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."

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.