To determine which scatterplot shows a linear association, we will analyze the relationships between the x and y values provided in each dataset. Here’s a breakdown of the datasets:
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First 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
- Analysis: The y-values do not show a consistent increase or decrease as x increases, indicating no clear linear relationship.
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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
- Analysis: The y-values generally increase as x increases, suggesting a positive linear association.
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Third 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
- Analysis: The y-values do not show a consistent trend with varying x-values, indicating no clear linear relationship.
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Fourth 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
- Analysis: The y-values fluctuate with no clear trend as x changes, indicating no clear linear relationship.
Conclusion: The second dataset exhibits a linear association as the y-values generally increase with the increase of x-values. The other datasets do not show any consistent linear trend. Therefore, the second scatterplot shows a linear association.