Statistical Literacy Suppose the scatter diagram of a random sample of data pairs ( x , y ) shows no linear relationship between x and y. Do you expect the value of the sample correlation coefficient r to be close to 1, -1, or 0?

Question

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Answer 1

Textbook Question

Chapter 4, Problem 1CR

Statistical Literacy Suppose the scatter diagram of a random sample of data pairs (x, y) shows no linear relationship between x and y. Do you expect the value of the sample correlation coefficient r to be close to 1, -1, or 0?

Expert Solution & Answer

To determine

The value of the sample correlation coefficient when the scatter diagram shows no linear relationship between x and y.

Answer to Problem 1CR

Solution: The sample correlation coefficient is close to 0.

Explanation of Solution

The range of the value of the correlation coefficient (r) is −1 to +1. The values −1 and +1 of r indicate a perfect linear relationship between the two variables. The value 0 indicates that there is no linear relationship between the variables.

So, if the scatter diagram shows that there is no linear relationship between x and y, then the value of the sample correlation coefficient is expected to be near to 0.

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Answer 2

Textbook Question

Chapter 4, Problem 1CR

Statistical Literacy Suppose the scatter diagram of a random sample of data pairs (x, y) shows no linear relationship between x and y. Do you expect the value of the sample correlation coefficient r to be close to 1, -1, or 0?

Expert Solution & Answer

To determine

The value of the sample correlation coefficient when the scatter diagram shows no linear relationship between x and y.

Answer to Problem 1CR

Solution: The sample correlation coefficient is close to 0.

Explanation of Solution

The range of the value of the correlation coefficient (r) is −1 to +1. The values −1 and +1 of r indicate a perfect linear relationship between the two variables. The value 0 indicates that there is no linear relationship between the variables.

So, if the scatter diagram shows that there is no linear relationship between x and y, then the value of the sample correlation coefficient is expected to be near to 0.

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Answer 3

Textbook Question

Chapter 4, Problem 1CR

Statistical Literacy Suppose the scatter diagram of a random sample of data pairs (x, y) shows no linear relationship between x and y. Do you expect the value of the sample correlation coefficient r to be close to 1, -1, or 0?

Expert Solution & Answer

To determine

The value of the sample correlation coefficient when the scatter diagram shows no linear relationship between x and y.

Answer to Problem 1CR

Solution: The sample correlation coefficient is close to 0.

Explanation of Solution

The range of the value of the correlation coefficient (r) is −1 to +1. The values −1 and +1 of r indicate a perfect linear relationship between the two variables. The value 0 indicates that there is no linear relationship between the variables.

So, if the scatter diagram shows that there is no linear relationship between x and y, then the value of the sample correlation coefficient is expected to be near to 0.

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Answer 4

Textbook Question

Chapter 4, Problem 1CR

Statistical Literacy Suppose the scatter diagram of a random sample of data pairs (x, y) shows no linear relationship between x and y. Do you expect the value of the sample correlation coefficient r to be close to 1, -1, or 0?

Expert Solution & Answer

To determine

The value of the sample correlation coefficient when the scatter diagram shows no linear relationship between x and y.

Answer to Problem 1CR

Solution: The sample correlation coefficient is close to 0.

Explanation of Solution

The range of the value of the correlation coefficient (r) is −1 to +1. The values −1 and +1 of r indicate a perfect linear relationship between the two variables. The value 0 indicates that there is no linear relationship between the variables.

So, if the scatter diagram shows that there is no linear relationship between x and y, then the value of the sample correlation coefficient is expected to be near to 0.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

The value of the sample correlation coefficient when the scatter diagram shows no linear relationship between x and y.

Answer to Problem 1CR

Solution: The sample correlation coefficient is close to 0.

Explanation of Solution

The range of the value of the correlation coefficient (r) is −1 to +1. The values −1 and +1 of r indicate a perfect linear relationship between the two variables. The value 0 indicates that there is no linear relationship between the variables.

So, if the scatter diagram shows that there is no linear relationship between x and y, then the value of the sample correlation coefficient is expected to be near to 0.

Answer 8

Expert Solution & Answer

To determine

The value of the sample correlation coefficient when the scatter diagram shows no linear relationship between x and y.

Answer to Problem 1CR

Solution: The sample correlation coefficient is close to 0.

Explanation of Solution

The range of the value of the correlation coefficient (r) is −1 to +1. The values −1 and +1 of r indicate a perfect linear relationship between the two variables. The value 0 indicates that there is no linear relationship between the variables.

So, if the scatter diagram shows that there is no linear relationship between x and y, then the value of the sample correlation coefficient is expected to be near to 0.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

The value of the sample correlation coefficient when the scatter diagram shows no linear relationship between x and y.

Answer 12

Answer to Problem 1CR

Solution: The sample correlation coefficient is close to 0.

Answer 13

Explanation of Solution

The range of the value of the correlation coefficient (r) is −1 to +1. The values −1 and +1 of r indicate a perfect linear relationship between the two variables. The value 0 indicates that there is no linear relationship between the variables.

So, if the scatter diagram shows that there is no linear relationship between x and y, then the value of the sample correlation coefficient is expected to be near to 0.