Based on the scatterplot, select the most likely value of the linear correlation coefficient $r$.

• A. $0.9$
• B. $-0.8$
• C. $0$
• D. $1$

Answer: (B)

Verified step by step guidance

1. Step 1: Understand that the linear correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables. It ranges from \(-1\) to \$1\(, where values close to \)1\( indicate a strong positive linear relationship, values close to \)-1\( indicate a strong negative linear relationship, and values near \)0$ indicate little to no linear relationship.
2. Step 2: Examine the scatterplot carefully to determine the overall pattern of the data points. Look for whether the points tend to rise together (positive correlation), fall together (negative correlation), or show no clear pattern (no correlation).
3. Step 3: Assess the strength of the relationship by observing how tightly the points cluster around an imaginary straight line. A tight cluster suggests a correlation coefficient close to \$1\( or \)-1\(, while a more scattered pattern suggests a value closer to \)0$.
4. Step 4: Determine the sign of the correlation coefficient based on the direction of the trend. If the points slope downward from left to right, the correlation is negative; if they slope upward, it is positive.
5. Step 5: Based on the scatterplot's pattern and direction, select the most appropriate value of \(r\) from the given options (\$0.9\(, \)-0.8\(, \)0\(, \)1$) that best matches the observed strength and direction of the linear relationship.