Question

Use the tables to create scatter plots and determine which scatter plot is the shows a linear association.
X 5 8 2 4 6 12 10 1 3 7
Y 800 700 350 450 500 1000 900 250 400 750

X 5 8 2 4 6 12 10 1 3 7
Y 550 800 250 300 700 1000 650 300 100 700

X 5 8 2 4 6 12 10 1 3 7
Y 550 800 350 450 700 1000 900 250 400 750

X 5 8 2 4 6 12 10 1 3 7
Y 550 800 250 500 500 400 650 150 400 750

Answer 1

Which one has a linear association on a graph.

Answer 2

To determine which scatter plot shows a linear association, we need to analyze the given sets of \(X\) and \(Y\) values. A linear association means that as \(X\) increases, \(Y\) also tends to increase or decrease in a straight-line manner.

Let's summarize the datasets provided first:

1. **Dataset 1**
X: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
Y: 800, 700, 350, 450, 500, 1000, 900, 250, 400, 750

2. **Dataset 2**
X: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
Y: 550, 800, 250, 300, 700, 1000, 650, 300, 100, 700

3. **Dataset 3**
X: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
Y: 550, 800, 350, 450, 700, 1000, 900, 250, 400, 750

4. **Dataset 4**
X: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
Y: 550, 800, 250, 500, 500, 400, 650, 150, 400, 750

### Analyzing Each Dataset for Linear Association

1. **Dataset 1**: Examination of Y values suggests high variability (going from 250 to 1000) with irregular increases and decreases relative to X. No clear linear trend.

2. **Dataset 2**: The Y values do not follow a consistent increasing or decreasing trend either; some values even repeat without an obvious pattern.

3. **Dataset 3**: Again, we see significant variability in Y values. The values go up and down quite a bit without a clear linear trend.

4. **Dataset 4**: The Y values behave inconsistently. For example, there are multiple peaks but no clear straight-line connection.

### Conclusion

In general:

- For a clear linear pattern, we would expect to see a consistent slope (either upwards or downwards) as we move along the X-axis.
- However, none of the datasets provided shows a perfectly linear relationship as they contain various fluctuations in Y.

### Recommendation

To solidly identify linear associations, plotting these data points on a graph would help visualize these relationships. By looking at the visual spread, you could easily identify which one has a closer fit to a straight line.

While all datasets show a degree of positive correlation with some points, based on numerical analysis alone without visual representation, no dataset clearly exhibits a linear correlation among the fourth group. Therefore, none of these datasets can be strongly identified as showing a linear association without further graphical visualization or statistical measures like correlation coefficients.