$$ r = \frac{103.6}{\sqrt{2742.9 \times 603.7}} = 0.08 $$

Question 1

Which of the following best describes what a scatterplot is used for in statistics?

Accepted Answer

To display the relationship between two quantitative variables

Question 2

Given the formula for Pearson’s correlation coefficient $$r$$:

$$ r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2$ \sum (y_i - \bar{y})^2$}} $$

What does a value of $$r = 0.94$$ indicate about the relationship between $$x$$ and $$y$$?

Accepted Answer

There is a strong positive linear relationship between $$x$$ and $$y$$

Question 3

A researcher finds a Pearson correlation coefficient of $$r = -0.56$$ between two variables. How should this be interpreted?

Accepted Answer

There is a moderate negative linear relationship

Question 4

Which of the following is a key assumption for the validity of Pearson’s correlation coefficient?

Accepted Answer

The data must be approximately normally distributed

Question 5

Suppose you calculate $$S_{XY} = 103.6$$, $$S_{XX} = 2742.9$$, and $$S_{YY} = 603.7. $$What is the Pearson correlation coefficient $$r$$?

Accepted Answer

$$ r = \frac{103.6}{\sqrt{2742.9 	imes 603.7}} = 0.08 $$

Question 6

Which of the following statements is TRUE regarding correlation and causation?

Accepted Answer

Correlation does not imply causation

Question 7

A dataset of beer characteristics shows a correlation of $$r = 0.92$$ between alcohol content and calories. What does this suggest?

Accepted Answer

There is a strong positive linear relationship between alcohol content and calories

Question 8

Which of the following scenarios best illustrates a confounding variable?

Accepted Answer

Both ice cream sales and drowning incidents increase in summer due to higher temperatures

Question 9

If a scatterplot shows no discernible pattern or trend, what is the most likely value for Pearson’s correlation coefficient $$r$$?

Accepted Answer

$$ r  is $$close to $$0$$

Question 10

A study finds a correlation of $$r = 0.78$$ between age and BMI, but the age data is not normally distributed. What is the best conclusion?

Accepted Answer

Pearson’s correlation coefficient may not be valid for this data

Question 11

Which of the following is an example of a spurious correlation?

Accepted Answer

The number of pirates decreases as global average temperature increases

Question 12

Which Excel function can be used to calculate the Pearson correlation coefficient between two arrays of data?

Accepted Answer

CORREL(array1, array2)

Question 13

Which of the following best describes a 'very weak' negative linear relationship according to the interpretation table for Pearson’s correlation?

Accepted Answer

$$ -0.19 \leq r \leq -0.01 $$

Question 14

Which of the following is NOT a requirement for using Pearson’s correlation coefficient?

Accepted Answer

The variables must be categorical

Question 15

A correlation matrix for beer data shows $$r = 0.41$$ between calories and sodium. How should this be interpreted?

Accepted Answer

There is a moderate positive linear relationship

Question 16

Which of the following is a real-world example where association is useful even without proven causality?

Accepted Answer

Insurance companies charging higher premiums to younger drivers due to higher accident rates

Question 17

If $$r = 0.00$$ for two variables, what does this mean?

Accepted Answer

There is no linear relationship between the variables

Question 18

Which of the following best explains why the correlation between ice cream sales and polio rates in the 1940s was misleading?

Accepted Answer

Both variables were influenced by a third variable (season/temperature)

Question 19

Which of the following is the correct formula for Pearson’s correlation coefficient $$r$$ using the sums of squares notation?

Accepted Answer

$$ r = \frac{S_{XY}}{\sqrt{S_{XX} S_{YY}}} $$

Question 20

Which of the following is a correct interpretation of $$r = -0.85$$?

Accepted Answer

There is a strong negative linear relationship

Correlation: Concepts, Calculation, and Interpretation in Statistics

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