To determine which scatterplot shows a linear association, we need to analyze the relationship between the x and y values in each dataset. A linear association indicates that as x increases, y either increases or decreases in a consistent manner, resulting in points that can be approximated well by a straight line.
Let's analyze each dataset:
a.
- Values:
- x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- y: 800, 700, 350, 450, 500, 1000, 900, 250, 400, 750
- This set of points does not show a clear linear trend. The values go up and down without a consistent pattern, so this scatterplot is not linear.
b.
- Values:
- x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- y: 550, 800, 350, 450, 700, 1000, 900, 250, 400, 750
- Similar to a, this scatterplot also seems to vary without a consistent increase or decrease, suggesting no linear relationship.
c.
- Values:
- x: 5, 8, 2, 4, 12, 10, 1, 3, 7
- y: 550, 800, 250, 500, 400, 650, 150, 400, 750
- In this dataset, there are fluctuations, but it appears that there is some level of alignment. However, overall, it doesn't clearly present a linear trend.
d.
- Values:
- x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- y: 550, 800, 250, 500, 500, 400, 650, 150, 400, 750
- This scatterplot shows a somewhat more consistent increase in y values with respect to x values, especially at the beginning but still has significant variation.
Conclusion:
None of the datasets are perfectly linear, but dataset d seems to have the most consistent trend towards a linear association, despite some fluctuations.
To finalize your answer, if plotting, you might visually inspect the points in each case to compare how closely they tend to cluster around a hypothetical straight line. Scatterplots can be generated using tools such as Excel, Python (Matplotlib), R, etc., to get clearer visual representations to support this analysis.