Question 1

Which of the following best describes a linear correlation between two variables?

Accepted Answer

A relationship where the plotted points of paired data result in a pattern that can be approximated by a straight line.

Question 2

Given the scatterplot below, which type of correlation is most likely present?

[Refer to the scatterplot in $$image_2(a$$)]

Accepted Answer

Positive linear correlation

Question 3

Which property of the linear correlation coefficient $$r is $$correct?

Accepted Answer

The value of $$r is $$always between $$-1$$ and $$1$$ inclusive; that is $$-1 \leq r \leq 1$$

Question 4

If a scatterplot shows no distinct pattern, what can be concluded about the correlation between $$x$$ and $$y$$?

Accepted Answer

There is no correlation between $$x$$ and $$y.$$

Question 5

Which formula is used to calculate the linear correlation coefficient $$r$$ for a sample?

Accepted Answer

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

Question 6

Which of the following is NOT a requirement for using the linear correlation coefficient $$r to $$make conclusions about a population?

Accepted Answer

The sample must be collected using a voluntary response sample.

Question 7

If the linear correlation coefficient $$r$$ for a data set is $$-0.971$$, what does this indicate?

Accepted Answer

There is a strong negative linear correlation between $$x$$ and $$y.$$

Question 8

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

Accepted Answer

$$r is $$very sensitive to outliers; a single outlier can dramatically affect its value.

Question 9

If $$r^2 = 0.81$, what does this mean in the context of explained variation?

Accepted Answer

81% of the variation in $$y is $$explained by the linear relationship between $$x$$ and $$y.$$

Question 10

Which of the following is a common error when interpreting correlation?

Accepted Answer

Assuming that correlation implies causality.

Question 11

A researcher finds a strong linear correlation between chocolate consumption and the number of Nobel Laureates in a country. What is the best conclusion?

Accepted Answer

There is a correlation, but causation cannot be concluded.

Question 12

Which scatterplot below best represents a situation where $$r = 0$$?

Accepted Answer

A scatterplot with points randomly scattered and no apparent pattern.

Question 13

If all $$x$$ values and $$y$$ values are interchanged in a data set, what happens to the value of $$r$$?

Accepted Answer

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

Question 14

Which of the following is an example of a lurking variable?

Accepted Answer

Education levels affecting the number of Nobel Laureates in a country.

Question 15

Which of the following would most likely inflate the correlation coefficient $$r$$?

Accepted Answer

Using data based on averages.

Question 16

A scatterplot shows a distinct curved pattern. Which statement is most accurate?

Accepted Answer

There may be a nonlinear association, but $$r$$ does not measure its strength.

Question 17

Which of the following best describes the Pearson product moment correlation coefficient?

Accepted Answer

It measures the strength of the linear correlation between paired quantitative $$x$$ and $$y$$ values in a sample.

Question 18

Which of the following is true about $$r^2$$?

Accepted Answer

$$0 \leq r^2$ \leq 1$$

Question 19

A scatterplot of disk drive prices versus capacity shows a strong upward linear trend. What can be said about the correlation coefficient $$r$$?

Accepted Answer

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

Correlation and the Linear Correlation Coefficient (r)

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