Bot GPT 4-o mini To determine which table has a non-linear association, we can visualize the data in a scatter plot format. Since I cannot generate plots directly, I can describe how to analyze the association based on the provided data points.
Let's analyze each of the given data sets qualitatively:
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First Data Set:
- \( x: 2, 5, 7, 9, 3, 1, 4, 8, 6, 10 \)
- \( y: 60, 75, 90, 97, 65, 50, 70, 60, 78, 100 \)
If we graph these points, we can see that they somewhat follow a pattern but with some fluctuations (not strictly increasing or decreasing), particularly around \( x = 3, 6, \) and \( 8 \). It suggests a non-linear relationship.
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Second Data Set:
- \( x: 2, 5, 7, 9, 3, 1, 4, 8, 6, 10 \)
- \( y: 60, 75, 80, 95, 65, 50, 70, 82, 78, 100 \)
Upon plotting, we see that this has a more systematic trend, appearing more linear-like with slight fluctuations but overall tending upwards.
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Third Data Set:
- \( x: 2, 5, 7, 9, 3, 1, 4, 8, 6, 10 \)
- \( y: 60, 75, 80, 65, 22, 59, 86, 100, 25, 97 \)
Here we see significant fluctuations, especially with lower values at \( x = 3 \) and \( x = 6 \) and a larger rise at \( x = 8 \). This indicates non-linearity.
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Fourth Data Set:
- This data is a switch of \( x \) and \( y \) from the first scenario. It’s effectively just another way of presenting the first data set. Since it maintains the same values, the association remains unchanged.
Evaluating these observations, it appears that the third data set has the most pronounced non-linear relationship. The values of \( y \) vary widely with respect to \( x \), resulting in a scatter plot which does not show either an increasing or decreasing linear trend.
Therefore, the table that most likely has a non-linear association is:
Third Data Set:
- \( x: 2, 5, 7, 9, 3, 1, 4, 8, 6, 10 \)
- \( y: 60, 75, 80, 65, 22, 59, 86, 100, 25, 97 \)
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