To determine which scatterplot depicts a linear association, you need to analyze how the y-values change in relation to the x-values. A linear association will typically show a straight-line pattern, where increases or decreases in x correspond to systematic increases or decreases in y.
Let’s examine each dataset one by one to identify which one appears to have a linear relationship:
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First Dataset:
- x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- y: 550, 800, 250, 300, 700, 1000, 650, 300, 100, 700
The y-values do not show a consistent pattern as x increases. The values fluctuate quite a bit. This suggests that there isn’t a linear relationship.
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Second Dataset:
- x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- y: 800, 700, 350, 450, 500, 1000, 900, 250, 400, 750
Again, the y-values fluctuate widely and do not exhibit a consistent increase or decrease, indicating a lack of linear association.
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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
The values of y vary significantly and don’t show a clear linear trend with respect to x, suggesting an absence of 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
Similarly to the previous datasets, there is significant fluctuation in the y-values and they do not seem to adhere to a linear pattern.
Based on this analysis, none of the datasets seems to show a clear linear association. If you have graphical representations of these datasets (actual scatterplots), reviewing those would give clearer insights into which one may exhibit a linear relationship, but based on the numerical data alone, there does not appear to be a linear association in any dataset.