Question 1

Which of the following best describes what the correlation coefficient $$r$$ measures?

Accepted Answer

The direction and strength of the linear relationship between two variables.

Question 2

A correlation coefficient $$r is $$calculated to be $$-0.92$$ for the relationship between hours spent watching TV and test scores among students. Which of the following best interprets this value?

Accepted Answer

There is a strong negative linear relationship between hours spent watching TV and test scores.

Question 3

Suppose a scatterplot of two variables shows points tightly clustered around a straight line that slopes upward. What can you say about the correlation coefficient $$r$$?

Accepted Answer

$$r is $$close to $$+1.$$

Question 4

A scientist measures the speed of sound at different altitudes and finds $$r = -0.98. $$What does this indicate about the relationship between altitude and speed of sound?

Accepted Answer

There is a very strong negative linear relationship between altitude and speed of sound.

Question 5

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

Accepted Answer

$$r is $$not affected by the slope of the best-fit line.

Question 6

A marketing researcher finds $$r = 0.81$$ between advertising budget and sales revenue for small retail stores. What does this value suggest?

Accepted Answer

There is a strong positive linear relationship between advertising budget and sales revenue.

Question 7

If the points in a scatterplot are widely scattered and do not follow any clear pattern, what is the most likely value of the correlation coefficient $$r$$?

Accepted Answer

$$r is $$close to $$0.$$

Question 8

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

Accepted Answer

$$r$$ measures the strength of a non-linear relationship.

Question 9

A data set has a correlation coefficient of $$r = 0.44. $$Which of the following best describes the strength and direction of the relationship?

Accepted Answer

Moderate positive linear relationship.

Question 10

Which of the following scenarios would most likely result in a correlation coefficient $$r$$ close to $$-1$$?

Accepted Answer

As the temperature increases, the amount of heating oil used decreases in a nearly perfect linear fashion.

Question 11

A researcher uses a calculator to find the correlation coefficient for a data set and gets $$r = 0.94. $$What does this value indicate about the data?

Accepted Answer

The data points are tightly clustered around a line with a positive slope.

Question 12

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

Accepted Answer

Changing the slope of the best-fit line.

Question 13

Given the following data: $$x = [1, 2, 3, 4, 5]$$, $$y = [2, 4, 6, 8, 10]$$, what is the value of the correlation coefficient $$r$$?

Accepted Answer

$$r = 1$$

Question 14

A data set is found to have a linear correlation coefficient of $$r = -0.82. $$Which of the following best describes the relationship between the two variables?

Accepted Answer

Strong negative linear relationship.

Question 15

Which of the following is the correct formula for the sample correlation coefficient $$r$$?

Accepted Answer

$$r = \frac{\sum (x_i - \overline{x})(y_i - \overline{y})}{\sqrt{\sum (x_i - \overline{x})^2$ \sum (y_i - \overline{y})^2$}}$$

Question 16

A scatterplot shows a strong upward trend, but one point is far away from the others. What is the likely effect of this outlier on the correlation coefficient $$r$$?

Accepted Answer

It can significantly decrease the value of $$r.$$

Question 17

If $$r = 0$$, what does this tell you about the relationship between two variables?

Accepted Answer

There is no linear relationship between the variables.

Question 18

A data set has $$r = 0.13. $$Which of the following best describes the relationship?

Accepted Answer

Very weak positive linear relationship.

Question 19

Which of the following is a limitation of the correlation coefficient $$r$$?

Accepted Answer

$$r$$ only measures linear relationships and may not detect strong non-linear associations.

Question 20

A student uses a calculator to find $$r = 0.54$$ for the relationship between time spent studying and test scores. Which of the following is the best interpretation?

Accepted Answer

There is a moderate positive linear relationship between time spent studying and test scores.

Correlation Coefficient: Understanding and Calculating Relationships Between Variables

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