Question

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

x 5 8 2 4 6 12 10 1 3 7
y 550 800 250 500 500 400 650 150 400 750
x 5 8 2 4 6 12 10 1 3 7 y 550 800 250 500 500 400 650 150 400 750

x 5 8 2 4 6 12 10 1 3 7
y 550 800 250 300 700 1000 650 300 100 700
x 5 8 2 4 6 12 10 1 3 7 y 550 800 250 300 700 1000 650 300 100 700

x 5 8 2 4 6 12 10 1 3 7
y 800 700 350 450 500 1000 900 250 400 750
x 5 8 2 4 6 12 10 1 3 7 y 800 700 350 450 500 1000 900 250 400 750

x 5 8 2 4 6 12 10 1 3 7
y 550 800 350 450 700 1000 900 250 400 750
x 5 8 2 4 6 12 10 1 3 7 y 550 800 350 450 700 1000 900 250 400 750
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Answer 1

To determine which scatterplot shows a linear association, we need to analyze the relationships between the given \(x\) and \(y\) values in each case. A linear association would show points that roughly align along a straight line, rather than being scattered randomly.

### Consider the data provided in each scatterplot:

1. **First Scatterplot:**
- **x:** \(5, 8, 2, 4, 6, 12, 10, 1, 3, 7\)
- **y:** \(550, 800, 250, 500, 500, 400, 650, 150, 400, 750\)

This set shows a mix of high and low values without a clear linear pattern.

2. **Second Scatterplot:**
- **x:** \(5, 8, 2, 4, 6, 12, 10, 1, 3, 7\)
- **y:** \(550, 800, 250, 300, 700, 1000, 650, 300, 100, 700\)

This data also appears scattered with no linear trend.

3. **Third Scatterplot:**
- **x:** \(5, 8, 2, 4, 6, 12, 10, 1, 3, 7\)
- **y:** \(800, 700, 350, 450, 500, 1000, 900, 250, 400, 750\)

Here, the values seem to show some ups and downs but don’t line up in a linear fashion.

4. **Fourth Scatterplot:**
- **x:** \(5, 8, 2, 4, 6, 12, 10, 1, 3, 7\)
- **y:** \(550, 800, 350, 450, 700, 1000, 900, 250, 400, 750\)

This scatterplot has values that are relatively closer together and suggest a more structured linear pattern among the values.

### Conclusion

From analyzing the response categories, it can be noted that the fourth scatterplot suggests a more linear association compared to the others due to the relative alignment of the pairs of values. Thus, **the fourth scatterplot shows a linear association.**