Question

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

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
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

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
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

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
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

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

Answer 1

To determine which scatterplot shows a linear association, we will analyze the relationships between the x and y values provided in each dataset. Here’s a breakdown of the datasets:

1. **First Dataset:**
- **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
- **Analysis:** The y-values do not show a consistent increase or decrease as x increases, indicating no clear linear relationship.

2. **Second Dataset:**
- **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
- **Analysis:** The y-values generally increase as x increases, suggesting a positive linear association.

3. **Third Dataset:**
- **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
- **Analysis:** The y-values do not show a consistent trend with varying x-values, indicating no clear linear relationship.

4. **Fourth Dataset:**
- **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:** The y-values fluctuate with no clear trend as x changes, indicating no clear linear relationship.

**Conclusion:** The second dataset exhibits a linear association as the y-values generally increase with the increase of x-values. The other datasets do not show any consistent linear trend. Therefore, the second scatterplot shows a linear association.