Question

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Correlation Quick Check
3 of 53 of 5 Items




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
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
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
550 800 250 500 500 400 650 150 400 750
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
x 5 8 2 4 6 12 10 1 3 7 y 550 800 250 300 700 1000 650 300 100 700
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Answer 1

To determine which scatterplot shows a linear association, we need to analyze the relationship between the values of \( x \) and \( y \) in each table.

1. **First Set:**
- \( x = [5, 8, 2, 4, 6, 12, 10, 1, 3, 7] \)
- \( y = [550, 800, 350, 450, 700, 1000, 900, 250, 400, 750] \)
- **Observation:** The values of \( y \) do not consistently increase or decrease as \( x \) changes. This does not exhibit a linear relationship.

2. **Second Set:**
- \( x = [5, 8, 2, 4, 6, 12, 10, 1, 3, 7] \)
- \( y = [800, 700, 350, 450, 500, 1000, 900, 250, 400, 750] \)
- **Observation:** Similar to the first set, \( y \) values also do not consistently increase or decrease with changes in \( x \).

3. **Third Set:**
- \( x = [5, 8, 2, 4, 6, 12, 10, 1, 3, 7] \)
- \( y = [550, 800, 250, 500, 500, 400, 650, 150, 400, 750] \)
- **Observation:** There is no clear linear correlation as the \( y \) values fluctuate without a clear upward or downward pattern.

4. **Fourth Set:**
- \( x = [5, 8, 2, 4, 6, 12, 10, 1, 3, 7] \)
- \( y = [550, 800, 250, 300, 700, 1000, 650, 300, 100, 700] \)
- **Observation:** Although there are some increases and decreases, overall fluctuations in \( y \) values do not suggest a linear relationship.

### Conclusion:
From the analysis, none of the scatterplots appear to show a clear linear association between \( x \) and \( y \). If you must choose one based on minimal fluctuations closest to a linear relationship, it would be wise to look for the dataset where the values of \( y \) are more consistently trending upward or downward as \( x \) changes. However, please provide additional context or criteria if you have specific details in mind to evaluate more effectively. If there was a mistake or a specific scatterplot was indicated based on previous observations, it is representative to choose that based on best fit rather than definitive linearity.