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Use the table to create a scatterplot. Determine the type of association.

This table presents the x and y values required to create scatter plots and determine the type of association.
x
25 30 80 150 250 350 425 450 500
y
375 225 120 75 50 100 175 275 400


(1 point)
Responses

linear association
linear association

no association
no association

non-linear association
non-linear association

negative linear association

1 answer

To determine the type of association between the given x and y values from the table, we'll first observe the trends in the data.

Here are the x and y value pairs listed:

  • (25, 375)
  • (30, 225)
  • (80, 120)
  • (150, 75)
  • (250, 50)
  • (350, 100)
  • (425, 175)
  • (450, 275)
  • (500, 400)

Plotting the points:

If we plot these points on a scatterplot, we can analyze how y behaves as x increases:

  • From x = 25 to x = 150, y decreases from 375 to 75.
  • From x = 150 to x = 250, y continues to decrease to 50.
  • However, beyond x = 250, y increases back up to 400 at x = 500.

Association Analysis:

  1. Initial Trend: For lower values of x (up to around 250), there is a clearly decreasing trend. This suggests a potential negative linear relationship.
  2. Later Trend: After x = 250, the y values start to increase despite x increasing, indicating a break from the previous pattern.

Conclusion:

The overall trend displays an initial negative correlation followed by an increase, indicating that the relationship is not consistent.

Thus, the best description of the association observed is non-linear association, as the points do not form a straight line but rather indicate a curved trend.

Final Answer: non-linear association.