To analyze the given data and determine the type of association, we can observe how the \( y \) values change as the \( x \) values increase.
Data Points:
Given the \( x \) and \( y \) values:
- \( (25, 375) \)
- \( (30, 225) \)
- \( (80, 120) \)
- \( (150, 75) \)
- \( (250, 50) \)
- \( (350, 100) \)
- \( (425, 175) \)
- \( (450, 275) \)
- \( (500, 400) \)
Scatter Plot Analysis:
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Graphing the Data:
- When you plot these points on a scatterplot, you should observe the trends in the data.
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Observing the Trend:
- As \( x \) increases from 25 to 250, \( y \) decreases from 375 to 50.
- After \( x = 250 \), the trend changes: \( y \) starts increasing again as \( x \) continues to increase.
Type of Association:
- Initially, there is a decreasing trend (from high \( y \) values to low \( y \) values).
- Then, after a certain point (around \( x = 250 \)), it begins to increase again (from low to higher \( y \) values).
Given this observation, we can classify the type of association:
- The data does not show a consistent linear pattern, as there’s a transition from decreasing to increasing.
- Therefore, the most accurate description of the association here is non-linear association.
Conclusion:
The correct response is: non-linear association.