https://file.aiquickdraw.com/mathbot/file/17289421468598ef4xnc0.jpg

The image shows two scatter plots with the same response variable \( y \). The first plot compares variables \( x \) and \( y \), while the second plot compares variables \( w \) and \( y \). The task is to determine which explanatory variable (either \( x \) or \( w \)) has a stronger relationship with \( y \).

### **Interpretation:**

- **First plot (x vs. y):** 
  The data points appear more scattered, with no strong visible trend. There seems to be a weak or non-linear relationship between \( x \) and \( y \).

- **Second plot (w vs. y):** 
  In the second plot, the points are more tightly clustered around a positive trend. This suggests a stronger positive relationship between \( w \) and \( y \).

### **Conclusion:**
The **second variable (w)** shows a stronger relationship with the response variable \( y \) because the points are more tightly clustered and exhibit a clear trend.

Thus, the correct answer is:
**"The second variable (w) has a stronger relationship with the response variable y."**

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Would you like further details on identifying relationships in scatter plots?  

Here are 5 follow-up questions you might find interesting:  
1. What statistical measures (e.g., correlation coefficient) can quantify relationships in scatter plots?  
2. How does linearity influence the strength of the relationship?  
3. Can a non-linear pattern still represent a strong relationship between two variables?  
4. What is the difference between explanatory and response variables?  
5. How can outliers affect the strength of a relationship?

**Tip:** A tighter cluster of points in a scatter plot usually indicates a stronger correlation between two variables.

Which explanatory variable has a stronger relationship with the response variable y?

Analyze two scatter plots to determine which explanatory variable has a stronger relationship with the response variable y. This problem focuses on bivariate data, scatter plots, and identifying correlations. Suitable for students in Grades 9-12.

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