Question 1

Which of the following best describes the role of the response variable in a scatter diagram?

Accepted Answer

It is the variable you want to predict, and is plotted on the vertical axis.

Question 2

A researcher collects data on hours studied (x) and exam scores (y) for a group of students. Which variable should be plotted on the horizontal axis in a scatter diagram?

Accepted Answer

Hours studied (x), because it is the explanatory variable.

Question 3

Which formula correctly represents the sample linear correlation coefficient $$r$$ between variables $$x$$ and $$y$$?

Accepted Answer

$$r = \frac{s_{xy}}{s_x s_y}$$

Question 4

Suppose the sample correlation coefficient between BMI and systolic blood pressure (SBP) for 10 males is $$r = 0.859. $$The critical value for $$n = 10 is$$ $$0.632. $$What can you conclude?

Accepted Answer

There is a positive linear relation between BMI and SBP.

Question 5

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

Accepted Answer

$$r is a $$unitless measure of association.

Question 6

A scatter diagram shows a strong negative linear association between two variables. Which of the following is the most likely value for the correlation coefficient $$r$$?

Accepted Answer

$$r = -0.90$$

Question 7

If the correlation coefficient $$r$$ between two variables is close to $$0$$, which of the following statements is correct?

Accepted Answer

There is no linear relationship between the variables.

Question 8

Which of the following scenarios best illustrates the difference between correlation and causation?

Accepted Answer

A high correlation between the percentage of females with bachelor’s degrees and births to unmarried mothers does not imply one causes the other.

Question 9

Given the formula for sample covariance $$s_{xy}$$:

$$s_{xy} = \frac{1}{n-1} \sum (x_i - \bar{x})(y_i - \bar{y})$$

What does a positive value of $$s_{xy}$$ indicate about the relationship between $$x$$ and $$y$$?

Accepted Answer

There is a positive association between $$x$$ and $$y.$$

Question 10

A scatter plot of the relationship between age and income shows a curved pattern. What does this suggest about the correlation coefficient $$r$$?

Accepted Answer

$$r$$ will be close to $$0.$$

Question 11

Which of the following steps is NOT part of rigorously testing whether a linear relation exists between two variables?

Accepted Answer

Calculate the mean of the explanatory variable.

Question 12

If an outlier is added to a data set, which property of the correlation coefficient $$r is $$most relevant?

Accepted Answer

$$r is $$not resistant to outliers.

Question 13

Suppose you have two variables, $$x$$ and $$y$$, measured in centimeters and kilograms, respectively. What effect does changing the units of $$x$$ and $$y$$ have on the correlation coefficient $$r$$?

Accepted Answer

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

Question 14

A scatter diagram shows that as the value of $$x$$ increases, the value of $$y$$ decreases. How would you describe the association?

Accepted Answer

Negative association

Question 15

Which of the following is TRUE about the sample correlation coefficient $$r$$ for a perfect positive linear relationship?

Accepted Answer

$$r = +1$$

Question 16

A time series data set shows a high correlation between two variables over time. Which of the following is the best explanation for this?

Accepted Answer

Both variables are moving in a specific direction over time, causing high correlation.

Question 17

Given the formula for the sample linear correlation coefficient:

$$r = \frac{1}{n-1} \sum (x_i - \bar{x})(y_i - \bar{y}) \Bigg/ \sqrt{\frac{1}{n-1} \sum (x_i - \bar{x})^2$ \cdot \frac{1}{n-1} \sum (y_i - \bar{y})^2$}$$

What is the denominator representing?

Accepted Answer

The product of the standard deviations of $$x$$ and $$y$$

Question 18

In a designed experiment, which statement about correlation and causation is correct?

Accepted Answer

Causation can be claimed if the experiment is properly controlled.

Question 19

A scatter plot of heights of women and the men they date shows a positive linear trend. If all heights were measured in inches instead of centimeters, what would happen to the correlation coefficient $$r$$?

Accepted Answer

$$r$$ would remain unchanged.

Scatter Diagrams and Correlation: Study Notes for Statistics Students

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