Question

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

x
x
5.0 4.6 8.5 5.9 7.8 5.3 7.0 7.2
y
y
12.0 9.0 15.0 11.0 13.0 8.0 14.5 10.0
x 5.0 4.6 8.5 5.9 7.8 5.3 7.0 7.2 y 12.0 9.0 15.0 11.0 13.0 8.0 14.5 10.0

x
x
5.0 4.6 8.5 7.8 6.8 5.3 7.0 7.2
y
y
12.0 8.5 6.0 10.0 12.0 10.0 12.0 10.0
x 5.0 4.6 8.5 7.8 6.8 5.3 7.0 7.2 y 12.0 8.5 6.0 10.0 12.0 10.0 12.0 10.0

x
x
5.0 4.6 5.9 7.8 6.4 6.8 5.3 7.2
y
y
9.5 9.0 11.0 13.0 11.5 12.0 10.0 12.5
x 5.0 4.6 5.9 7.8 6.4 6.8 5.3 7.2 y 9.5 9.0 11.0 13.0 11.5 12.0 10.0 12.5

x
x
5.0 4.6 8.5 7.8 6.4 6.8 7.0 7.2
y
y
3.7 2.7 6.5 2.0 5.6 3.0 7.8 6.7

Answer 1

To determine which scatterplot shows a linear association among the provided datasets, we need to assess how the values of "x" relate to the values of "y" in each case. A linear association implies that as "x" increases or decreases, "y" tends to increase or decrease in a consistent manner.

1. **First dataset:**
- (5.0, 12.0), (4.6, 9.0), (8.5, 15.0), (5.9, 11.0), (7.8, 13.0), (5.3, 8.0), (7.0, 14.5), (7.2, 10.0)
- This shows an upward trend but with some variability, indicating a potential linear association.

2. **Second dataset:**
- (5.0, 12.0), (4.6, 8.5), (8.5, 6.0), (7.8, 10.0), (6.8, 12.0), (5.3, 10.0), (7.0, 12.0), (7.2, 10.0)
- This shows a more scattered distribution with no clear linear relationship.

3. **Third dataset:**
- (5.0, 9.5), (4.6, 9.0), (5.9, 11.0), (7.8, 13.0), (6.4, 11.5), (6.8, 12.0), (5.3, 10.0), (7.2, 12.5)
- This appears to show a clearer upward trend, suggesting a linear association.

4. **Fourth dataset:**
- (5.0, 3.7), (4.6, 2.7), (8.5, 6.5), (7.8, 2.0), (6.4, 5.6), (6.8, 3.0), (7.0, 7.8), (7.2, 6.7)
- This plot shows no clear linear relationship, as points do not show a consistent pattern.

Evaluating the above points, the **third dataset** likely has the strongest linear association due to its upward trend. This dataset suggests that as "x" increases, "y" tends to also increase, indicating a linear relationship.