To determine which scatterplot shows a linear association, we would analyze the datasets described.
I cannot create actual scatterplots in this text format, but I can guide you through how to analyze the data numerically based on the descriptions given for each scatterplot.
Dataset Analysis:
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First Dataset:
- \( x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7 \)
- \( y: 800, 700, 350, 450, 500, 1000, 900, 250, 400, 750 \)
- The values of \( y \) do not show a clear increasing or decreasing trend as \( x \) increases.
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Second Dataset:
- \( x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7 \)
- \( y: 550, 800, 250, 300, 700, 1000, 650, 300, 100, 700 \)
- This dataset also lacks a clear linear trend; \( y \) values fluctuate widely as \( x \) increases.
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Third Dataset:
- \( x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7 \)
- \( y: 550, 800, 250, 500, 500, 400, 650, 150, 400, 750 \)
- This dataset again shows considerable fluctuation in \( y \) values relative to \( x \) and does not suggest a linear relationship.
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Fourth Dataset:
- \( x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7 \)
- \( y: 550, 800, 350, 450, 700, 1000, 900, 250, 400, 750 \)
- Similar to the previous datasets, it shows varying \( y \) values.
Conclusion:
From this analysis, none of the provided datasets exhibit a clear linear association since \( y \) values do not consistently increase or decrease in relation to \( x \).
If you feel that one of the datasets might suggest linearity upon visual inspection (for example, consistent upward or downward patterns), plotting the points on a graph is crucial to confirming this. In a hypothetical case, if one of them did appear to create a straight line or a narrow band upon plotting, that would be indicative of a linear association.
If you need more analysis or specifics, feel free to clarify!