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 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
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 80 95 65 50 70 82 78 100
x 2 5 7 9 3 1 4 8 6 10 y 60 75 80 95 65 50 70 82 78 100

x
2 5 7 9 3 1 4 8 6 10
y
60 75 80 65 22 59 86 100 25 97

Answer 1

To determine which set of data has a non-linear association, we need to visualize the given (x,y) pairs by plotting them on a scatterplot and observing the pattern formed by the points.

Here are the datasets provided:

### Dataset 1:
- **x:** 2, 5, 7, 9, 3, 1, 4, 8, 6, 10
- **y:** 60, 75, 90, 97, 65, 50, 70, 60, 78, 100

### Dataset 2:
- **x:** 60, 75, 80, 95, 65, 50, 70, 82, 78, 100
- **y:** 2, 5, 7, 9, 3, 1, 4, 8, 6, 10

### Dataset 3:
- **x:** 2, 5, 7, 9, 3, 1, 4, 8, 6, 10
- **y:** 60, 75, 80, 95, 65, 50, 70, 82, 78, 100

### Dataset 4:
- **x:** 2, 5, 7, 9, 3, 1, 4, 8, 6, 10
- **y:** 60, 75, 80, 65, 22, 59, 86, 100, 25, 97

### Analyzing the Datasets:
1. **For Dataset 1:**
- Looking at the values, y increases generally as x increases but fluctuates. A plot would likely show a general upward trend with some waves, indicating some degree of linearity but not perfectly so.

2. **For Dataset 2:**
- Inverse relationship; it appears as a scatter of points. Not likely linear because y decreases as x increases.

3. **For Dataset 3:**
- This dataset mirrors Dataset 1 in its x-values. The y-values also appear to increase non-linearly. It would likely look similar to Dataset 1.

4. **For Dataset 4:**
- Some y-values drop significantly (like at x=3), creating a non-linear curve. There are spikes and drops making it likely to be non-linear overall.

### Conclusion:
From this analysis, **Dataset 4** appears to have the most non-linear association due to the significant jumps and drops in the y-values compared to the x-values.

Thus, **Dataset 4** represents the variable with a non-linear association.