To determine which scatterplot shows a linear association, we can describe how each dataset would be plotted and which may indicate a linear relationship between the x and y values.
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First dataset:
- x values: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- y values: 550, 800, 250, 300, 700, 1000, 650, 300, 100, 700
- Analysis: These points vary considerably with no clear linear trend.
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Second dataset:
- x values: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- y values: 550, 800, 250, 500, 500, 400, 650, 150, 400, 750
- Analysis: These points also show some variation, but they don’t align in a straight line.
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Third dataset:
- x values: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- y values: 800, 700, 350, 450, 500, 1000, 900, 250, 400, 750
- Analysis: The y values vary considerably with respect to the x values, showing no clear linear pattern.
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Fourth dataset:
- x values: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- y values: 550, 800, 350, 450, 700, 1000, 900, 250, 400, 750
- Analysis: Similar to the others, this dataset also fluctuates without showing a strong linear relationship.
It appears that none of the datasets clearly establish a linear association upon quick analysis. However, visually plotting the scatterplots for each dataset will give a clearer indication of which dataset may have a better linear fit.
Conclusion:
After considering the patterns, if you had to choose, the dataset that typically has the highest variance in both x and y being unevenly spaced could potentially suggest less linearity. If you have the means to plot these datasets, that would provide the most definitive answer.
If you want, further analysis can be done with specific calculations, like correlation coefficients or regression analysis, to quantify their linear correlations. If you need assistance on computational methods, feel free to ask!