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

Responses

A. 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

B. 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

C. 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

D.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
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1 answer

To determine which scatterplot shows a non-linear association from the provided data, we can analyze each pair of x and y values qualitatively.

A.

  • Data:
    • x: 50, 46, 90, 59, 78, 64, 68, 53, 70, 72
    • y: 75, 71, 100, 80, 90, 82, 85, 77, 87, 89
  • Analysis: The points appear to exhibit a more linear trend, as y values seem to increase with x values.

B.

  • Data:
    • x: 50, 46, 98, 59, 78, 64, 68, 53, 70, 72
    • y: 75, 71, 90, 55, 70, 100, 90, 25, 40, 76
  • Analysis: The points vary significantly without a clear trend, and some y values seem to drop drastically, suggesting a non-linear association.

C.

  • Data:
    • x: 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
    • y: 90, 100, 57, 80, 60, 75, 72, 82, 70, 67
  • Analysis: The points show some fluctuation but still somewhat follow a trend, indicating possible linear association.

D.

  • Data:
    • x: 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
    • y: 35, 30, 75, 45, 70, 50, 55, 36, 62, 67
  • Analysis: The values of y drop significantly for lower values of x, and then there are some increases in y that do not correlate well with the increasing x values, indicating a non-linear association.

Conclusion:

Scatterplot B and D both demonstrate a non-linear association, but B displays extreme variance without a consistent pattern, making it the most evident choice for non-linearity. Thus, the answer is:

B shows a non-linear association.