To determine which scatterplot shows a linear association, we need to analyze the relationship between the pairs of \( x \) and \( y \) values from the given tables. Let's summarize the observations from each dataset:
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First Dataset:
- \( x: 5.0, 4.6, 8.5, 7.8, 6.8, 5.3, 7.0, 7.2 \)
- \( y: 12.0, 8.5, 6.0, 10.0, 12.0, 10.0, 12.0, 10.0 \)
- This dataset exhibits no clear linear trend, as the \( y \) values vary in a non-linear way with changing \( x \) values.
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Second Dataset:
- \( x: 5.0, 4.6, 5.9, 7.8, 6.4, 6.8, 5.3, 7.2 \)
- \( y: 9.5, 9.0, 11.0, 13.0, 11.5, 12.0, 10.0, 12.5 \)
- This dataset appears to show a positive linear trend, as \( y \) tends to increase with increasing \( x \).
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Third Dataset:
- \( x: 5.0, 4.6, 8.5, 7.8, 6.4, 6.8, 7.0, 7.2 \)
- \( y: 3.7, 2.7, 6.5, 2.0, 5.6, 3.0, 7.8, 6.7 \)
- The values of \( y \) vary quite a bit and do not demonstrate a consistent trend with changing \( x \).
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Fourth Dataset:
- \( x: 5.0, 4.6, 8.5, 5.9, 7.8, 5.3, 7.0, 7.2 \)
- \( y: 12.0, 9.0, 15.0, 11.0, 13.0, 8.0, 14.5, 10.0 \)
- The \( y \) values fluctuate without a clear linear relationship as \( x \) changes.
Conclusion: The second dataset shows a more consistent positive linear association overall based on the values provided. You may plot these points on a scatterplot to visually confirm the linear association.