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Correlation Quick Check

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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

1 answer

To determine which scatterplot shows a linear association, we should look for a pattern where the points roughly form a straight line, whether ascending or descending.

Let's analyze each of the datasets:

  1. Scatterplot 1:

    • Points: (5, 800), (8, 700), (2, 350), (4, 450), (6, 500), (12, 1000), (10, 900), (1, 250), (3, 400), (7, 750)
    • This dataset shows a general downward trend in the y-values as x increases, but there are some points that deviate significantly (around (12, 1000)), which makes it less linear.

  2. Scatterplot 2:

    • Points: (5, 550), (8, 800), (2, 250), (4, 300), (6, 700), (12, 1000), (10, 650), (1, 300), (3, 100), (7, 700)
    • This dataset seems to have varying trends, and some points do not form a linear pattern, especially the point (1, 300) and (3, 100).

  3. Scatterplot 3:

    • Points: (5, 550), (8, 800), (2, 350), (4, 450), (6, 700), (12, 1000), (10, 900), (1, 250), (3, 400), (7, 750)
    • Similar to the previous data, it does not present a strong linear association.

  4. Scatterplot 4:

    • Points: (5, 550), (8, 800), (2, 250), (4, 500), (6, 500), (12, 400), (10, 650), (1, 150), (3, 400), (7, 750)
    • This scatterplot shows more random variability without a clear linear trend.

Conclusion: None of the scatterplots exhibit a clear linear association, however, based on the observations:

  • If forced to choose, Scatterplot 1 shows the closest to a linear association trend (despite the outlier) because most other plots have more variability and less directionality in their trends.

To make a more informed decision, it's essential to visually examine actual scatterplots based on the provided data points. If visual representation is available, it would significantly aid in this analysis.