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Chapter 3: Q 18. (page 173)

More crying? Refer to Exercise 16Does the fact that r=0.45 suggest that making an infant cry will increase his or her IQ later in life? Explain your reasoning.

Short Answer

Expert verified

No.

Step by step solution

01

Given information

02

Explanation

From Exercise 16it is known there exists a weak correlation between the two variables.

The correlation is a statistical measure that is used to explain the relationship between two variables.

The exercise's association reveals a weak relationship between the variables count of crying peaks and an infant's IQat the age of three. Because correlation does not necessarily imply causation.

Thus,

r=0.45does not imply that making an infant cry will lead an increase in her or his IQ in later life.

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Most popular questions from this chapter

What鈥檚 my grade? In Professor Friedman鈥檚 economics course, the correlation

between the students鈥� total scores prior to the final examination and their final exam scores is r = 0.6. The pre-exam totals for all students in the course have a mean of 280 and a standard deviation of 30. The final exam scores have a mean of 75 and a standard deviation of 8. Professor Friedman has lost Julie鈥檚 final exam but knows that her total before the exam was 300. He decides to predict her final exam score from her pre-exam total.

a. Find the equation for the least-squares regression line Professor Friedman should use to make this prediction.

b. Use the least-squares regression line to predict Julie鈥檚 final exam score.

c. Explain the meaning of the phrase 鈥渓east squares鈥� in the context of this question.

d. Julie doesn鈥檛 think this method accurately predicts how well she did on the final exam. Determine r2. Use this result to argue that her actual score could have been much higher (or much lower) than the predicted value.

By looking at the equation of the least-squares regression line, you can see that the correlation between height and arm span is

a. greater than zero.

b. less than zero.

c. 0.93.

d. 6.4.

e. Can鈥檛 tell without seeing the data.

Rushing for points What is the relationship between rushing yards and points scored in the National Football League? The table gives the number of rushing yards and the number of points scored for each of the 16 games played by the Jacksonville Jaguars in a recent season.

a. Make a scatterplot with rushing yards as the explanatory variable. Describe what you see.

b. The number of rushing yards in Game 16 is an outlier in the x-direction. What effect do you think this game has on the correlation? On the equation of the least-squares regression line? Calculate the correlation and equation of the least-squares regression line with and without this game to confirm your answers.

c. The number of points scored in Game 13 is an outlier in the y-direction. What effect do you think this game has on the correlation? On the equation of the least-squares regression line? Calculate the correlation and equation of the least-squares regression line with and without this game to confirm your answers.

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

Predicting wins Earlier we investigated the relationship between x =

payroll (in millions of dollars) and y = number of wins for Major League Baseball teams in 2016. Here is a scatterplot of the data, along with the regression line y^=60.7+0.139x

a. Predict the number of wins for a team that spends \(200 million on payroll.

b. Predict the number of wins for a team that spends \)400 million on payroll.

c. How confident are you in each of these predictions? Explain your reasoning.
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