Question 1

Which of the following best describes the purpose of a scatter diagram (scatterplot) in statistics?

Accepted Answer

To show the relationship between two quantitative variables measured on the same individual.

Question 2

Suppose a researcher collects data on atmospheric pressure (in mb) and wind speed (in knots) during hurricanes. If the scatterplot shows that as atmospheric pressure increases, wind speed decreases, what is the direction of the association?

Accepted Answer

Negative association

Question 3

Which formula correctly represents 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 4

A correlation coefficient $$r is $$calculated to be $$-0.86$$ between the number of colas consumed per week and bone mineral density. Which of the following is the best interpretation?

Accepted Answer

There is a strong negative linear association between colas consumed and bone mineral density.

Question 5

Which of the following statements about correlation and causation is correct?

Accepted Answer

Correlation does not imply causation unless the data come from a designed experiment.

Question 6

Given the least-squares regression line $$\hat{y} = b_1$ x + b_0$, what does the slope b_1$ represent in context?

Accepted Answer

The expected change in the response variable $$y$$ for each one-unit increase in the explanatory variable $$x$$, on average.

Question 7

A residual is defined as:

Accepted Answer

$$e = y - \hat{y}$$, the difference between the observed and predicted value of $$y.$$

Question 8

Which of the following is a property of the correlation coefficient $$r$$?

Accepted Answer

$$-1 \leq r \leq 1$$

Question 9

If the residual plot for a regression model shows a clear curved pattern, what does this indicate?

Accepted Answer

A linear model may not be appropriate for the data.

Question 10

The coefficient of determination $$R^2 is $$interpreted as:

Accepted Answer

The proportion of the variation in the response variable explained by the least-squares regression line.

Question 11

A researcher uses the regression equation $$\hat{y} = 74.80 + 17.80x to $$predict the appraised value of houses, where $$x is $$the number of rooms. What is the correct interpretation of the slope?

Accepted Answer

For each additional room, the expected appraised value increases by $17,800.

Question 12

Which of the following is a reason why you should not use a regression line to make predictions for values of $$x$$ far outside the range of the observed data?

Accepted Answer

The linear relationship may not hold outside the scope of the model.

Question 13

In a contingency table, what is a marginal distribution?

Accepted Answer

The frequency or relative frequency distribution of either the row or column variable.

Question 14

Simpson’s Paradox occurs when:

Accepted Answer

An association between two variables reverses or disappears when a third variable is introduced.

Question 15

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

Accepted Answer

An observation that significantly affects the slope and/or intercept of the regression line.

Question 16

If the correlation coefficient $$r$$ between two variables is close to zero, which of the following is true?

Accepted Answer

There is little to no evidence of a linear relationship between the variables.

Question 17

A conditional distribution in a contingency table is:

Accepted Answer

The relative frequency of each category of the response variable given a specific value of the explanatory variable.

Question 18

Which of the following is NOT a requirement for using a linear regression model?

Accepted Answer

The residuals must increase or decrease systematically as $$x$$ increases.

Chapter 4: Correlation, Regression, and Contingency Tables in Introductory Statistics

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