Question 1

Which of the following best describes the response (or dependent) variable in a bivariate data set?

Accepted Answer

The variable whose value can be explained by the value of the explanatory (or independent) variable.

Question 2

A scatter diagram is used to:

Accepted Answer

Display the relationship between two quantitative variables.

Question 3

Suppose you are analyzing the relationship between the depth at which drilling begins (in feet) and the time to drill five feet (in minutes). Which variable should be considered the explanatory variable?

Accepted Answer

Depth at which drilling begins (in feet)

Question 4

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

Accepted Answer

$$r$$ measures the strength and direction of a linear relationship between two quantitative variables.

Question 5

Given the formula for the sample linear correlation coefficient:

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

What do $$\bar{x}$$ and $$s_x$$ represent?

Accepted Answer

$$\bar{x} is $$the mean of the explanatory variable and $$s_x is $$its standard deviation.

Question 6

If a scatter diagram shows that as one variable increases, the other variable tends to decrease, what type of association is present?

Accepted Answer

Negative association

Question 7

A correlation coefficient of $$r = 0$$ indicates:

Accepted Answer

There is no linear relationship between the two variables.

Question 8

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

Accepted Answer

There is a strong negative linear relationship between the variables.

Question 9

Suppose you find a strong positive correlation between ice cream sales and the number of drowning incidents in a city. Which of the following best explains this relationship?

Accepted Answer

A lurking variable, such as temperature, is related to both ice cream sales and drowning incidents.

Question 10

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

Accepted Answer

$$r is $$resistant to outliers.

Question 11

You are given the following data for $$x$$ and $$y$$:

$$x$$: 2, 5
$$y$$: 7, 19

Find the equation of the line passing through these points.

Accepted Answer

$$y = 4x - 1$$

Question 12

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

Accepted Answer

Because a third variable (lurking variable) may be influencing both variables.

Question 13

If the points in a scatter diagram lie exactly on a straight line with positive slope, what is the value of the linear correlation coefficient $$r$$?

Accepted Answer

$$r = 1$$

Question 14

A researcher finds $$r = 0.02$$ between two variables. What does this suggest?

Accepted Answer

There is essentially no linear relationship.

Question 15

Which of the following scenarios is most likely to produce a nonlinear relationship in a scatter diagram?

Accepted Answer

The relationship between age and income, where income increases up to a certain age and then decreases.

Question 16

Which of the following is the correct formula for the sample linear correlation coefficient $$r$$?

Accepted Answer

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

Question 17

A scatter diagram shows a U-shaped pattern. What does this suggest about the relationship between the two variables?

Accepted Answer

There is a nonlinear relationship.

Question 18

Why should the correlation coefficient not be used exclusively to judge linear association without also using a scatter diagram?

Accepted Answer

Because the correlation coefficient does not reveal the form of the relationship or the presence of outliers.

Question 19

If the sum of squared residuals for a regression line is minimized, what does this indicate?

Accepted Answer

The regression line is the best linear fit for the data according to the least-squares criterion.

Scatter Diagrams, Correlation, and Linear Regression in Statistics

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