To determine which table has a non-linear association, we can analyze and graph each set of \(x\) and \(y\) values on a scatterplot. A non-linear association would show data points that do not follow a straight line trend.
Let's summarize the four datasets in a clearer format before evaluating them:
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Dataset 1:
- \(x: 2, 5, 7, 9, 3, 1, 4, 8, 6, 10\)
- \(y: 60, 75, 80, 95, 65, 50, 70, 82, 78, 100\)
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Dataset 2:
- \(x: 2, 5, 7, 9, 3, 1, 4, 8, 6, 10\)
- \(y: 60, 75, 90, 97, 65, 50, 70, 60, 78, 100\)
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Dataset 3 (flipped):
- \(x: 60, 75, 80, 95, 65, 50, 70, 82, 78, 100\)
- \(y: 2, 5, 7, 9, 3, 1, 4, 8, 6, 10\)
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Dataset 4:
- \(x: 2, 5, 7, 9, 3, 1, 4, 8, 6, 10\)
- \(y: 60, 75, 80, 65, 22, 59, 86, 100, 25, 97\)
Analysis:
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Dataset 1 - When plotted, this data appears to show a general upward trend. Therefore, it likely has a linear association.
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Dataset 2 - The values of \(y\) seem to increase, but there is an outlier at \(y = 60\) when \(x = 4\) and at \(y = 50\) when \(x = 1\). This might also suggest a non-linear relationship.
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Dataset 3 (flipped) - Since it's simply the axes swapped, the relationship is reversed but still linear.
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Dataset 4 - The \(y\) values show a more significant variation, with \(y\) dropping noticeably for \(x = 3\) and having other irregularities. The graph of this data set may produce a more scattered appearance, indicating a non-linear association.
Conclusion:
From the explanations above, Dataset 4 appears to have the most prominent non-linear association due to irregular fluctuations in \(y\) values when compared to \(x\). A scatterplot of this data would likely yield a scatter where data points do not conform to a straight line.