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Chapter 10: Q4BSC (page 468)

Scatterplots Match these values of r with the five scatterplots shown below: 0.268, 0.992, -1, 0.746, and 1.

Short Answer

Expert verified

The r values for the five scatterplots are:

  1. \(r = - 1\)
  2. \(r = 0.746\)
  3. \(r = 0.268\)
  4. \(r = 0.992\)
  5. \(r = 1\)

Step by step solution

01

Given information

Five scatterplots (a),(b),(c),(d),(e) are given along with five measures of correlation coefficients.

02

Procedure to estimate values of r from scatterplots

The value of correlation is between -1 and 1. The signs + or 鈥� indicate that there is direct and indirect linear association between the pair of variables.

A scatterplot is a graph that shows the paired observations where one variable is scaled

03

Relationship between scatterplot and value of r

The magnitude shows the strength of linear association between the pair of variables.

If the value is equal to 0, it indicates that there is no association between the variables. The scatter plot shows a random pattern in this case.

As the value approaches 1 or -1, the pattern of observations in scatterplot aligns in a straight line (either upward or downward).Depending on the alignment of the these observations about a straight line the measure of correlation changes.

04

Evaluating each scatterplot

(a) The scatter plot has all observations aligned about a straight line that slopes downward. Thus, the value of r is estimated to be -1.

(b) The scatter plot has all observations are aligned close to a straight line that slopes upwards. Thus, the value of r is estimated between 0 to 1. Thus, the value of r is estimated to be 0.746.

(c) The scatter plot has observations assigned randomly on the graph. Thus, the value of r is estimated to be very low but positive. In this case, it can take be estimated as 0.268.

(d) The scatter plot has observations aligned close to a straight line pattern in an upward direction. Thus, the value of ris expected to be very close to +1. In this case, it can take be estimated as 0.992.

(e) The scatter plot has observations perfectly aligned about the straight line in upward direction. Thus, the value of r is estimated to be 1.

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Most popular questions from this chapter

In Exercises 5鈥�8, we want to consider the correlation between heights of fathers and mothers and the heights of their sons. Refer to theStatCrunch display and answer the given questions or identify the indicated items.

The display is based on Data Set 5 鈥淔amily Heights鈥� in Appendix B.

Identify the multiple regression equation that expresses the height of a son in terms of the height of his father and mother.

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Pain Intensity Before Duragesic Treatment

1.2

1.3

1.5

1.6

8

3.4

3.5

2.8

2.6

2.2

3

7.1

2.3

2.1

3.4

6.4

5

4.2

2.8

3.9

5.2

6.9

6.9

5

5.5

6

5.5

8.6

9.4

10

7.6










Pain Intensity After Duragesic Treatment

0.4

1.4

1.8

2.9

6

1.4

0.7

3.9

0.9

1.8

0.9

9.3

8

6.8

2.3

0.4

0.7

1.2

4.5

2

1.6

2

2

6.8

6.6

4.1

4.6

2.9

5.4

4.8

4.1










Correlation Use the given data to construct a scatterplot, then use the methods of Section 10-1 to test for a linear correlation between the pain intensity before and after treatment. If there does appear to be a linear correlation, can we conclude that the drug treatment is effective?

Critical Thinking: Is the pain medicine Duragesic effective in reducing pain? Listed below are measures of pain intensity before and after using the drug Duragesic (fontanels) (based on data from Janssen Pharmaceutical Products, L.P.). The data are listed in order by row, and corresponding measures are from the same subject before and after treatment. For example, the first subject had a measure of 1.2 before treatment and a measure of 0.4 after treatment. Each pair of measurements is from one subject, and the intensity of pain was measured using the standard visual analog score. A higher score corresponds to higher pain intensity.

Pain intensity before Duragestic Treatment

1.2

1.3

1.5

1.6

8

3.4

3.5

2.8

2.6

2.2

3

7.1

2.3

2.1

3.4

6.4

5

4.2

2.8

3.9

5.2

6.9

6.9

5

5.5

6

5.5

8.6

9.4

10

7.6

Pain intensity after Duragestic Treatment

0.4

1.4

1.8

2.9

6.0

1.4

0.7

3.9

0.9

1.8

0.9

9.3

8.0

6.8

2.3

0.4

0.7

1.2

4.5

2.0

1.6

2.0

2.0

6.8

6.6

4.1

4.6

2.9

5.4

4.8

4.1

Regression:Use the given data to find the equation of the regression line. Let the response (y) variable be the pain intensity after treatment. What would be the equation of the regression line for a treatment having absolutely no effect?

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DJIA

14,198

13,338

10,606

11,625

12,929

13,589

16,577

18,054

Sunspot

Number

7.5

2.9

3.1

16.5

55.7

57.6

64.7

79.3

Hypothesis Test The mean sunspot number for the past three centuries is 49.7. Use a 0.05 significance level to test the claim that the eight listed sunspot numbers are from a population with a mean equal to 49.7.

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).

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