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 550 800 250 300 700 1000 650 300 100 700

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 550 800 350 450 700 1000 900 250 400 750

Answer 1

To determine which scatterplot shows a linear association, we need to analyze the given sets of data. A linear association implies that as the values of \( x \) change, the values of \( y \) change in a consistent direction (either increasing or decreasing).

Let's examine the relationships in each table.

1. **First Set:**
- \( y \) values: 800, 700, 350, 450, 500, 1000, 900, 250, 400, 750
- The pattern does not appear consistent (not clearly increasing or decreasing).

2. **Second Set:**
- \( y \) values: 550, 800, 250, 300, 700, 1000, 650, 300, 100, 700
- There appears to be a lot of fluctuation; this set does not suggest linearity.

3. **Third Set:**
- \( y \) values: 550, 800, 250, 500, 500, 400, 650, 150, 400, 750
- The values do not change in a consistent way. There are ups and downs, indicating a lack of linear association.

4. **Fourth Set:**
- \( y \) values: 550, 800, 350, 450, 700, 1000, 900, 250, 400, 750
- Like the others, there is significant fluctuation. While some increases and decreases are present, the trend is not consistent enough to suggest a linear relationship.

It can be useful to visualize these relationships through scatterplots. Generally, if a scatterplot shows points that closely align along a straight line (either positively or negatively sloped), it suggests a linear association.

Scattering all points from each table into a graph through plotting software or manually would clarify whether any of them align linearly. Based on the qualitative analysis above, none of the sets provided show a strong linear association.

If you can provide physical scatterplots or more context, I can give a more quantitative analysis or look for specific relationships. However, based on this analysis, none suggest a clear linear association outright from the data alone.