commute time score.
 
Part 2
​(b) Draw a scatter diagram of the data. Which of the following represents the​ data?
 
 
A.
 
 
 
60700110ScoreTime (min)
 
  •  
  •  
  •  
A scatter diagram has a horizontal axis labeled Score from 60 to 70 in increments of 1 and a vertical axis labeled Time in minutes from 0 to 110 in increments of 10. The following 7 approximate points are plotted, listed here from left to right: (64.0, 4); (69.8, 14); (65.6, 26); (68.8, 34); (66.8, 54); (67.6, 66); (67.2, 104). The vertical spread of the points decreases from left to right.
 
B.
 
 
 
60700110Time (min)Score
 
  •  
  •  
  •  
A scatter diagram has a horizontal axis labeled Time in minutes from 60 to 70 in increments of 1 and a vertical axis labeled Score from 0 to 110 in increments of 10. The following 7 approximate points are plotted, listed here from left to right: (64.0, 104); (65.6, 66); (66.8, 54); (67.2, 34); (67.6, 26); (68.8, 14); (69.8, 4). The points follow the general pattern of a straight line that falls from left to right.
 
C.
 
 
 
01106070ScoreTime (min)
 
  •  
  •  
  •  
A scatter diagram has a horizontal axis labeled Score from 0 to 110 in increments of 10 and a vertical axis labeled Time in minutes from 60 to 70 in increments of 1. The following 7 approximate points are plotted, listed here from left to right: (4, 64.0); (14, 65.6); (26, 66.8); (34, 67.2); (54, 67.6); (66, 68.8); (104, 69.8). The points follow the general pattern of a curve that rises from left to right at a decreasing rate.
 
D.
 
 
 
01106070Time (min)Score
 
  •  
  •  
  •  
A scatter diagram has a horizontal axis labeled Time in minutes from 0 to 110 in increments of 10 and a vertical axis labeled Score from 60 to 70 in increments of 1. The following 7 approximate points are plotted, listed here from left to right: (4, 69.8); (14, 68.8); (26, 67.6); (34, 67.2); (54, 66.8); (66, 65.6); (104, 64.0). The points follow the general pattern of a straight line that falls from left to right.
Part 3
​(c) Determine the linear correlation coefficient between commute time and​ well-being score.
 
r=enter your response here
​(Round to three decimal places as​ needed.)
Part 4
​(d) Does a linear relation exist between the commute time and​ well-being index​ score? Select the correct choice below and fill in the answer box to complete your choice.
 
​(Round to three decimal places as​ needed.)
 
A.
​No, the variables commute time and​ well-being score are not linearly related because r is negative and the absolute value of the correlation coefficient is less than the critical value
enter your response here.
 
B.
​Yes, the variables commute time and​ well-being score are negatively associated because r is positive and the absolute value of the correlation coefficient is greater than the critical value
enter your response here.
 
C.
​No, the variables commute time and​ well-being score are not linearly related because r is positive and the absolute value of the correlation coefficient is less than the critical value
enter your response here.
 
D.
​Yes, the variables commute time and​ well-being score are negatively associated because r is negative and the absolute value of the correlation coefficient is greater than the critical value
enter your response here.
 
E.
​Yes, the variables commute time and​ well-being score are positively associated because r is negative and the absolute value of the correlation coefficient is greater than the critical value
enter your response here.
 
F.
​Yes, the variables commute time and​ well-being score are positively associated because r is positive and the absolute value of the correlation coefficient is greater than the critical value
enter your response here.
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