Question 1

Which of the following best describes the purpose of a scatterplot in statistics?

Accepted Answer

To show the relationship between two quantitative variables

Question 2

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

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

What does $$s_x$$ represent in this formula?

Accepted Answer

The standard deviation of the $$x$$ values

Question 3

A researcher finds a correlation coefficient $$r = -0.85$$ between hours spent watching TV and exam scores. Which of the following best describes this relationship?

Accepted Answer

Strong negative linear relationship

Question 4

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

Accepted Answer

$$r$$ measures the strength and direction of a linear relationship

Question 5

Suppose you have a dataset where $$r \approx 0. $$Which of the following is the most accurate interpretation?

Accepted Answer

There is no linear relationship

Question 6

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

Accepted Answer

$$r$$ can be used to infer causation

Question 7

A scatterplot shows a clear upward trend, but the points curve rather than form a straight line. What is the best description of the relationship?

Accepted Answer

Nonlinear relationship

Question 8

If the correlation coefficient between two variables is $$r = 1$$, what does this indicate?

Accepted Answer

There is a perfect positive linear relationship

Question 9

Which of the following scenarios is most likely to result in a correlation coefficient $$r$$ close to zero?

Accepted Answer

A strong nonlinear relationship

Question 10

A study finds a correlation of $$r = 0.05$$ between shoe size and intelligence in adults. What is the best interpretation?

Accepted Answer

There is a weak or non-existent linear relationship

Question 11

Which of the following is a common misconception about correlation?

Accepted Answer

Correlation implies causation

Question 12

A scatterplot of club-head speed (x) and driving distance (y) for golfers shows a strong positive linear trend. Which value of $$r is $$most likely?

Accepted Answer

$$r = 0.90$$

Question 13

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

Accepted Answer

Outliers can greatly increase or decrease $$r$$

Question 14

If two variables have a correlation coefficient $$r = -1$$, what does this mean about their relationship?

Accepted Answer

They have a perfect negative linear relationship

Question 15

Which of the following is the correct interpretation of a correlation coefficient $$r = 0.6$$?

Accepted Answer

Moderate positive linear relationship

Question 16

A dataset shows a strong nonlinear relationship between $$x$$ and $$y. $$What is the likely value of the correlation coefficient $$r$$?

Accepted Answer

$$r is $$close to 0

Question 17

Which of the following is NOT a reason to use a scatterplot?

Accepted Answer

To summarize the distribution of a single variable

Question 18

Suppose you calculate $$r = 0.75$$ for the relationship between hours studied and exam score. Which of the following best describes this relationship?

Accepted Answer

Strong positive linear relationship

Question 19

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

Accepted Answer

A third variable may be influencing both variables

Question 20

A researcher finds $$r = 0$$ between two variables, but the scatterplot shows a clear parabolic pattern. What is the best explanation?

Accepted Answer

There is a strong nonlinear relationship

Describing the Relation Between Two Variables: Scatterplots and Correlation

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