Question

use the tables to create scatterplots and determine which scatterplot shows a linear association.

a. x 5 8 2 4 6 12 10 1 3 7
y 800 700 350 450 500 1000 900 250 400 750

b. x 5 8 2 4 6 12 10 1 3 7
y 550 800 350 450 700 1000 900 250 400 750

c. x 5 8 2 4 12 10 1 3 7
y 550 800 250 500 400 650 150 400 750

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

Answer 1

To determine which scatterplot shows a linear association, we need to analyze the relationship between the x and y values in each dataset. A linear association indicates that as x increases, y either increases or decreases in a consistent manner, resulting in points that can be approximated well by a straight line.

### Let's analyze each dataset:

#### a.
- Values:
- x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- y: 800, 700, 350, 450, 500, 1000, 900, 250, 400, 750
- This set of points does not show a clear linear trend. The values go up and down without a consistent pattern, so this scatterplot is not linear.

#### b.
- Values:
- x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- y: 550, 800, 350, 450, 700, 1000, 900, 250, 400, 750
- Similar to a, this scatterplot also seems to vary without a consistent increase or decrease, suggesting no linear relationship.

#### c.
- Values:
- x: 5, 8, 2, 4, 12, 10, 1, 3, 7
- y: 550, 800, 250, 500, 400, 650, 150, 400, 750
- In this dataset, there are fluctuations, but it appears that there is some level of alignment. However, overall, it doesn't clearly present a linear trend.

#### d.
- Values:
- x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
- y: 550, 800, 250, 500, 500, 400, 650, 150, 400, 750
- This scatterplot shows a somewhat more consistent increase in y values with respect to x values, especially at the beginning but still has significant variation.

### Conclusion:
None of the datasets are perfectly linear, but dataset **d** seems to have the most consistent trend towards a linear association, despite some fluctuations.

To finalize your answer, if plotting, you might visually inspect the points in each case to compare how closely they tend to cluster around a hypothetical straight line. Scatterplots can be generated using tools such as Excel, Python (Matplotlib), R, etc., to get clearer visual representations to support this analysis.