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Global Warming If we find that there is a linear correlation between the concentration of carbon dioxide (\(C{O_2}\)) in our atmosphere and the global mean temperature, does that indicate that changes in (\(C{O_2}\))cause changes in the global mean temperature? Why or why not?

Short Answer

Expert verified

No, it does not indicate that change in \(C{O_2}\) causes change in global mean temperature.

Step by step solution

01

Given information

The two variables are: concentration of \(C{O_2}\) and global mean temperature. The two have a linear correlation between them.

02

Describe correlation between two variables

Linear correlation between two variables implies that one variable changes with the change in another variable in a linear manner, which can be described by a linear line.

The association does not implythat one variable causes change in the other. It is possible that the association exists due to a lurking variable which is not a part of the study.

Thus, it is stated that correlation does not imply causation.

Therefore, the two variablesnamely concentration of \(C{O_2}\) and the global mean temperature are known to have linear correlation but may not be the possible because of change in the other.

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Most popular questions from this chapter

Testing for a Linear Correlation. In Exercises 13โ€“28, construct a scatterplot, and find the value of the linear correlation coefficient r. Also find the P-value or the critical values of r from Table A-6. Use a significance level of A = 0.05. Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section 10-2 exercises.)

CSI Statistics Police sometimes measure shoe prints at crime scenes so that they can learn something about criminals. Listed below are shoe print lengths, foot lengths, and heights of males (from Data Set 2 โ€œFoot and Heightโ€ in Appendix B). Is there sufficient evidence to conclude that there is a linear correlation between shoe print lengths and heights of males? Based on these results, does it appear that police can use a shoe print length to estimate the height of a male?

Shoe print(cm)

29.7

29.7

31.4

31.8

27.6

Foot length(cm)

25.7

25.4

27.9

26.7

25.1

Height (cm)

175.3

177.8

185.4

175.3

172.7

Cigarette Tar and Nicotine The table below lists measured amounts (mg) of tar, carbonmonoxide (CO), and nicotine in king size cigarettes of different brands (from Data Set 13โ€œCigarette Contentsโ€ in Appendix B).

a. Is there is sufficient evidence to support a claim of a linear correlation between tar and nicotine?

b. What percentage of the variation in nicotine can be explained by the linear correlation between nicotine and tar?

c. Letting yrepresent the amount of nicotine and letting xrepresent the amount of tar, identify the regression equation.

d. The Raleigh brand king size cigarette is not included in the table, and it has 23 mg of tar. What is the best predicted amount of nicotine? How does the predicted amount compare to the actual amount of 1.3 mg of nicotine?

Tar

25

27

20

24

20

20

21

24

CO

18

16

16

16

16

16

14

17

Nicotine

1.5

1.7

1.1

1.6

1.1

1.0

1.2

1.4

Exercises 13โ€“28 use the same data sets as Exercises 13โ€“28 in Section 10-1. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5 on page 493.

Using the listed duration and interval after times, find the best predicted โ€œinterval afterโ€ time for an eruption with a duration of 253 seconds. How does it compare to an actual eruption with a duration of 253 seconds and an interval after time of 83 minutes?

Adjusted Coefficient of Determination For Exercise 2, why is it better to use values of adjusted \({R^2}\)instead of simply using values of \({R^2}\)?

Exercises 13โ€“28 use the same data sets as Exercises 13โ€“28 in Section 10-1. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5 on page 493.

Use the shoe print lengths and heights to find the best predicted height of a male who has a shoe print length of 31.3 cm. Would the result be helpful to police crime scene investigators in trying to describe the male?

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