Ask a New Question
Menu

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

Responses

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
x 50 46 98 59 78 64 68 53 70 72 y 75 71 90 55 70 100 90 25 40 76

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

1 answer

To determine which scatterplot shows a non-linear association, we need to analyze the x and y values provided for each scatterplot.

  1. First Set of Data:

    • x: 50, 46, 90, 59, 78, 64, 68, 53, 70, 72
    • y: 75, 71, 100, 80, 90, 82, 85, 77, 87, 89
    • Observation: As x increases, y also tends to increase. This suggests a positive linear association.

  2. Second Set of Data:

    • x: 50, 46, 98, 59, 78, 64, 68, 53, 70, 72
    • y: 75, 71, 90, 55, 70, 100, 90, 25, 40, 76
    • Observation: The y values show significant fluctuation, with no clear upward or downward trend. This suggests a non-linear association.

  3. Third Set of Data:

    • x: 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
    • y: 35, 30, 75, 45, 70, 50, 55, 36, 62, 67
    • Observation: Initially, y decreases as x increases, followed by an upward trend. This suggests a non-linear association.

  4. Fourth Set of Data:

    • x: 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
    • y: 90, 100, 57, 80, 60, 75, 72, 82, 70, 67
    • Observation: There doesn't seem to be a clear association with either increasing or decreasing trends; the data fluctuates significantly.

Conclusion: The second scatterplot (the one with x and y values: 50, 46, 98, 59, 78, 64, 68, 53, 70, 72 and 75, 71, 90, 55, 70, 100, 90, 25, 40, 76) shows a non-linear association because the y values exhibit large fluctuations with no clear trend as x changes. The third scatterplot also suggests a non-linear association due to the varying trend as x increases.

However, if only one scatterplot can be cited, the second one is the clearest example of non-linearity due to drastic changes in y with no pattern as x changes.