Question 1

Which of the following best describes the direction of association in a scatterplot where, as one variable increases, the other variable tends to decrease?

Accepted Answer

Negative direction

Question 2

A scatterplot of average hourly wage versus hours needed to earn an iPhone shows a downward trend that is not straight. Which statement is most accurate?

Accepted Answer

There is a negative association, but correlation is not an appropriate summary.

Question 3

Which variable is typically placed on the y-axis in a scatterplot?

Accepted Answer

The response variable

Question 4

What is the effect of changing the units of measurement (e.g., from dollars to euros) on the value of the correlation coefficient $$r$$?

Accepted Answer

It does not affect the value of $$r.$$

Question 5

Suppose you have a scatterplot with a few points far from the main cluster. What is the term for these points, and why are they important?

Accepted Answer

Outliers; they can strongly affect correlation and deserve special attention.

Question 6

Which of the following is NOT a condition for using the correlation coefficient $$r$$?

Accepted Answer

Both variables must be categorical.

Question 7

If the correlation coefficient $$r$$ between two variables is $$-0.388$$, how would you describe the association?

Accepted Answer

Moderately weak negative association

Question 8

Which of the following statements about correlation is TRUE?

Accepted Answer

Correlation has no units and is unaffected by shifting or scaling the data.

Question 9

A researcher finds a correlation of $$r = 0.97$$ between the number of storks and the number of babies born in a region. What is the most appropriate interpretation?

Accepted Answer

There is a strong positive association, but this does not prove causation.

Question 10

Which transformation is most appropriate to straighten a scatterplot that bends downward?

Accepted Answer

Take the reciprocal of $$y$$: $$y^{-1}$$

Question 11

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

$$ r = \frac{1}{n-1} \sum_{i=1}^{n} z_{x_i} z_{y_i} $$

What do $$z_{x_i}$$ and $$z_{y_i}$$ represent?

Accepted Answer

The standardized (z-score) values of $$x$$ and $$y$$

Question 12

Which of the following best describes the effect of outliers on the correlation coefficient $$r$$?

Accepted Answer

Outliers can dramatically change the value of $$r.$$

Question 13

A scatterplot of food costs versus vacation days per year shows no apparent pattern. The correlation coefficient is $$r = -0.040. $$What does this indicate?

Accepted Answer

There is likely no association between the variables.

Question 14

Which of the following is a correct way to report a correlation found in a study?

Accepted Answer

There is a strong association between the two variables.

Question 15

If a scatterplot is not straight, which of the following is the best course of action before calculating the correlation coefficient?

Accepted Answer

Re-express one or both variables to try to straighten the plot.

Question 16

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

Accepted Answer

$$r$$ can be greater than 1 or less than -1.

Question 17

A timeplot of an author's weight over several years shows a clear seasonal pattern. What statistical tool can help highlight long-term patterns in such data?

Accepted Answer

A smoother (such as lowess)

Question 18

Why is it important to examine scatterplots before interpreting values from a correlation table?

Accepted Answer

To check for linearity and outliers, which can affect the interpretation of correlation.

Question 19

Which of the following real-world scenarios is most appropriate for using correlation analysis?

Accepted Answer

Examining the relationship between systolic and diastolic blood pressure.

Question 20

Suppose you have a scatterplot of shutter speed and f/stop that is not linear, but after transforming f/stop by squaring it, the scatterplot becomes linear. What does this suggest?

Accepted Answer

There is a strong linear relationship between shutter speed and the square of f/stop.

Scatterplots, Association, and Correlation: Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards