To determine which scatterplot shows a linear association, we need to analyze the relationships between the given \(x\) and \(y\) values in each case. A linear association would show points that roughly align along a straight line, rather than being scattered randomly.
Consider the data provided in each scatterplot:
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First Scatterplot:
- x: \(5, 8, 2, 4, 6, 12, 10, 1, 3, 7\)
- y: \(550, 800, 250, 500, 500, 400, 650, 150, 400, 750\)
This set shows a mix of high and low values without a clear linear pattern.
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Second Scatterplot:
- x: \(5, 8, 2, 4, 6, 12, 10, 1, 3, 7\)
- y: \(550, 800, 250, 300, 700, 1000, 650, 300, 100, 700\)
This data also appears scattered with no linear trend.
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Third Scatterplot:
- x: \(5, 8, 2, 4, 6, 12, 10, 1, 3, 7\)
- y: \(800, 700, 350, 450, 500, 1000, 900, 250, 400, 750\)
Here, the values seem to show some ups and downs but don’t line up in a linear fashion.
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Fourth Scatterplot:
- x: \(5, 8, 2, 4, 6, 12, 10, 1, 3, 7\)
- y: \(550, 800, 350, 450, 700, 1000, 900, 250, 400, 750\)
This scatterplot has values that are relatively closer together and suggest a more structured linear pattern among the values.
Conclusion
From analyzing the response categories, it can be noted that the fourth scatterplot suggests a more linear association compared to the others due to the relative alignment of the pairs of values. Thus, the fourth scatterplot shows a linear association.