To determine which scatterplot shows a linear association, we can analyze the data given in each of the four sets.
Data Sets
-
First Data Set:
- 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
-
Second Data Set:
- 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
-
Third Data Set:
- 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
-
Fourth Data Set:
- 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
Analysis of Scatterplots
-
First Data Set:
- The values of y do not seem to increase or decrease in a consistent manner as x changes, indicating a possible non-linear relationship.
-
Second Data Set:
- The y-values generally increase as x increases, with some fluctuations in between. This suggests a potential linear association.
-
Third Data Set:
- The y-values fluctuate widely and do not seem to form any clear upward or downward trend. This indicates a lack of a linear relationship.
-
Fourth Data Set:
- The y-values vary without establishing a clear trend related to x. Some values are repeating, showing inconsistency.
Conclusion
Based on the analysis, the second data set appears to exhibit a linear association, as the y-values move in a generally increasing manner with x. The other data sets do not show a clear linear relationship.
Recommended Action
To confirm this, you can plot the points for the second data set on a graph. If the points tend to align closer to a straight line, that will further support the observation of a linear association.