Multiple Choice
In the context of scatterplots, correlation occurs when which of the following is true about two variables?
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11. Correlation
Scatterplots & Intro to Correlation
Multiple Choice
In the context of scatterplots and correlation, which statement best describes the relationship between correlation and causation?
A
A correlation between two variables implies that changes in one variable cause changes in the other.
B
If a scatterplot shows a strong linear trend, then causation has been established.
C
A zero correlation means two variables must be independent and therefore cannot have a causal relationship.
D
Correlation does not imply causation; an association can exist even if neither variable causes the other.
Verified step by step guidance1
Understand the concept of correlation: Correlation measures the strength and direction of a linear relationship between two variables, typically quantified by the correlation coefficient \(r\), which ranges from \(-1\) to \$1$.
Recognize what causation means: Causation implies that changes in one variable directly cause changes in another variable, which requires more than just observing a relationship; it often requires controlled experiments or additional evidence.
Analyze the difference between correlation and causation: A correlation indicates an association or relationship between variables, but it does not prove that one variable causes the other to change.
Consider examples where correlation does not imply causation: For instance, two variables might be correlated due to a lurking variable or coincidence, so a strong correlation or a zero correlation does not automatically establish or rule out causation.
Conclude that the correct interpretation is that correlation does not imply causation; an observed association can exist even if neither variable causes the other.
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