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Chapter 10: Q4CQQ (page 468)

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).

If you had computed the value of the linear correlation coefficient to be 1.500, what should you conclude?

Short Answer

Expert verified

It can be concluded that there is an error in the calculation.

Step by step solution

01

Given information

The table representing the number of enrolled students (in thousands) and the number of burglaries for randomly selected large colleges in recent years is provided.

The value of \(r{\rm{ is }}1.500\).

02

Draw inference from the correlation coefficient measure

The value of r lies between –1 and 1 inclusive, where the negative sign represents an indirect relationship. Also, the magnitude of 1 represents a perfect and linear relationship.

This implies that the value of r cannot be 1.500.

In conclusion, there must be an error in the calculation.

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Most popular questions from this chapter

In Exercises 9 and 10, use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.

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

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.)

CSI Statistics Use the paired foot length and height data from the preceding exercise. Is there sufficient evidence to conclude that there is a linear correlation between foot lengths and heights of males? Based on these results, does it appear that police can use foot 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

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 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?

In exercise 10-1 12. Clusters Refer to the following Minitab-generated scatterplot. The four points in the lower left corner are measurements from women, and the four points in the upper right corner are from men.

a. Examine the pattern of the four points in the lower left corner (from women) only, and subjectively determine whether there appears to be a correlation between x and y for women.

b. Examine the pattern of the four points in the upper right corner (from men) only, and subjectively determine whether there appears to be a correlation between x and y for men.

c. Find the linear correlation coefficient using only the four points in the lower left corner (for women). Will the four points in the upper left corner (for men) have the same linear correlation coefficient?

d. Find the value of the linear correlation coefficient using all eight points. What does that value suggest about the relationship between x and y?

e. Based on the preceding results, what do you conclude? Should the data from women and the data from men be considered together, or do they appear to represent two different and distinct populations that should be analyzed separately?
See all solutions

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