To determine which scatterplot shows a non-linear association among the provided datasets, we need to visualize how the values of \( x \) relate to the values of \( y \).
Here's a brief analysis based on the data provided:
-
First Dataset:
- x: 50, 46, 90, 59, 78, 64, 68, 53, 70, 72
- y: 75, 71, 100, 80, 90, 82, 85, 77, 87, 89
- Trend: This appears to have a roughly linear trend as \( x \) increases.
-
Second Dataset:
- x: 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
- y: 35, 30, 75, 45, 70, 50, 55, 36, 62, 67
- Trend: This dataset shows some clustering that is not in a linear arrangement; it seems to be more varied and may suggest a non-linear association.
-
Third Dataset:
- x: 50, 46, 98, 59, 78, 64, 68, 53, 70, 72
- y: 75, 71, 90, 55, 70, 100, 90, 25, 40, 76
- Trend: The points seem to vary quite a bit, and there are values of \( y \) that drop sharply at certain \( x \) values, indicating some non-linear behavior.
-
Fourth Dataset:
- x: 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
- y: 90, 100, 57, 80, 60, 75, 72, 82, 70, 67
- Trend: This dataset appears to have a more linear correlation as well.
Conclusion: The second dataset, with \( x: 50, 46, 80, 59, 78, 64, 68, 53, 70, 68 \) and \( y: 35, 30, 75, 45, 70, 50, 55, 36, 62, 67 \), shows the strongest indication of a non-linear association based on the clustering of points that do not follow a linear trend. The third dataset also shows signs of non-linearity due to the erratic nature of \( y \) values in relation to \( x \). Therefore, either the second or third dataset could suggest a non-linear association, with a stronger argument for the second dataset due to its visibly different layout.
You may plot these datasets to further verify the relationships visually.
1 answer