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 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

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 550 800 250 500 500 400 650 150 400 750

Answer 1

To determine which scatterplot shows a linear association, we need to analyze the relationship between the x-values and the y-values in each set of data. Here's a breakdown of the response values for each of the scatterplots:

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

This scatterplot shows no clear linear trend since the y-values fluctuate without a consistent pattern as x increases.

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

Similar to the first scatterplot, the relationship appears erratic, with no distinct upward or downward trend.

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

This scatterplot also does not show a linear relationship. The points are scattered without any clear linear trend.

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

The y-values start high, dip around x = 2 and x = 8-10, and then return at x = 6-7. This does not show a consistent pattern either, indicating a lack of linear association.

### Conclusion
After analyzing all scatterplots, none of them show a linear association. However, visually, if a third plot appeared to have fewer fluctuations in its y-values for given x-values, it may hint toward some linear trend, but based on the information provided and without able to create actual visual plots, they all exhibit non-linear behavior overall.

If you could visually plot these points on a graph, you'd get a clearer representation of their relationships. But based on the sequences alone, none presents a linear association distinctly.