To determine which scatterplot shows a linear association, we can analyze the given (x, y) pairs from the sets of data provided.
Dataset 1
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
Observation: This dataset appears to show a positive trend, as the \(y\) values generally increase with increasing \(x\).
Dataset 2
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
Observation: The \(y\) values do not consistently increase or decrease as \(x\) changes; there are fluctuations. This suggests a weak or non-linear association.
Dataset 3
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
Observation: This dataset also does not have a clear trend in \(y\) with respect to \(x\), indicating a non-linear association.
Dataset 4
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
Observation: The values for \(y\) do not linearly correlate with \(x\) since there are many repeated values and the trend isn't consistent.
Conclusion
Among the four datasets, Dataset 1 shows the strongest linear association due to the positive trend in the \(y\) values as \(x\) increases. The other datasets exhibit non-linear or weak associations based on their given points.