To determine which set of data shows a linear association, we need to identify the correlation between the corresponding x and y values in the four provided datasets. Here’s a brief analysis of each dataset:
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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 points appear to have no clear pattern; they do not seem to form a straight line.
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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 points show a clear upward trend, which suggests 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 points do not follow a consistent linear pattern; they appear scattered without a clear relation.
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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 points also do not align in a linear manner; they are spread out without consistent direction.
Conclusion: The second dataset shows a clear linear association, characterized by points that predominantly trend upward. The other datasets do not demonstrate a clear linear relationship.