To determine which scatterplot shows a linear association, we will analyze the provided data sets. Let's break down each set of x and y values in terms of their potential linearity.
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First Data Set:
- x: 5.0, 4.6, 8.5, 7.8, 6.4, 6.8, 7.0, 7.2
- y: 3.7, 2.7, 6.5, 2.0, 5.6, 3.0, 7.8, 6.7
- Analysis: The y values do not consistently increase or decrease with x values, indicating a non-linear association.
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Second Data Set:
- x: 5.0, 4.6, 8.5, 5.9, 7.8, 5.3, 7.0, 7.2
- y: 12.0, 9.0, 15.0, 11.0, 13.0, 8.0, 14.5, 10.0
- Analysis: While there is some variability, there seems to be a more increasing trend than in the first data set. However, the data does not form a consistent linear path.
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Third Data Set:
- x: 5.0, 4.6, 5.9, 7.8, 6.4, 6.8, 5.3, 7.2
- y: 9.5, 9.0, 11.0, 13.0, 11.5, 12.0, 10.0, 12.5
- Analysis: The y values are varying but skew towards a plateau or slight increase. There does appear to be a more consistent relationship, albeit not perfectly linear.
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Fourth Data Set:
- x: 5.0, 4.6, 8.5, 7.8, 6.8, 5.3, 7.0, 7.2
- y: 12.0, 8.5, 6.0, 10.0, 12.0, 10.0, 12.0, 10.0
- Analysis: The y values vary considerably, especially with values such as 12.0, 8.5, and 6.0. This set does not show a linear association.
Conclusion:
Based on the analyses, the second data set shows the strongest potential for a linear association among the four provided. However, it should be visualized in a scatterplot to confirm the extent of the linearity, as best practices would require a graphical representation to make a full determination.
If you can create scatterplots from the data sets, you would likely see that the second data set provides the most linear appearance, while the first and fourth do not, and the third is somewhat linear but not as strong as the second.