To determine which scatterplot shows a linear association, we can analyze the patterns in the given data points. A linear association means that as the values of \( x \) increase, the values of \( y \) either consistently increase or decrease in a linear fashion.
Let's take a closer look at the \( y \)-values for each set of \( x \)-values.
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First Set of Data:
- \( y \): 800, 700, 350, 450, 500, 1000, 900, 250, 400, 750
- The values do not show a clear increasing or decreasing trend; they fluctuate significantly.
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Second Set of Data:
- \( y \): 550, 800, 350, 450, 700, 1000, 900, 250, 400, 750
- Although it has a slight increase initially, the values vary widely, indicating non-linearity.
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Third Set of Data:
- \( y \): 550, 800, 250, 300, 700, 1000, 650, 300, 100, 700
- Again, the values exhibit a lot of variation with no clear linear trend.
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Fourth Set of Data:
- \( y \): 550, 800, 250, 500, 500, 400, 650, 150, 400, 750
- Similar to the others, the \( y \)-values are not showing a consistent trend.
Based on this analysis, none of the provided datasets seem to portray a strong linear association since the \( y \)-values in each case vary substantially and do not adhere to the characteristics of a linear relationship.
However, if we were to graph these sets of points, we would look for straight-line patterns. From the descriptions, none of the datasets appear to yield a clear linear association without further statistical measures.
If a visual representation (scatterplots) is necessary, it could provide additional clarity, but based on the given data alone, all sets display more variability than a consistent linear trend.
In conclusion, none of the provided scatterplots show a distinct linear association.