To determine which scatterplot shows a non-linear association, we can analyze the data provided in the tables. A non-linear association suggests that the relationship between the variables does not form a straight line, and we will look for patterns that indicate curves or varying relationships between \( x \) and \( y \).
Let's briefly summarize the data points from each table:
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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
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Second 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
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Third 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
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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
Analyze the Visual Patterns
We will look for points that suggest whether the relationship could be linear (a straight line) or non-linear (curved or with variability).
- First Set: Looks to mainly increase or stay constant in \( y \) but could be explored for linearity visually.
- Second Set: \( y \) decreases for smaller \( x \) values, and then it slightly increases. Suggests non-linear behavior.
- Third Set: No clear linear pattern as it has points fluctuating dramatically, especially lower \( y \) values with some sudden shifts.
- Fourth Set: Shows a slight tendency to be increasing but could still be linear depending on the exact fit.
Conclusion
Based on this analysis:
- The Second Set of Data seems to have a non-linear association because \( y \) values significantly drop as \( x \) values increase up to a point, and then they start to increase again, indicating fluctuations that do not fit a straight line.
Thus, the scatterplot that shows a non-linear association is the Second Set of Data.