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Let's analyze the scatter plots and address each question based on the relationships they show:

1. **For which data set is the correlation coefficient \( r \) closest to 0?**
   - A correlation coefficient close to 0 suggests no strong linear relationship between the variables. From the scatter plots, **Figure 1** shows a weak or non-linear pattern, meaning that \( r \) would be close to 0 for this data set.

2. **For which data set is the correlation coefficient \( r \) closest to -1?**
   - A correlation coefficient of \( r = -1 \) indicates a strong negative linear relationship. **Figure 2** shows a clear negative linear pattern, where as \( x \) increases, \( y \) consistently decreases. This suggests that the correlation coefficient for Figure 2 is closest to -1.

3. **Which data set indicates the strongest positive linear relationship between its two variables?**
   - A strong positive linear relationship is represented by a clear upward trend where as \( x \) increases, \( y \) also increases consistently. **Figure 4** displays this behavior most strongly, indicating the strongest positive linear relationship.

To summarize:
1. Figure 1 has \( r \) closest to 0.
2. Figure 2 has \( r \) closest to -1.
3. Figure 4 shows the strongest positive linear relationship.

Would you like further details on any of these explanations? Here are five related questions to expand your understanding:

1. How is the correlation coefficient \( r \) mathematically calculated?
2. Can a correlation coefficient of 0 imply a non-linear relationship?
3. How do outliers affect the correlation coefficient?
4. Is it possible for a strong correlation to exist without causation?
5. What are the limitations of using scatter plots to interpret data relationships?

**Tip:** A correlation coefficient \( r \) close to 1 or -1 implies a stronger linear relationship, either positive or negative, while values closer to 0 indicate weaker or no linear relationship.

For which data set is the correlation coefficient closest to 0, -1, and which has the strongest positive linear relationship?

Understand how to interpret scatter plots and identify the correlation coefficient closest to 0, -1, and the strongest positive relationship. This problem focuses on understanding linear relationships and using Pearson's r to determine correlation.

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