Question 1

Which of the following best describes the purpose of a scatterplot in statistics?

Accepted Answer

To visualize the relationship between two quantitative variables by plotting pairs of observations on the $$x$$-$$y$$ plane.

Question 2

Suppose you are investigating whether skipping classes affects academic performance. Which variable should be plotted on the $$x-$$axis of a scatterplot?

Accepted Answer

Number of classes skipped, because it is the explanatory variable.

Question 3

A scatterplot of IQ versus MRI brain scan pixel count shows that as MRI count increases, IQ tends to increase as well. What type of association is this?

Accepted Answer

Positive linear association

Question 4

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

Accepted Answer

$$r is a $$unitless measure that ranges from $$-1 to$$ $$1.$$

Question 5

If the correlation coefficient $$r$$ between two variables is $$-0.93$$, what does this indicate about their relationship?

Accepted Answer

There is a strong negative linear relationship between the two variables.

Question 6

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

Accepted Answer

The value of $$r$$ does not change if all values of either variable are added to a constant.

Question 7

Which of the following scenarios best illustrates the concept that 'association does not imply causation'?

Accepted Answer

A positive correlation between the number of firefighters at a fire and the amount of damage, due to the size of the blaze being a lurking variable.

Question 8

Given the formula for the correlation coefficient $$r$$:

$$ r = \frac{1}{n-1} \sum_{i=1}^{n} z_{x,i} z_{y,i} $$

where $$z_{x,i}$$ and $$z_{y,i}$$ are the standardized values of $$x$$ and $$y$$, what is the first step in calculating $$r$$ from raw data?

Accepted Answer

Standardize the $$x$$ and $$y$$ values by subtracting their means and dividing by their standard deviations.

Question 9

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

Accepted Answer

A scatterplot where the points are randomly scattered with no apparent pattern.

Question 10

A researcher finds a strong positive correlation between ice cream sales and drowning incidents. Which of the following is the best explanation for this association?

Accepted Answer

A lurking variable, such as temperature, is associated with both ice cream sales and drowning incidents.

Question 11

Which of the following patterns in a scatterplot would indicate a non-linear relationship?

Accepted Answer

A parabolic (U-shaped) pattern.

Question 12

If you swap the $$x$$ and $$y$$ variables in a scatterplot, what happens to the value of the correlation coefficient $$r$$?

Accepted Answer

The value of $$r$$ remains unchanged.

Question 13

Which of the following is a correct interpretation of a correlation coefficient $$r = 0.8$$ between two variables?

Accepted Answer

There is a strong positive linear association between the two variables.

Question 14

Which of the following is most likely to affect the value of the correlation coefficient $$r$$?

Accepted Answer

The presence of outliers in the data.

Question 15

A scatterplot of the number of hours studied and exam scores for a group of students shows a strong positive linear relationship. Which of the following is the most appropriate conclusion?

Accepted Answer

Students who study more hours tend to have higher exam scores.

Question 16

Which of the following best describes a lurking variable?

Accepted Answer

A variable that is not included in the study but affects both the explanatory and response variables.

Question 17

Suppose you have two variables, $$x$$ and $$y$$, and you add 10 to every value of $$x. $$What happens to the correlation coefficient $$r$$?

Accepted Answer

The value of $$r$$ does not change.

Question 18

Which of the following is a correct step in the statistical process of investigating the relationship between two variables?

Accepted Answer

Formulate a research question, collect data, examine the data, and interpret the results.

Question 19

Which of the following is an example of a strong negative linear relationship?

Accepted Answer

As the number of classes skipped increases, final grade decreases, with $$r = -0.93.$$

Scatterplots, Association, and Correlation: Visualizing and Quantifying Relationships Between Quantitative Variables

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