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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 – 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

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.

Exercises 13–28 use the same data sets as Exercises 13–28 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 CPI/subway fare data from the preceding exercise and find

the best predicted subway fare for a time when the CPI reaches 500. What is wrong with this prediction?

Different hotels on Las Vegas Boulevard (“the strip”) in Las Vegas are randomly selected, and their ratings and prices were obtained from Travelocity. Using technology, with xrepresenting the ratings and yrepresenting price, we find that the regression equation has a slope of 130 and a y-intercept of -368.

a. What is the equation of the regression line?

b. What does the symbol\(\hat y\)represent?

Testing for a Linear Correlation. In Exercises 13–28, 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 “pizza connection” 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

Stocks and Sunspots. Listed below are annual high values of the Dow Jones Industrial Average (DJIA) and annual mean sunspot numbers for eight recent years. Use the data for Exercises 1–5. A sunspot number is a measure of sunspots or groups of sunspots on the surface of the sun. The DJIA is a commonly used index that is a weighted mean calculated from different stock values.

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

Correlation Use a 0.05 significance level to test for a linear correlation between the DJIA values and the sunspot numbers. Is the result as you expected? Should anyone consider investing in stocks based on sunspot numbers?
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