Question

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

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 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 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, we'll analyze the relationships between the x and y values from each dataset. Below is the analysis of each dataset:

1. **First dataset:**
- **X values:** 50, 46, 98, 59, 78, 64, 68, 53, 70, 72
- **Y values:** 75, 71, 90, 55, 70, 100, 90, 25, 40, 76

The points show a scatter with some high and low values, suggesting a possible non-linear relationship, but visual inspection would be needed to confirm.

2. **Second dataset:**
- **X values:** 50, 46, 90, 59, 78, 64, 68, 53, 70, 72
- **Y values:** 75, 71, 100, 80, 90, 82, 85, 77, 87, 89

The points appear to move in a somewhat linear pattern, suggesting a positive linear association.

3. **Third dataset:**
- **X values:** 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
- **Y values:** 35, 30, 75, 45, 70, 50, 55, 36, 62, 67

Here, the points are scattered with no clear linear pattern, suggesting a more complex relationship.

4. **Fourth dataset:**
- **X values:** 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
- **Y values:** 90, 100, 57, 80, 60, 75, 72, 82, 70, 67

This set also shows a more scattered arrangement, having both high and low values across the x-range, which could indicate a non-linear relationship.

**Conclusion:**
The first and third datasets may show non-linear associations, while the second dataset likely shows a linear association. The fourth dataset also looks non-linear. However, without a visual representation of the scatterplots, the third dataset seems to distinctly lack a clear pattern, indicating the most obvious non-linear association.

Thus, **the third dataset likely demonstrates a non-linear association.**