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Use the tables to create scatterplots and determine which scatterplot shows a non-linear association.(1 point) Responses x 50 46 80 59 78 64 68 53 70 68 y 35 30 75 45 70 50 55 36 62 67 x 50 46 80 59 78 64 68 53 70 68 y 35 30 75 45 70 50 55 36 62 67 x 50 46 80 59 78 64 68 53 70 68 y 90 100 57 80 60 75 72 82 70 67 x 50 46 80 59 78 64 68 53 70 68 y 90 100 57 80 60 75 72 82 70 67 x 50 46 90 59 78 64 68 53 70 72 y 75 71 100 80 90 82 85 77 87 89 x 50 46 90 59 78 64 68 53 70 72 y 75 71 100 80 90 82 85 77 87 89 x 50 46 98 59 78 64 68 53 70 72 y 75 71 90 55 70 100 90 25 40 76

1 answer

To determine which scatterplot shows a non-linear association, we need to analyze the relationship between the x and y values provided in the tables.

Each pair of x and y values provided can be plotted on a scatterplot. We can summarize the data to help visualize the trends:

  1. First dataset:

    • x: 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
    • y: 35, 30, 75, 45, 70, 50, 55, 36, 62, 67
    • This dataset appears to have a generally positive association, as y increases with x, but check for linearity.

  2. Second dataset:

    • x: 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
    • y: 90, 100, 57, 80, 60, 75, 72, 82, 70, 67
    • This dataset has more variation in y values. Here, it seems like there isn’t a consistent trend related to x, indicating a possible non-linear association.

  3. Third dataset:

    • x: 50, 46, 90, 59, 78, 64, 68, 53, 70, 72
    • y: 75, 71, 100, 80, 90, 82, 85, 77, 87, 89
    • This dataset also shows a positive trend, suggesting a linear relationship.

  4. Fourth dataset:

    • x: 50, 46, 98, 59, 78, 64, 68, 53, 70, 72
    • y: 75, 71, 90, 55, 70, 100, 90, 25, 40, 76
    • This dataset appears to have significant variability in y values as well. The lack of consistent change as x values increase suggests a non-linear relationship.

Based on these analyses, the second and fourth datasets show signs of non-linear associations due to the variability and lack of a consistent trend in y values relative to x. You should plot each of them to confirm visually, but likely candidates for non-linear relationships are the second and fourth datasets.