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Chapter 3: Q T3.7. (page 216)

When we standardize the values of a variable, the distribution of standardized values has a mean of 0 and a standard deviation of 1. Suppose we measure two variables X and Y on each of several subjects. We standardize both variables and then compute the least squares regression line. Suppose the slope of the least-squares regression line is 20.44. We may conclude that

a. the intercept will also be −0.44.

b. the intercept will be 1.0.

c. the correlation will be 1/−0.44.

d. the correlation will be 1.0.

e. the correlation will also be −0.44.

Short Answer

Expert verified

The correct option is (e) the correlation will also be −0.44

Step by step solution

01

Given information

x=y=0sx=sy=1b=−0.44

02

Concept

b=rsysx

03

Explanation

b=rsysxr=bsxsy=−0.4411=−0.44

Hence, the correct option is (e).

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Most popular questions from this chapter

Correlation isn’t everything Marc and Rob are both high school English teachers. Students think that Rob is a harder grader, so Rob and Marc decide to grade the same 10 essays and see how their scores compare. The correlation is r=0.98 but Rob’s scores are always lower than Marc’s. Draw a possible scatterplot that illustrates this situation.

Long jumps Here are the 40-yard-dash times (in seconds) and long-jump distances (in inches) for a small class of 12 students:

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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

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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.

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