Question 1

Which of the following best describes the relationship shown in the scatter plot of GDP (in trillions of dollars) versus CO$$_2$$ emissions (in millions of metric tons)?

Accepted Answer

There is a positive linear correlation between GDP and CO$$_2$$ emissions.

Question 2

Which formula is used to calculate the sample correlation coefficient $$r$$ for $$n$$ pairs of data $$(x, y)$$?

Accepted Answer

$$r = \frac{n\sum xy - (\sum x)(\sum y)}{\sqrt{[n\sum x^2$ - (\sum x)^2$][n\sum y^2$ - (\sum y)^2$]}}$$

Question 3

If the correlation coefficient $$r$$ for a dataset is $$-0.91$$, what does this indicate about the relationship between the two variables?

Accepted Answer

There is a strong negative linear correlation.

Question 4

Which of the following statements about correlation and causation is TRUE?

Accepted Answer

A strong correlation does not necessarily imply causation.

Question 5

Suppose $$r = 0.07$$ for a dataset. Which of the following best describes the relationship between the variables?

Accepted Answer

There is no linear correlation.

Question 6

Which of the following is NOT a possible explanation for a significant correlation between two variables?

Accepted Answer

The relationship is always due to a direct cause-and-effect.

Question 7

Given the following data pairs: $$(1,2), (2,4), (3,6), (4,8)$$, what is the value of the correlation coefficient $$r$$?

Accepted Answer

$$r = 1$$

Question 8

Which of the following best describes a scenario where $$r = 0.88$$?

Accepted Answer

There is a strong positive linear correlation.

Question 9

A researcher finds a significant positive correlation between hours studied and exam scores. Which of the following is a valid interpretation?

Accepted Answer

As hours studied increase, exam scores tend to increase.

Question 10

Which of the following values of $$r$$ indicates the weakest linear relationship?

Accepted Answer

$$r = 0.07$$

Question 11

If $$r = 1$$ for a dataset, what does this mean?

Accepted Answer

There is a perfect positive linear correlation.

Question 12

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

Accepted Answer

$$-1 \leq r \leq 1$$

Question 13

A scientist finds $$r = 0$$ for the relationship between two variables. What does this imply?

Accepted Answer

There is no linear correlation between the variables.

Question 14

Which of the following is an example of a nonlinear correlation?

Accepted Answer

The relationship between the speed of a car and the distance it travels in a given time if the car accelerates.

Question 15

Which of the following best describes the independent variable in a correlation study?

Accepted Answer

The variable that is manipulated or considered the explanatory variable ($$x).$$

Question 16

A correlation coefficient $$r is $$calculated to be $$-0.42. $$Which of the following best describes this correlation?

Accepted Answer

There is a weak negative linear correlation.

Correlation and Regression: Study Notes for Introductory Statistics

Study Guide - Practice Questions

Study Guide - Flashcards