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 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
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

1 answer

Based on the data provided, we can analyze the points in each table to identify whether the association between the x and y values is linear or non-linear.

  1. First Table:

    • x: 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
    • y: 35, 30, 75, 45, 70, 50, 55, 36, 62, 67
    • The scatterplot likely shows a weak positive trend in certain ranges but is not consistent, indicating potential non-linearity.
  2. Second Table:

    • x: 50, 46, 98, 59, 78, 64, 68, 53, 70, 72
    • y: 75, 71, 90, 55, 70, 100, 90, 25, 40, 76
    • This table depicts a more varied y response at different x values, suggesting a non-linear association.
  3. Third Table:

    • x: 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
    • y: 90, 100, 57, 80, 60, 75, 72, 82, 70, 67
    • The data shows more variation with response y values not following a consistent pattern as x increases, hinting towards non-linearity.
  4. Fourth Table:

    • x: 50, 46, 90, 59, 78, 64, 68, 53, 70, 72
    • y: 75, 71, 100, 80, 90, 82, 85, 77, 87, 89
    • This set of data appears to show a clearer linear trend as y values increase with x.

Conclusion:

After looking at the trends described from the data in each table, the second and third tables most likely depict non-linear associations due to the scatter of y values not consistently increasing or decreasing with corresponding x values. However, the second table appears to have a more significant and varied dispersion indicating a clear non-linear association.

If you are only to select one, the second scatterplot is the best candidate showing a non-linear association.