To determine which scatterplot shows a linear association between the variables \( x \) and \( y \), let's analyze each table presented.
Analysis of Each Pair:
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First Table:
- \( y = [550, 800, 250, 500, 500, 400, 650, 150, 400, 750] \)
- The data points do not follow a clear linear trend. The values of \( y \) fluctuate in a non-linear manner as \( x \) increases.
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Second Table:
- \( y = [550, 800, 250, 300, 700, 1000, 650, 300, 100, 700] \)
- Similar to the first table, this data does not exhibit a clear linear pattern, with varying \( y \) values that do not consistently increase or decrease as \( x \) increases.
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Third Table:
- \( y = [550, 800, 350, 450, 700, 1000, 900, 250, 400, 750] \)
- This data shows considerable fluctuations in \( y \) as \( x \) increases; thus, there doesn’t appear to be a linear association.
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Fourth Table:
- \( y = [800, 700, 350, 450, 500, 1000, 900, 250, 400, 750] \)
- Similar to the previous entries, there is inconsistent behavior in \( y \), with no clear upward or downward linear trajectory.
Conclusion:
None of the tables exhibit a clear linear association based on the given \( x \) and \( y \) values. The distributions in all four sets show significant variability without a consistent trend.
However, if you were to plot these points, you would want to look for trends that have a consistent slope (upwards or downwards) to identify a linear association, which is not evident in the data provided here. Thus, none of these scatterplots show a linear association.