Question 1

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

Accepted Answer

To visually display the relationship between two quantitative variables

Question 2

Suppose you create a scatterplot of students' study hours (X) and their exam scores (Y). The points form a tight, upward-sloping line. What can you infer about the correlation coefficient $$r$$?

Accepted Answer

$$r is $$close to $$+1$$

Question 3

Which of the following is the correct formula for the correlation coefficient $$r$$ using standardized values?

Accepted Answer

$$r = \frac{\sum z_x z_y}{n-1}$$

Question 4

A researcher finds a correlation coefficient of $$r = -0.85$$ between hours spent watching TV and GPA among college students. What does this indicate?

Accepted Answer

There is a strong negative linear relationship between TV watching and GPA

Question 5

Which of the following statements about correlation is TRUE?

Accepted Answer

Correlation is always between $$-1$$ and $$+1$$

Question 6

If a scatterplot shows a cloud of points with no discernible pattern or trend, what can you say about the correlation coefficient $$r$$?

Accepted Answer

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

Question 7

Which of the following is a potential effect of an outlier in a scatterplot on the correlation coefficient?

Accepted Answer

It can dramatically change the value and even the sign of the correlation

Question 8

Given the following data for two variables $$X$$ and $$Y$$: $$X = [2, 4, 6]$$, $$Y = [3, 7, 11]. $$What is the correlation coefficient $$r$$?

Accepted Answer

$$r = 1$$

Question 9

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

Accepted Answer

A lurking variable may influence both variables, creating a spurious association

Question 10

Suppose you standardize both variables $$X$$ and $$Y$$ before calculating the correlation. What does this process involve?

Accepted Answer

Subtracting the mean and dividing by the standard deviation for each variable

Question 11

Which of the following is NOT an assumption or condition for using correlation?

Accepted Answer

Both variables must be categorical

Question 12

A scatterplot of two variables shows a strong, curved pattern. What does this suggest about the correlation coefficient $$r$$?

Accepted Answer

$$r$$ may be close to $$0$$ even though there is a strong association

Question 13

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

Accepted Answer

There is a moderate positive linear relationship between the two variables

Question 14

If the correlation between two variables is $$r = 0$$, what does this mean?

Accepted Answer

There is no linear relationship between the variables

Question 15

Which of the following formulas can be used to calculate the correlation coefficient $$r$$ from raw data?

Accepted Answer

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

Question 16

Which of the following best describes a lurking variable?

Accepted Answer

A variable not included in the analysis that influences both variables under study

Question 17

Why is it important to determine which variable goes on the X or Y axis in a scatterplot?

Accepted Answer

It reflects which variable is considered explanatory and which is response

Question 18

Which of the following is a correct statement about the properties of the correlation coefficient?

Accepted Answer

The sign of $$r$$ gives the direction of the association

Question 19

A researcher finds a correlation of $$r = 0.95$$ between two variables. What does this suggest about the data points in the scatterplot?

Accepted Answer

The points are tightly clustered around a straight line

Question 20

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

Accepted Answer

Assuming that correlation implies causation

Scatterplots, Association, and Correlation: Study Notes

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