To determine which scatterplot shows a linear association among the provided datasets, we need to assess how the values of "x" relate to the values of "y" in each case. A linear association implies that as "x" increases or decreases, "y" tends to increase or decrease in a consistent manner.
-
First dataset:
- (5.0, 12.0), (4.6, 9.0), (8.5, 15.0), (5.9, 11.0), (7.8, 13.0), (5.3, 8.0), (7.0, 14.5), (7.2, 10.0)
- This shows an upward trend but with some variability, indicating a potential linear association.
-
Second dataset:
- (5.0, 12.0), (4.6, 8.5), (8.5, 6.0), (7.8, 10.0), (6.8, 12.0), (5.3, 10.0), (7.0, 12.0), (7.2, 10.0)
- This shows a more scattered distribution with no clear linear relationship.
-
Third dataset:
- (5.0, 9.5), (4.6, 9.0), (5.9, 11.0), (7.8, 13.0), (6.4, 11.5), (6.8, 12.0), (5.3, 10.0), (7.2, 12.5)
- This appears to show a clearer upward trend, suggesting a linear association.
-
Fourth dataset:
- (5.0, 3.7), (4.6, 2.7), (8.5, 6.5), (7.8, 2.0), (6.4, 5.6), (6.8, 3.0), (7.0, 7.8), (7.2, 6.7)
- This plot shows no clear linear relationship, as points do not show a consistent pattern.
Evaluating the above points, the third dataset likely has the strongest linear association due to its upward trend. This dataset suggests that as "x" increases, "y" tends to also increase, indicating a linear relationship.