To determine which scatterplot shows a linear association, we need to analyze the given sets of data. A linear association implies that as the values of \( x \) change, the values of \( y \) change in a consistent direction (either increasing or decreasing).
Let's examine the relationships in each table.
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First Set:
- \( y \) values: 800, 700, 350, 450, 500, 1000, 900, 250, 400, 750
- The pattern does not appear consistent (not clearly increasing or decreasing).
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Second Set:
- \( y \) values: 550, 800, 250, 300, 700, 1000, 650, 300, 100, 700
- There appears to be a lot of fluctuation; this set does not suggest linearity.
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Third Set:
- \( y \) values: 550, 800, 250, 500, 500, 400, 650, 150, 400, 750
- The values do not change in a consistent way. There are ups and downs, indicating a lack of linear association.
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Fourth Set:
- \( y \) values: 550, 800, 350, 450, 700, 1000, 900, 250, 400, 750
- Like the others, there is significant fluctuation. While some increases and decreases are present, the trend is not consistent enough to suggest a linear relationship.
It can be useful to visualize these relationships through scatterplots. Generally, if a scatterplot shows points that closely align along a straight line (either positively or negatively sloped), it suggests a linear association.
Scattering all points from each table into a graph through plotting software or manually would clarify whether any of them align linearly. Based on the qualitative analysis above, none of the sets provided show a strong linear association.
If you can provide physical scatterplots or more context, I can give a more quantitative analysis or look for specific relationships. However, based on this analysis, none suggest a clear linear association outright from the data alone.