Use the tables to create scatterplots and determine which scatterplot shows a non-linear association.(1 point)

Question

Responses

x
50 46 90 59 78 64 68 53 70 72
y
75 71 100 80 90 82 85 77 87 89
x 50 46 90 59 78 64 68 53 70 72 y 75 71 100 80 90 82 85 77 87 89

x
50 46 80 59 78 64 68 53 70 68
y
35 30 75 45 70 50 55 36 62 67
x 50 46 80 59 78 64 68 53 70 68 y 35 30 75 45 70 50 55 36 62 67

x
50 46 98 59 78 64 68 53 70 72
y
75 71 90 55 70 100 90 25 40 76
x 50 46 98 59 78 64 68 53 70 72 y 75 71 90 55 70 100 90 25 40 76

x
50 46 80 59 78 64 68 53 70 68
y
90 100 57 80 60 75 72 82 70 67

Answer 1

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:

1. 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.

2. 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.

3. 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.

4. 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.