Question

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

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

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

Answer 1

To determine which of the provided scatterplots shows a non-linear association, we’ll analyze the pairs of \(x\) and \(y\) values based on the datasets you provided.

1. **First Dataset:**
- \(x\): 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
- \(y\): 35, 30, 75, 45, 70, 50, 55, 36, 62, 67

This dataset appears to show a potential positive association, but the points may not follow a clear linear path.

2. **Second Dataset:**
- \(x\): 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
- \(y\): 90, 100, 57, 80, 60, 75, 72, 82, 70, 67

This dataset seems to show a more scattered pattern, especially indicating a possible non-linear relationship.

3. **Third Dataset:**
- \(x\): 50, 46, 90, 59, 78, 64, 68, 53, 70, 72
- \(y\): 75, 71, 100, 80, 90, 82, 85, 77, 87, 89

The points in this dataset move in an overall increasing manner and suggest a stronger linear association.

4. **Fourth Dataset:**
- \(x\): 50, 46, 98, 59, 78, 64, 68, 53, 70, 72
- \(y\): 75, 71, 90, 55, 70, 100, 90, 25, 40, 76

This dataset shows varied responses with declines and increases at certain \(x\) values, indicating a more complicated, possibly non-linear association.

### Conclusion:
Upon analysis, the second and fourth datasets suggest a non-linear association, but focusing on one specific request, the fourth dataset has the most evident oscillation which deviates significantly from a linear path. Thus, the fourth dataset most likely exhibits a non-linear association.

To make precise conclusions, plotting these data points on scatterplots would provide a visual confirmation of the relationships.