Question 1

Which of the following best describes extrapolation in regression analysis?

Accepted Answer

Using a regression line to predict $$y$$ values for $$x$$ values outside the observed range of data.

Question 2

Why is extrapolation considered dangerous in statistical analysis?

Accepted Answer

Because the relationship given by the regression equation may not hold outside the range of sampled $$x$$ values.

Question 3

What is a regression outlier?

Accepted Answer

An observation that lies far away from the trend that the rest of the data follows.

Question 4

Which of the following statements about influential observations is TRUE?

Accepted Answer

Influential observations tend to pull the regression line toward that data point and away from the rest of the data points.

Question 5

A strong correlation between two variables $$x$$ and $$y$$ implies:

Accepted Answer

That there is a strong linear association between $$x$$ and $$y.$$

Question 6

Which of the following is an example of a lurking variable?

Accepted Answer

Temperature affecting both ice cream sales and drowning rates.

Question 7

Simpson’s Paradox occurs when:

Accepted Answer

The direction of an association between two variables changes after including a third variable.

Question 8

In the example of crime rate and education, what is the confounding variable?

Accepted Answer

Urbanization

Question 9

Given the following probabilities from a study: Probability of death for smokers $$= \frac{139}{582}$$, Probability of death for nonsmokers $$= \frac{230}{732}. $$What statistical phenomenon might explain why the overall death rate for smokers appears lower than for nonsmokers?

Accepted Answer

Confounding due to age groups (Simpson’s Paradox)

Question 10

Which of the following best illustrates Simpson’s Paradox in a medical context?

Accepted Answer

Treatment B appears more effective overall, but when data is broken down by kidney stone size, Treatment A is more effective for both small and large stones.

Question 11

Which of the following is NOT a reason to plot data before performing regression analysis?

Accepted Answer

To ensure the regression equation will be valid for extrapolation.

Question 12

If two explanatory variables are both associated with a response variable and with each other, what is this situation called?

Accepted Answer

Confounding

Question 13

Suppose you observe a strong positive correlation between ice cream sales and drowning incidents. Which of the following is the most likely explanation?

Accepted Answer

A lurking variable, such as temperature, affects both ice cream sales and drowning incidents.

Question 14

Which formula would you use to calculate the probability of death for smokers in a study?

Accepted Answer

$$P(	ext{Death} | 	ext{Smoker}) = \frac{	ext{Number of deaths among smokers}}{	ext{Total number of smokers}}$$

Question 15

Which of the following is a correct statement about lurking variables?

Accepted Answer

Lurking variables can influence the association between the variables of primary interest.

Question 16

A researcher finds a strong correlation between reading level and shoe size among children. What is the most likely lurking variable?

Accepted Answer

Age

Question 17

Which of the following is a multi-step problem involving Simpson’s Paradox? Suppose in a hospital, Treatment A has a success rate of $$78\%$$ and Treatment B has a success rate of $$83\%$$ overall. When broken down by stone size, Treatment A has a success rate of $$93\%$$ for small stones and $$73\%$$ for large stones, while Treatment B has $$87\%$$ for small stones and $$69\%$$ for large stones. What is the confounding variable?

Accepted Answer

Stone size

Question 18

Which of the following is a correct interpretation of Simpson’s Paradox in the context of smoking and survival rates?

Accepted Answer

The overall survival rate for smokers appears higher, but when data is grouped by age, smokers have lower survival rates in each age group.

(Lecture 8) Cautions in Analyzing Associations: Outliers, Lurking Variables, and Simpson’s Paradox

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