To determine the relationship between the hours spent driving and the distance traveled, we can examine the correlation coefficient. This value measures the strength and direction of a linear relationship between two variables.
1. Calculate the Correlation Coefficient:
- The correlation coefficient between the hours spent driving and the distance traveled is [tex]\( \rho = 1.0 \)[/tex].
2. Interpret the Correlation Coefficient:
- The range of the correlation coefficient is from -1 to 1.
- When the correlation coefficient is close to 1, it indicates a strong positive linear relationship.
- When the correlation coefficient is close to -1, it indicates a strong negative linear relationship.
- When the correlation coefficient is close to 0, it indicates no linear relationship; however, there still might be a non-linear relationship.
3. Determine the Relationship Type:
- Since the correlation coefficient is [tex]\( 1.0 \)[/tex], which is both positive and exactly 1, it suggests a perfect positive linear relationship between the hours spent driving and the distance traveled.
Based on this understanding, the correct statement from the options provided is:
B. There is a positive linear relationship between the hours spent driving and the distance traveled.
