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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 6.8 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

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

1 answer

To determine which scatterplot shows a linear association, we can analyze the sets of data provided to identify any trends or patterns.

Here is the breakdown of the four datasets:

  1. First Data Set:

    • Points: (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 dataset has a general downward trend with some clusters, indicating a possible non-linear association.

  2. Second Data Set:

    • Points: (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 dataset does not show a clear pattern and appears scattered without an apparent linear trend.

  3. Third Data Set:

    • Points: (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 dataset shows a more consistent upward trend, indicating a strong linear association.

  4. Fourth Data Set:

    • Points: (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 dataset shows some upward and downward trends but lacks a clear pattern indicating linearity, since the points are quite scattered.

Given this analysis, the third dataset appears to show the best linear association. You would see a clear upward trend if you plotted these points on a scatterplot.