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Each of these relationships reflects a correlation. Which relationship most likely reflects correlation but not causation? $\newline$ Choices: $\newline$ (A) Biking to work more often is associated with taking the bus to work more often. $\newline$ (B) Driving a longer distance to work is associated with using more gas. $\newline$ (C) Commuting a shorter distance to work is associated with having more free time.

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Correlation and causation

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Q. Each of these relationships reflects a correlation. Which relationship most likely reflects correlation but not causation?

\newline

Choices:

\newline

(A) Biking to work more often is associated with taking the bus to work more often.

\newline

(B) Driving a longer distance to work is associated with using more gas.

\newline

(C) Commuting a shorter distance to work is associated with having more free time.

Analyze Relationship: Analyze the relationship of option (A): Does biking to work more often cause someone to take the bus more often? The answer is likely No, as these are alternative modes of transportation. An increase in one does not cause an increase in the other; instead, they might both be influenced by a third factor, such as a change in weather or a transit strike.
Gas Usage Increase: Analyze the relationship of option (B): Does driving a longer distance to work cause an increase in gas usage? The answer is Yes, as using more gas is a direct consequence of driving a longer distance. This reflects both correlation and causation.
Free Time Increase: Analyze the relationship of option (C): Does commuting a shorter distance to work cause someone to have more free time? The answer is likely Yes, as having more free time could be a direct consequence of spending less time commuting. This also reflects both correlation and causation.
Correlation vs Causation: Finally, select the option that most likely reflects correlation but not causation. The answer is 'Biking to work more often is associated with taking the bus to work more often.' $(A)$ as an increase in one mode of transportation does not cause an increase in the other; they are likely correlated due to a third factor.

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