To determine which scatterplot shows a linear association based on the given data, let's analyze the provided datasets individually.
Dataset 1:
- 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
Dataset 2:
- 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
Dataset 3:
- 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
Dataset 4:
- 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:
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Dataset 1:
- The y-values are somewhat uneven with no clear increasing or decreasing trend; they seem to fluctuate. Thus, it does not appear to show a linear association.
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Dataset 2:
- The y-values increase steadily as x increases, showing a clear positive trend. This suggests a linear association.
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Dataset 3:
- The y-values fluctuate without an apparent increasing or decreasing trend, indicating no linear association.
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Dataset 4:
- While there are some fluctuations, there are points that increase and decrease in a somewhat less clear pattern. Thus, it does not exhibit a strong linear association.
Conclusion:
Dataset 2 shows a clear linear association in the scatterplot. To visualize this, you would plot x against y for each dataset and look for a straight line pattern to confirm this conclusion.