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Chapter 3: Q 13. (page 172)

Manatees are large, gentle, slow-moving sea creatures found along the coast of Florida. Many manatees are injured or killed by boats. Here is a scatterplot showing the relationship between the number of boats registered in Florida (in thousands) and the number of manatees killed by boats for the years 1977 to 2015.13Isr>0orr<0? Closer to r=0orr=卤1?Explain your reasoning.

Short Answer

Expert verified

Data points are following the linear positive pattern which implies that the correlation is greater than 0 and closer to 1 that is, r>0 and closer to 1

Step by step solution

01

Given information

The figure is:

02

Explanation

The scatter plot is a graph that shows the association between two variables. It displays the level of correlation between two variables, known as the dependent and independent variables.

If the data points in the scatter plot create a linear pattern with a positive slope, the relationship between the variables is said to have the perfect positive.

The data points in the presented graph follow a linear positive pattern, indicating that the correlation is bigger than 0 and closer to 1 i.e., r>0 and closer to 1

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Most popular questions from this chapter

Will I bomb the final? We expect that students who do well on the midterm exam in a course will usually also do well on the final exam. Gary Smith of Pomona College looked at the exam scores of all 346 students who took his statistics class over a 10-year period. Assume that both the midterm and final exams were scored out of 100 points.

a. State the equation of the least-squares regression line if each student scored the same on the midterm and the final.

b. The actual least-squares line for predicting final exam score y from midterm-exam score x was y^=46.6+0.41x. Predict the score of a student who scored

50 on the midterm and a student who scored 100 on the midterm.

c. Explain how your answers to part (b) illustrate regression to the mean.

The stock market Some people think that the behavior of the stock market in January predicts its behavior for the rest of the year. Take the explanatory variable x to be the percent change in a stock market index in January and the response variable y to be the change in the index for the entire year. We expect a positive correlation between x and y because the change during January contributes to the full year鈥檚 change. Calculation from data for an 18-year period gives x炉=1.75% sx=5.36% y炉=9.07% sy=15.35% r=0.596

a. Find the equation of the least-squares line for predicting full-year change from January change.

b. Suppose that the percent change in a particular January was 2 standard deviations above average. Predict the percent change for the entire year without using the least-squares line.

Stand mixers The scatterplot shows the weight (in pounds) and cost (in dollars) of 11 stand mixers.35 The mixer from Walmart (highlighted in red) was much lighter鈥攁nd cheaper than the other mixers.

a. Describe what influence the highlighted point has on the equation of the least-squares regression line.

b. Describe what influence the highlighted point has on the standard deviation of the residuals and r2

Will I bomb the final? We expect that students who do well on the midterm exam in a course will usually also do well on the final exam. Gary Smith of Pomona College looked at the exam scores of all 346 students who took his statistics class over a 10-year period. 17 The least-squares line for predicting final-exam score from midterm-exam score was y铃�=46.6+0.41x . Octavio scores 10 points above the class mean on the midterm. How many points above the class mean do you predict that he will score on the final? (This is an example of the phenomenon that gave 鈥渞egression鈥� its name: students who do well on the midterm will on the average do less well, but still above average, on the final.)

An AP庐 Statistics student designs an experiment to see whether today鈥檚 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鈥攐ne with a calculator and one without鈥攊n 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^ = 鈭�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
See all solutions

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