More Olympics Athletes who participate in the shot put, discus throw, and hammer throw tend to have different physical characteristics than other track and field athletes. The scatterplot shown here enhances the scatterplot from Exercise 5 by plotting these athletes with blue squares. How are the relationships between height and weight the same for the two groups of athletes? How are the relationships different?

Short Answer

Expert verified

Similarities:

For both groups, there is a linear and positive relationship between height and weight, with no outliers.

Differences:

For discus throwers, hammers throwers, and shot putters, the link between height and weight is weaker. Weights for discus throwers, hammers throwers, and shot putters should be higher than for other athletes.

Step by step solution

01

Given information

In Blue: Athletes from shot put, discus throw, hammers throw

In Black: Other track and field athletes

02

Explanation

Similarities:

Note that

Because the pattern slopes upwards for both groups of athletes in the scatterplot, this demonstrates a positive relationship between height and weight for both groups.

And

There is no substantial curvature in either group's points, and both groups' associations appear to be linear.

Also,

Neither group appears to have outliers because there are no significant deviations from the pattern in the other points.

Differences:

Note that

Because the squares appear to be spread out more than the dots in the scatterplot, there appears to be a weaker association between height and weight for athletes like the hammer throw, discus throw and shot put.

Also,

The weight of athletes in the hammer throw, discus throw, and shot put appears to be higher than the weight of other athletes in the scatterplot because most of the squares are above the dots.

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Most popular questions from this chapter

An AP® Statistics student designs an experiment to see whether today’s high school students are becoming too calculator-dependent. She prepares two quizzes, both of which contain 40 questions that are best done using paper-and-pencil methods. A random sample of 30 students participates in the experiment. Each student takes both quizzes—one with a calculator and one without—in random order. To analyze the data, the student constructs a scatterplot that displays a linear association between the number of correct answers with and without a calculator for the 30 students. A least-squares

regression yields the equation. calculator^ = −1.2 + 0.865 (pencil) r = 0.79

Which of the following statements is/are true?

I. If the student had used Calculator as the explanatory variable, the correlation would remain the same.

II. If the student had used Calculator as the explanatory variable, the slope of the least-squares line would remain the same.

III. The standard deviation of the number of correct answers on the paper-and-pencil quizzes was smaller than the standard deviation on the calculator quizzes.

a. I only

b. II only

c. III only

d. I and III only

e. I, II, and III

Penguins diving A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater.41 For all but the shallowest dives, there is an association between x = depth (in meters) and y = dive duration (in minutes) that is different for each penguin. The study gives a scatterplot for one penguin titled “The Relation of Dive Duration (y) to Depth (x).” The scatterplot shows an association that is positive, linear, and strong.

a. Explain the meaning of the term positive association in this context.

b. Explain the meaning of the term linear association in this context.

c. Explain the meaning of the term strong association in this context.

d. Suppose the researchers reversed the variables, using x = dive duration and y = depth.

Scientists examined the activity level of 7 fish at different temperatures. Fish activity was rated on a scale of 0 (no activity) to 100 (maximal activity). The temperature was measured in degrees Celsius. A computer regression printout and a residual plot are provided. Notice that the horizontal axis on the residual plot is labeled “Fitted value,” which means the same thing as “predicted value.”

What is the correlation between temperature and fish activity?

a. 0.95

b. 0.91

c. 0.45

d. –0.91

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Suppose that a tall child with an arm span of 120 cm and a height of 118 cm was added to the sample used in this study. What effect will this addition have on the correlation and the slope of the least-squares regression line?

a. Correlation will increase, and the slope will increase.

b. Correlation will increase, and the slope will stay the same.

c. Correlation will increase, and the slope will decrease.

d. Correlation will stay the same, and the slope will stay the same.

e. Correlation will stay the same, and the slope will increase.

Which of the following is not a characteristic of the least-squares regression line?

a. The slope of the least-squares regression line is always between –1 and 1.

b. The least-squares regression line always goes through the point (x¯,y¯) .

c. The least-squares regression line minimizes the sum of squared residuals.

d. The slope of the least-squares regression line will always have the same sign as the correlation.

e. The least-squares regression line is not resistant to outliers.

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