To determine which scatterplot shows a linear association, we'll analyze the provided data for each case systematically.
1. First set of data:
- x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- y: 550, 800, 250, 300, 700, 1000, 650, 300, 100, 700
Observation: The values of y do not increase or decrease consistently with x; the changes appear erratic.
2. Second set of data:
- x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- y: 800, 700, 350, 450, 500, 1000, 900, 250, 400, 750
Observation: This dataset also shows fluctuations without a clear pattern or consistent increase/decrease.
3. Third set of data:
- x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- y: 550, 800, 250, 500, 500, 400, 650, 150, 400, 750
Observation: This set results in various values of y for corresponding x that do not establish a trend either.
4. Fourth set of data:
- x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- y: 550, 800, 350, 450, 700, 1000, 900, 250, 400, 750
Observation: Here, y appears to trend upwards at certain intervals when plotted against x, but not consistently enough to confirm a linear relationship.
Conclusion:
Based on these observations, none of the datasets clearly show a consistent linear association. However, if we had to rank them, the fourth dataset seems to have the most potential for a linear relationship as it shows a slight increasing trend despite some irregular fluctuations.
Realistically, to determine which one shows a linear association decisively, we would have to plot these points on a graph. In practice, providing visual representations would allow for clearer identification of linear patterns.
If you have access to graphing tools or can plot them manually, the fourth dataset could be a good candidate to analyze further for linearity.