객관식
In the context of scatterplots and correlation, which statement best describes the relationship between correlation and causation?
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11. Correlation
Scatterplots & Intro to Correlation
객관식
Four scatterplots (A–D) are shown. Which plot shows the strongest linear correlation (i.e., has the correlation coefficient with the greatest absolute value)?
A
Plot B: points form a clear U-shaped (curved) pattern.
B
Plot C: points are widely scattered with no clear pattern.
C
Plot D: points show a weak downward trend with substantial scatter.
D
Plot A: points are tightly clustered around an upward-sloping straight line.
검증된 단계별 안내1
Recall that the correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables. Its value ranges from \(-1\) (perfect negative linear correlation) to \(+1\) (perfect positive linear correlation), with values close to 0 indicating little or no linear correlation.
Examine each scatterplot to identify the pattern of the points: a strong linear correlation means points lie close to a straight line, either sloping upward (positive \(r\)) or downward (negative \(r\)).
For Plot B, the points form a U-shaped curve, which is a nonlinear pattern. Even if the points are close to the curve, the linear correlation coefficient \(r\) will be close to zero because \(r\) only measures linear relationships.
Plot C shows points widely scattered with no clear pattern, indicating a very weak or no linear correlation, so \(r\) will be near zero.
Plot D shows a weak downward trend with substantial scatter, suggesting a small negative correlation, but not very strong.
Plot A shows points tightly clustered around an upward-sloping straight line, indicating a strong positive linear correlation. Therefore, Plot A has the correlation coefficient \(r\) with the greatest absolute value.
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