Q: Given the regression equation $$\text{MPG} = 44.27 - 0.007258 \times \text{Weight (lbs)}$$, what is the predicted MPG for a car weighing 3000 lbs?

$$44.27 - 0.007258 \times 3000 = 22.496$$

Question 1

Which of the following best describes the difference between an explanatory variable and a response variable in a statistical study?

Accepted Answer

An explanatory variable may explain or influence changes in a response variable, while a response variable measures an outcome of a study.

Question 2

Given the Titanic data, what type of graphical display is most appropriate for visualizing the conditional distribution of survival by class?

Accepted Answer

A segmented or stacked bar chart

Question 3

Suppose you want to measure the strength of association between two categorical variables. Which of the following is NOT an appropriate measure?

Accepted Answer

Correlation coefficient $$r$$

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 between two quantitative variables.

Question 5

Given the regression equation $$	ext{MPG} = 44.27 - 0.007258 	imes 	ext{Weight (lbs)}$$, what is the predicted MPG for a car weighing 3000 lbs?

Accepted Answer

$$44.27 - 0.007258 	imes 3000 = 22.496$$

Question 6

Which of the following best describes the meaning of the slope in a least-squares regression line?

Accepted Answer

The amount of change in $$\hat{y}$$ for a one-unit increase in $$x$$

Question 7

If the correlation coefficient $$r = -0.88$$ for the relationship between hours without sleep and number of tasks completed, what does this indicate?

Accepted Answer

There is a strong negative linear relationship between the variables.

Question 8

Which of the following is a property of the least-squares regression line?

Accepted Answer

It always passes through the point $$(\bar{x}, \bar{y}).$$

Question 9

What is the formula for the slope $$b of $$the least-squares regression line?

Accepted Answer

$$b = r \frac{s_y}{s_x}$$

Question 10

Which of the following is an example of extrapolation?

Accepted Answer

Using a regression line based on data from 15 to 24 hours without sleep to predict performance after 40 hours without sleep.

Question 11

Which of the following statements about residuals is TRUE?

Accepted Answer

The mean of the least-squares residuals is always zero.

Question 12

What is a lurking variable?

Accepted Answer

A variable that has an important effect on the relationship among the variables in a study but is not included among the variables studied.

Question 13

Which of the following is a correct interpretation of $$r^2 ($$the coefficient of determination)?

Accepted Answer

$$r^2 is $$the proportion of variation in $$y$$ explained by the regression of $$y on$$ $$x.$$

Question 14

Which of the following is a potential danger when using correlation and regression analysis?

Accepted Answer

Assuming that association implies causation.

Question 15

Simpson’s Paradox refers to which of the following situations?

Accepted Answer

The direction of an association between two variables changes when a third variable is included and the data are analyzed at separate levels of that variable.

Question 16

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

Accepted Answer

$$r is $$not affected by outliers.

Question 17

If a residual plot shows a curved pattern, what does this indicate?

Accepted Answer

A linear regression model is not appropriate for the data.

Question 18

Which of the following best describes an influential observation in regression analysis?

Accepted Answer

An observation that, if removed, would significantly change the result of the calculation.

Question 19

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

Accepted Answer

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

Association, Correlation, and Regression: Analyzing Relationships Between Variables

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