Question

Determine which table has a non-linear association by graphing it on a scatterplot.(1 point) Responses x 2 5 7 9 3 1 4 8 6 10 y 60 75 80 65 22 59 86 100 25 97 x 2 5 7 9 3 1 4 8 6 10 y 60 75 80 65 22 59 86 100 25 97 x 60 75 80 95 65 50 70 82 78 100 y 2 5 7 9 3 1 4 8 6 10 x 60 75 80 95 65 50 70 82 78 100 y 2 5 7 9 3 1 4 8 6 10 x 2 5 7 9 3 1 4 8 6 10 y 60 75 90 97 65 50 70 60 78 100 x 2 5 7 9 3 1 4 8 6 10 y 60 75 90 97 65 50 70 60 78 100 x 2 5 7 9 3 1 4 8 6 10 y 60 75 80 95 65 50 70 82 78 100

Answers

Answered by GPT-4o mini
To determine which table has a non-linear association, we would typically plot the pairs of (x, y) values on a scatterplot and visually assess the relationship. Given the data provided in your prompt, I'll summarize it:

1. **Table 1** (listed twice):
- x: 2, 5, 7, 9, 3, 1, 4, 8, 6, 10
- y: 60, 75, 80, 65, 22, 59, 86, 100, 25, 97

2. **Table 2** (listed twice):
- x: 60, 75, 80, 95, 65, 50, 70, 82, 78, 100
- y: 2, 5, 7, 9, 3, 1, 4, 8, 6, 10

3. **Table 3** (listed twice):
- x: 2, 5, 7, 9, 3, 1, 4, 8, 6, 10
- y: 60, 75, 90, 97, 65, 50, 70, 60, 78, 100

4. **Table 4** (listed twice):
- x: 2, 5, 7, 9, 3, 1, 4, 8, 6, 10
- y: 60, 75, 80, 95, 65, 50, 70, 82, 78, 100

### Analysis:

1. **Table 1**:
The values of \(y\) vary significantly, especially the value at \(x=3\) (y=22), indicating a potential non-linear relationship.

2. **Table 2**:
This dataset seems to represent an inverse relationship with generally increasing \(x\) values leading to decreasing \(y\) values. This might indicate a linear relationship (negative slope).

3. **Table 3**:
The values of \(y\) appear somewhat linear but could include variability depending on the visual representation.

4. **Table 4**:
Similar to Table 3, the values of \(y\) seem to follow a somewhat linear and predictable pattern.

### Conclusion:
**Table 1** is likely to demonstrate a non-linear association due to the extreme deviation at \(x=3\) where \(y=22\). This inconsistency suggests a non-linear pattern, particularly when plotted as a scatterplot. To confirm, you would plot each table's data and visually inspect them to see which exhibits a clear non-linear trend.
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