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Chapter 10: Q3BSC (page 468)

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 13鈥�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.)

Pizza and the Subway The 鈥減izza connection鈥� is the principle that the price of a slice of pizza in New York City is always about the same as the subway fare. Use the data listed below to determine whether there is a significant linear correlation between the cost of a slice of pizza and the subway fare.

Year

1960

1973

1986

1995

2002

2003

2009

2013

2015

Pizza Cost

0.15

0.35

1

1.25

1.75

2

2.25

2.3

2.75

Subway Fare

0.15

0.35

1

1.35

1.5

2

2.25

2.5

2.75

CPI

30.2

48.3

112.3

162.2

191.9

197.8

214.5

233

237.2

Coefficient of Determination Using the heights and weights described in Exercise 1, the linear correlation coefficient r is 0.394. Find the value of the coefficient of determination. What practical information does the coefficient of determination provide?

Interpreting the Coefficient of Determination. In Exercises 5鈥�8, use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables.

Crickets and Temperature r = 0.874 (x = number of cricket chirps in 1 minute, y = temperature in 掳F)

The following exercises are based on the following sample data consisting of numbers of enrolled students (in thousands) and numbers of burglaries for randomly selected large colleges in a recent year (based on data from the New York Times).

Enrollment (thousands)

53

28

27

36

42

Burglaries

86

57

32

131

157

True or false: If the sample data lead us to the conclusion that there is sufficient evidence to support the claim of a linear correlation between enrollment and number of burglaries, then we could also conclude that higher enrollments cause increases in numbers of burglaries.

Explore! Exercises 9 and 10 provide two data sets from 鈥淕raphs in Statistical Analysis,鈥� by F. J. Anscombe, the American Statistician, Vol. 27. For each exercise,

a. Construct a scatterplot.

b. Find the value of the linear correlation coefficient r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables.

c. Identify the feature of the data that would be missed if part (b) was completed without constructing the scatterplot.

x

10

8

13

9

11

14

6

4

12

7

5

y

9.14

8.14

8.74

8.77

9.26

8.10

6.13

3.10

9.13

7.26

4.74
See all solutions

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