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 formula is used to calculate the linear correlation coefficient $$r$$ for a sample of paired data?

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 4

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

Accepted Answer

The value of $$r is $$always between $$-1$$ and $$1$$ inclusive.

Question 5

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 6

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

Accepted Answer

$$r$$ can be used to measure the strength of a nonlinear relationship.

Question 7

What does the value $$r^2$$ represent in the context of linear correlation?

Accepted Answer

The proportion of the variation in $$y$$ that is explained by the linear relationship between $$x$$ and $$y.$$

Question 8

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

Accepted Answer

Assuming that correlation implies causality.

Question 9

A scatterplot of the number of hours studied and exam scores shows a strong positive linear pattern. What is the most likely value for $$r$$?

Accepted Answer

$$r = 0.95$$

Question 10

Which requirement must be met before using the linear correlation coefficient $$r to $$make conclusions about a population?

Accepted Answer

The sample of paired $$(x, y)$$ data must be a simple random sample of quantitative data.

Question 11

If all values of $$x$$ and $$y$$ are converted to a different scale, what happens to the value of $$r$$?

Accepted Answer

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

Question 12

Which scatterplot below best represents a negative linear correlation?

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

Accepted Answer

Scatterplot (b)

Question 13

A researcher finds $$r = 0.074$$ for the relationship between two variables. What does this indicate?

Accepted Answer

There is no significant linear correlation between the variables.

Question 14

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

Accepted Answer

The data must be categorical.

Question 15

If a scatterplot shows a curved pattern, but $$r = 0.330$$, what is the best interpretation?

Accepted Answer

There is a nonlinear relationship between $$x$$ and $$y.$$

Question 16

Which of the following best describes a lurking variable?

Accepted Answer

A variable that affects the variables being studied but is not included in the study.

Question 17

A scatterplot of disk drive capacity (in TB) and price shows a strong positive linear pattern. If $$r^2 = 0.85$, what does this mean?

Accepted Answer

85% of the variation in price is explained by the linear relationship with capacity.

Question 18

Which of the following is true about the linear correlation coefficient $$r$$ for a population?

Accepted Answer

It is represented by the Greek letter $$\rho ($$rho).

Question 19

Which scenario is most likely to inflate the value of $$r$$?

Accepted Answer

Using data based on averages.

Question 20

A scatterplot shows the following points: (0,8), (0.2,2), (0.4,6), (0.6,7), (0.8,3). What type of correlation is most likely present?

Accepted Answer

No correlation

Correlation and Linear Regression: Understanding the Linear Correlation Coefficient (r)

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