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

Responses

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

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 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
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 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
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 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

1 answer

To determine which set of data shows a linear association, we need to identify the correlation between the corresponding x and y values in the four provided datasets. Here’s a brief analysis of each dataset:

  1. First Dataset:

    • x: 5.0, 4.6, 8.5, 7.8, 6.4, 6.8, 7.0, 7.2
    • y: 3.7, 2.7, 6.5, 2.0, 5.6, 3.0, 7.8, 6.7
    • Analysis: The points appear to have no clear pattern; they do not seem to form a straight line.
  2. Second Dataset:

    • 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
    • Analysis: The points show a clear upward trend, which suggests a positive linear association.
  3. Third Dataset:

    • 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
    • Analysis: The points do not follow a consistent linear pattern; they appear scattered without a clear relation.
  4. Fourth Dataset:

    • 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
    • Analysis: The points also do not align in a linear manner; they are spread out without consistent direction.

Conclusion: The second dataset shows a clear linear association, characterized by points that predominantly trend upward. The other datasets do not demonstrate a clear linear relationship.