To determine which set of data has a non-linear association, we need to visualize the given (x,y) pairs by plotting them on a scatterplot and observing the pattern formed by the points.
Here are the datasets provided:
Dataset 1:
- x: 2, 5, 7, 9, 3, 1, 4, 8, 6, 10
- y: 60, 75, 90, 97, 65, 50, 70, 60, 78, 100
Dataset 2:
- x: 60, 75, 80, 95, 65, 50, 70, 82, 78, 100
- y: 2, 5, 7, 9, 3, 1, 4, 8, 6, 10
Dataset 3:
- x: 2, 5, 7, 9, 3, 1, 4, 8, 6, 10
- y: 60, 75, 80, 95, 65, 50, 70, 82, 78, 100
Dataset 4:
- x: 2, 5, 7, 9, 3, 1, 4, 8, 6, 10
- y: 60, 75, 80, 65, 22, 59, 86, 100, 25, 97
Analyzing the Datasets:
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For Dataset 1:
- Looking at the values, y increases generally as x increases but fluctuates. A plot would likely show a general upward trend with some waves, indicating some degree of linearity but not perfectly so.
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For Dataset 2:
- Inverse relationship; it appears as a scatter of points. Not likely linear because y decreases as x increases.
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For Dataset 3:
- This dataset mirrors Dataset 1 in its x-values. The y-values also appear to increase non-linearly. It would likely look similar to Dataset 1.
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For Dataset 4:
- Some y-values drop significantly (like at x=3), creating a non-linear curve. There are spikes and drops making it likely to be non-linear overall.
Conclusion:
From this analysis, Dataset 4 appears to have the most non-linear association due to the significant jumps and drops in the y-values compared to the x-values.
Thus, Dataset 4 represents the variable with a non-linear association.