Question

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
550 800 250 300 700 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
550 800 350 450 700 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
550 800 250 500 500 400 650 150 400 750

Answer 1

To determine which scatterplot shows a linear association among the provided datasets, we can analyze the relationship between the given \( x \) and \( y \) values.

A linear association typically displays a straight-line pattern as the values increase or decrease. Here’s an analysis of each dataset:

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

The scatter plot would likely show a mixed pattern without a definitive linear trend.

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

Here too, the scatterplot might reveal variability and would not represent a clear linear trend.

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

Similar to the previous ones, this dataset would likely show some scatter but still not a clear linear trend.

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

This dataset also exhibits variability but does not present a consistent linear trend.

Upon reviewing the datasets, **None** seem to represent a clear linear association based on how \( y \) varies with \( x \). Typically, one might expect to see a trend where as \( x \) increases, \( y \) either consistently increases or decreases, but none of these datasets illustrates that.

To visualize this more closely, plotting each of those values on a scatter plot (if done) would help to confirm the linearity. However, based purely on analyzing the numbers, we can conclude that **none of these scatterplots** seem to show a discernible linear association.

If you were given specific scatterplots to visually assess and select the one with a linear association, please provide those visuals or more information.