Question

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

25 8

2

4

6 12 10 1 3

7

y 550

800

350

450

700

1000

900

250

400 750

15

8

2

4

6 12 10

1

3 7

y 800

700

350

450

500

1000

900

250

400

750

5

8

2

4

6 12 10 1 3

7

y 550

800

250

500

500

400

650

150

400

750

5

8

2

4

6

12 10 1 3 7

550

800

250

300

700

1000

650

300

100

700

Answer 1

To determine which scatterplot shows a linear association, we need to analyze the provided data points in terms of their x (independent variable) and y (dependent variable) values. Given the layout of the data points, I will interpret them and look for trends.

### Data Points Breakdown

1. **Set 1**
- X: 1, 2, 3, 4, 6, 7, 8, 10, 12
- Y: 250, 350, 400, 450, 550, 700, 800, 900, 1000

2. **Set 2**
- X: 1, 2, 3, 4, 6, 7, 8, 10, 12
- Y: 150, 250, 300, 400, 500, 700, 800, 900, 1000

3. **Set 3**
- X: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12
- Y: 250, 400, 500, 550, 650, 700, 800, 900, 1000

4. **Set 4**
- X: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12
- Y: 100, 150, 300, 400, 500, 650, 700, 800, 900

### Analysis of Linear Association

- **Linear association** implies that as the x values increase, the y values should change in a consistent rate, forming a straight line or close to it.

1. **Set 1**:
- Trend: Increasing. Y values increase as X increases. Possibly a linear relationship, but would need to check for variability.

2. **Set 2**:
- Trend: Also increasing but can be verified further. There's a noticeable increase, but the lower values (150 at x=1) might not follow a linear pattern.

3. **Set 3**:
- Trend: More consistently increasing, with each x increment resulting in a clear and regular increase in y, suggesting a strong linear association.

4. **Set 4**:
- Trend: The initial increase is not as strong (starting from 100) and includes values that repeat (e.g., 400). This suggests less of a linear trend.

### Conclusion

Based on the breakdown, **Set 3** shows the strongest indication of a linear association with clear, consistent increases in y for increasing x values. Thus, if I had to select which scatterplot shows the clearest linear association, I would choose **Set 3**.

To fully confirm this, visualizing these points on a scatterplot would idealize the trend, but based on data alone, Set 3 seems to suggest a strong linear association.