Subjects statistics

Commute Wellbeing 75D167

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1. **Problem Statement:** Given the data of commute time (in minutes) and well-being score, and the correlation coefficient $r = -0.946$, interpret the relationship between commute time and well-being score. 2. **Understanding Correlation Coefficient:** The correlation coefficient $r$ measures the strength and direction of a linear relationship between two variables. It ranges from $-1$ to $1$. - If $r$ is close to $1$, there is a strong positive linear relationship. - If $r$ is close to $-1$, there is a strong negative linear relationship. - If $r$ is close to $0$, there is little to no linear relationship. 3. **Given:** $r = -0.946$ which is very close to $-1$, indicating a strong negative linear relationship between commute time and well-being score. 4. **Interpretation:** As commute time increases, the well-being score tends to decrease significantly. 5. **Graph A Analysis:** The scatter plot labeled A shows a downward trend with commute time on the x-axis and well-being score on the y-axis, consistent with the strong negative correlation. 6. **Conclusion:** The data and graph A confirm that longer commute times are associated with lower well-being scores, supported by the correlation coefficient $r = -0.946$. **Final answer:** There is a strong negative correlation between commute time and well-being score, meaning longer commutes are linked to lower well-being.