Question

Use the tables to create scatterplots and determine which scatterplot shows a linear association.(1 point)Responsesx 5 8 2 4 6 12 10 1 3 7y 800 700 350 450 500 1000 900 250 400 750x 5 8 2 4 6 12 10 1 3 7 y 800 700 350 450 500 1000 900 250 400 750x 5 8 2 4 6 12 10 1 3 7y 550 800 250 500 500 400 650 150 400 750x 5 8 2 4 6 12 10 1 3 7 y 550 800 250 500 500 400 650 150 400 750x 5 8 2 4 6 12 10 1 3 7y 550 800 250 300 700 1000 650 300 100 700x 5 8 2 4 6 12 10 1 3 7 y 550 800 250 300 700 1000 650 300 100 700x 5 8 2 4 6 12 10 1 3 7y 550 800 350 450 700 1000 900 250 400 750

Answer 1

To analyze the scatterplots for linear association based on the provided data sets, we will look at the coordinates (x, y) given in each instance.

Here they are summarized for clarity:

1. **First Set:**
- (5, 800)
- (8, 700)
- (2, 350)
- (4, 450)
- (6, 500)
- (12, 1000)
- (10, 900)
- (1, 400)
- (3, 750)

2. **Second Set:**
- (5, 800)
- (8, 700)
- (2, 350)
- (4, 450)
- (6, 500)
- (12, 1000)
- (10, 900)
- (1, 400)
- (3, 750)

3. **Third Set:**
- (5, 550)
- (8, 800)
- (2, 250)
- (4, 500)
- (6, 500)
- (12, 400)
- (10, 650)
- (1, 150)
- (3, 400)

4. **Fourth Set:**
- (5, 550)
- (8, 800)
- (2, 250)
- (4, 500)
- (6, 500)
- (12, 400)
- (10, 650)
- (1, 150)
- (3, 400)

5. **Fifth Set:**
- (5, 550)
- (8, 800)
- (2, 250)
- (4, 300)
- (6, 700)
- (12, 1000)
- (10, 650)
- (1, 300)
- (3, 100)

6. **Sixth Set:**
- (5, 550)
- (8, 800)
- (2, 350)
- (4, 450)
- (6, 700)
- (12, 1000)
- (10, 900)
- (1, 250)
- (3, 400)
- (7, 750)

To assess which scatterplot might show a linear association, we look for a consistent pattern where the y-values increase or decrease steadily with the x-values.

- **First Set** and **Second Set** both seem to follow a somewhat linear trend but have some deviations.
- **Third Set** and **Fourth Set** show more variance in the y-values, suggesting a weaker association.
- **Fifth Set** has a more scattered distribution around the y-axis, making it less likely to show linear association.
- **Sixth Set** has some linear aspects but also shows scatter.

Based on these observations, the **first** and **second sets** most closely approximate a linear relationship, though it is important to plot them visually for confirmation. Hence, while both may indicate some potential for linearity, we can conclude **the first set** shows the strongest linear association.