To determine which scatterplot shows a linear association, we can analyze the provided (x, y) data points from each set.
1st Set of Data:
- 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
Plotting these points, there is no clear linear trend.
2nd Set of Data:
- 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
Plotting these points suggests a more scattered set; there is variability but no clear linear tendency.
3rd Set of Data:
- 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
These points are quite scattered and do not suggest a linear relationship.
4th Set of Data:
- 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
When plotted, this set of points appears to follow a clearer upward trend, suggesting a linear association.
Conclusion:
Based on the descriptions and analyses, the 4th set of data has the scatterplot that shows the strongest linear association.