Question 1

Which of the following best describes the relationship shown in a scatter diagram where, as the explanatory variable increases, the response variable also increases?

Accepted Answer

Positive association

Question 2

Given the formula for the sample linear correlation coefficient:

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

What does it mean if $$r = 0$$?

Accepted Answer

There is no linear relationship between the variables.

Question 3

Suppose you calculate a sample correlation coefficient $$r = 0.85$$ for a data set with $$n = 10. $$Using the critical value table, does a linear relation exist between the variables at the 0.05 significance level?

Accepted Answer

Yes, because $$0.85 \u003e 0.632.$$

Question 4

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

Accepted Answer

$$r is $$resistant to outliers.

Question 5

A researcher finds a strong positive correlation between ice cream sales and drowning incidents. Which of the following best explains this result?

Accepted Answer

A lurking variable, such as temperature, affects both variables.

Question 6

Given the least-squares regression line $$\hat{y} = b_1$ x + b_0$, what does the slope b_1$ represent in the context of predicting distance from club-head speed?

Accepted Answer

The average increase in distance for each additional mile per hour of club-head speed.

Question 7

Why should you avoid using a regression line to predict values for the explanatory variable far outside the range of the observed data?

Accepted Answer

The linear relationship may not hold outside the observed range.

Question 8

Which of the following is the correct formula for the slope $$b_1 of $$the least-squares regression line?

Accepted Answer

$$b_1 = r$$ \cdot \frac{s_y}{s_x}$$

Question 9

In a contingency table, what does the marginal distribution of a variable represent?

Accepted Answer

The distribution of one variable, ignoring the other variable.

Question 10

If the conditional distribution of employment status by education level shows that the proportion employed increases as education increases, what can you conclude?

Accepted Answer

Higher education is associated with higher employment rates.

Question 11

Simpson’s Paradox is best described as:

Accepted Answer

A situation where the association between two variables reverses when a third variable is considered.

Question 12

Given the following data for two variables $$x$$ and $$y$$:

$$x$$: 1, 3, 3, 6, 7
$$y$$: 18, 13, 9, 6, 4

What is the sign of the correlation coefficient $$r$$?

Accepted Answer

Negative

Question 13

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

Accepted Answer

$$r is $$resistant to outliers.

Question 14

A residual in regression analysis is defined as:

Accepted Answer

The difference between the observed value and the predicted value of $$y.$$

Question 15

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

Accepted Answer

A lurking variable may be responsible for the observed association.

Question 16

If the sum of the products $$\sum \left( \frac{x_i - \overline{x}}{s_x} \right) \left( \frac{y_i - \overline{y}}{s_y} \right) is $$negative, what can you say about the relationship between $$x$$ and $$y$$?

Accepted Answer

There is a negative linear relationship.

Question 17

Which of the following is a correct interpretation of the y-intercept $$b_0 in a $$regression equation, when it is meaningful?

Accepted Answer

The value of $$y$$ when $$x = 0.$$

Question 18

Which of the following is the main criterion for the least-squares regression line?

Accepted Answer

It minimizes the sum of the squared residuals.

Question 19

If a scatter diagram shows points randomly scattered with no apparent pattern, what can you conclude about the relationship between the variables?

Accepted Answer

There is no linear relationship.

Describing the Relation Between Two Variables: Scatter Diagrams, Correlation, Regression, and Contingency Tables

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