Question 1

Which of the following best describes the relationship shown in the scatterplot of students' heights (in inches) and weights (in pounds)?

Accepted Answer

There is a positive linear association with a possible outlier.

Question 2

The correlation coefficient $$r$$ for the relationship between students' heights and weights is 0.644. What does this value indicate?

Accepted Answer

There is a moderate positive linear relationship.

Question 3

Which of the following is NOT a condition that must be checked before interpreting the correlation coefficient $$r$$?

Accepted Answer

Categorical Variables Condition

Question 4

Suppose you calculate a correlation coefficient $$r = 0.996$$ between speed limit and average number of accidents per week. What is the best interpretation?

Accepted Answer

There is a strong positive linear relationship between speed limit and accidents.

Question 5

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

Accepted Answer

$$r$$ measures the strength of any association, linear or nonlinear.

Question 6

A scatterplot of baking temperature (°F) and score shows a curved pattern. Which condition for correlation is violated?

Accepted Answer

Straight Enough Condition

Question 7

If a scatterplot shows a strong association but the correlation coefficient $$r is $$close to zero, what is the most likely explanation?

Accepted Answer

The association is nonlinear.

Question 8

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

Accepted Answer

A hidden variable that affects both variables being studied.

Question 9

Why is it important to check for outliers before interpreting the correlation coefficient $$r$$?

Accepted Answer

Outliers can distort the value of $$r$$, making it misleading.

Question 10

Which of the following best explains why correlation does not imply causation?

Accepted Answer

A third variable may be influencing both variables.

Question 11

Given the following pairs of variables, which is most appropriate for calculating a correlation coefficient?

Accepted Answer

Fat content (g) and calories in hamburgers

Question 12

If the correlation coefficient $$r$$ between two variables is exactly $$-1$$, what does this mean?

Accepted Answer

All data points fall exactly on a straight line with a negative slope.

Question 13

Which of the following is a correct statement about the symmetry property of correlation?

Accepted Answer

The correlation of $$x$$ with $$y is $$the same as the correlation of $$y$$ with $$x.$$

Question 14

A researcher finds a correlation of $$r = 0.961$$ between fat content and calories in hamburgers. What is the best conclusion?

Accepted Answer

There is a strong positive linear relationship between fat content and calories.

Question 15

Which of the following scenarios would most likely result in a misleading correlation coefficient?

Accepted Answer

A scatterplot with a nonlinear pattern.

Question 16

If you switch the units of measurement for both variables in a correlation analysis (e.g., from inches to centimeters and pounds to kilograms), what happens to the value of $$r$$?

Accepted Answer

The value of $$r$$ remains unchanged.

Question 17

Which of the following is an example of a common mistake when interpreting correlation?

Accepted Answer

Assuming a strong correlation means one variable causes the other.

Question 18

A scatterplot of shoe size and IQ shows no pattern. What is the most likely value of the correlation coefficient $$r$$?

Accepted Answer

$$r is $$close to 0.

Question 19

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

Accepted Answer

An outlier can make a small correlation large or a large correlation small.

Question 20

Which of the following is the correct formula for the correlation coefficient $$r$$ between variables $$x$$ and $$y$$?

Accepted Answer

$$r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{(n-1)s_x s_y}$$

Scatterplots, Association, and Correlation: Understanding Relationships Between Quantitative Variables

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