Question

Use the tables to create scatterplots and determine which scatterplot shows a linear association.(1 point)
Responses

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 800 700 350 450 500 1000 900 250 400 750

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 550 800 350 450 700 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
x 5 8 2 4 6 12 10 1 3 7 y 550 800 250 500 500 400 650 150 400 750

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

Answer 1

To determine which scatterplot shows a linear association, we would typically look for a pattern in the points plotted on a graph where \(x\) values are on the horizontal axis and \(y\) values are on the vertical axis. A linear association means that the points will closely follow a straight line (either increasing or decreasing).

Let's analyze the provided data sets one by one, based on their \(x\) and \(y\) values.

1. **First Dataset:**
- \(x\): 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- \(y\): 800, 700, 350, 450, 500, 1000, 900, 250, 400, 750

This dataset appears to fluctuate without a clear upward or downward trend. Thus, it does not exhibit a linear association.

2. **Second Dataset:**
- \(x\): 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- \(y\): 550, 800, 350, 450, 700, 1000, 900, 250, 400, 750

Similar to the first dataset, there is considerable fluctuation in the \(y\) values without a clear linear trend.

3. **Third Dataset:**
- \(x\): 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- \(y\): 550, 800, 250, 500, 500, 400, 650, 150, 400, 750

This dataset also shows irregularities in the data points, lacking a discernible linear trend.

4. **Fourth Dataset:**
- \(x\): 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- \(y\): 550, 800, 250, 300, 700, 1000, 650, 300, 100, 700

This dataset categorically shows a more defined pattern. The values of \(y\) seem to increase with the increase in \(x\) until a certain point and then fluctuate a bit towards the end, but there are segments that mimic a linear increase.

After evaluating all the datasets, if we rely solely on the appearances suggested by the numbers without graphing, the fourth dataset appears to show the closest behavior to a linear association due to its relatively consistent increase in many parts, even if it is not perfectly linear throughout.

In summary, based on analysis:
- **The fourth dataset shows the most linear association.**