To determine which of the provided scatterplots shows a non-linear association, we’ll analyze the pairs of \(x\) and \(y\) values based on the datasets you provided.
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First Dataset:
- \(x\): 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
- \(y\): 35, 30, 75, 45, 70, 50, 55, 36, 62, 67
This dataset appears to show a potential positive association, but the points may not follow a clear linear path.
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Second Dataset:
- \(x\): 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
- \(y\): 90, 100, 57, 80, 60, 75, 72, 82, 70, 67
This dataset seems to show a more scattered pattern, especially indicating a possible non-linear relationship.
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Third Dataset:
- \(x\): 50, 46, 90, 59, 78, 64, 68, 53, 70, 72
- \(y\): 75, 71, 100, 80, 90, 82, 85, 77, 87, 89
The points in this dataset move in an overall increasing manner and suggest a stronger linear association.
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Fourth Dataset:
- \(x\): 50, 46, 98, 59, 78, 64, 68, 53, 70, 72
- \(y\): 75, 71, 90, 55, 70, 100, 90, 25, 40, 76
This dataset shows varied responses with declines and increases at certain \(x\) values, indicating a more complicated, possibly non-linear association.
Conclusion:
Upon analysis, the second and fourth datasets suggest a non-linear association, but focusing on one specific request, the fourth dataset has the most evident oscillation which deviates significantly from a linear path. Thus, the fourth dataset most likely exhibits a non-linear association.
To make precise conclusions, plotting these data points on scatterplots would provide a visual confirmation of the relationships.