1. **Stating the problem:** We want to understand what the sample correlation coefficient $r$ measures and determine which value indicates a stronger correlation between $r=0.918$ and $r=-0.932$. 2. **Definition and formula:** The sample correlation coefficient $r$ measures the strength and direction of a linear relationship between two variables $X$ and $Y$. It is calculated by the formula: $$r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}}$$ where $x_i$ and $y_i$ are individual sample points, and $\bar{x}$ and $\bar{y}$ are the sample means. 3. **Interpretation:** The value of $r$ ranges from $-1$ to $1$. - $r = 1$ means a perfect positive linear correlation. - $r = -1$ means a perfect negative linear correlation. - $r = 0$ means no linear correlation. 4. **Strength of correlation:** The strength depends on the absolute value $|r|$. - The closer $|r|$ is to $1$, the stronger the linear relationship. - The sign of $r$ indicates the direction (positive or negative). 5. **Comparing $r=0.918$ and $r=-0.932$:** - $|0.918| = 0.918$ - $|-0.932| = 0.932$ Since $0.932 > 0.918$, the correlation with $r = -0.932$ is stronger. 6. **Conclusion:** The sample correlation coefficient $r$ measures the strength and direction of a linear relationship between two variables. Between $r=0.918$ and $r=-0.932$, the value $r=-0.932$ indicates a stronger correlation because its absolute value is larger, even though it is negative, meaning a strong negative linear relationship.