Question 1

Which of the following statements about the linear correlation coefficient $$r is $$TRUE?

Accepted Answer

$$r$$ measures the strength and direction of a linear relationship between two variables.

Question 2

Suppose the correlation coefficient between hours studied and exam score is $$r = 0.85. $$What does this indicate?

Accepted Answer

There is a strong positive linear relationship between hours studied and exam score.

Question 3

If $$r = -0.92$$ for the relationship between temperature and heating costs, what can be concluded?

Accepted Answer

There is a strong negative linear relationship between temperature and heating costs.

Question 4

Which value of $$r$$ indicates the weakest linear relationship?

Accepted Answer

$$r = 0.02$$

Question 5

A researcher finds $$r = 0$$ between two variables. Which of the following is the best interpretation?

Accepted Answer

There is no linear relationship between the two variables.

Question 6

Which of the following is NOT a property of the linear correlation coefficient $$r$$?

Accepted Answer

$$r$$ can be greater than $$1 if $$the relationship is very strong.

Question 7

If $$r = 1$$, what does this imply about the relationship between two variables?

Accepted Answer

There is a perfect positive linear relationship.

Question 8

A scientist finds $$r = -0.3$$ between two variables. According to the guidelines, how would you describe the strength of this relationship?

Accepted Answer

Weak negative linear relationship

Question 9

Which scenario best illustrates a moderate positive linear correlation?

Accepted Answer

As the amount of time spent studying increases, test scores tend to increase, with $$r = 0.5.$$

Question 10

Which of the following statements is correct regarding the interpretation of $$r$$?

Accepted Answer

If $$r is $$close to $$0$$, there is no linear relationship, but there may still be a nonlinear relationship.

Question 11

A dataset has $$r = 0.77. $$Which of the following best describes the strength and direction of the relationship?

Accepted Answer

Strong positive linear relationship

Question 12

Which of the following would NOT affect the value of the linear correlation coefficient $$r$$?

Accepted Answer

Changing the units of measurement for $$x$$ and $$y$$

Question 13

Suppose $$r = -1$$ for the relationship between two variables. Which of the following is TRUE?

Accepted Answer

There is a perfect negative linear relationship.

Question 14

A study finds $$r = 0.03$$ between two variables. What does this suggest?

Accepted Answer

There is a very weak or no linear relationship.

Question 15

Which of the following is a possible value for the linear correlation coefficient $$r$$?

Accepted Answer

$$r = -0.8$$

Question 16

If $$r is $$close to $$-1$$, which of the following is the best interpretation?

Accepted Answer

There is a strong negative linear relationship.

Question 17

A researcher claims that $$r = 0.95$$ between two variables means that one variable causes the other. Is this claim justified?

Accepted Answer

No, because correlation does not imply causation.

Question 18

Which of the following best describes the relationship if $$r = 0.6$$?

Accepted Answer

Moderate positive linear relationship

Question 19

If the correlation coefficient between two variables is $$r = -0.78$$, what does this indicate?

Accepted Answer

Strong negative linear relationship

Question 20

Which of the following is a correct interpretation of $$r = 0$$?

Accepted Answer

There is no linear relationship between the variables.

Properties of the Linear Correlation Coefficient

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