Question

victor, vladimir, venus, and vivian each have a different set of data points. each used the linear regression feature of his/her graphing calculator to find a linear function that models his/her data. the value of the correlation coefficient (r) associated with victor’s function was −0.91, the value of r for vladimir’s function was 0.73, the value of r for venus’s function was −0.44, and the value of r for vivian’s function was 0.88. who has the best model for his or her data? a venus b victor c vivian d vladimir

Explanation:

To determine the best linear model, we use the correlation coefficient \( r \). The closer \( |r| \) is to 1, the stronger the linear relationship, meaning a better model.

• Victor: \( | - 0.91| = 0.91 \)
• Vladimir: \( |0.73| = 0.73 \)
• Venus: \( | - 0.44| = 0.44 \)
• Vivian: \( |0.88| = 0.88 \)

Comparing these absolute values, \( 0.91 \) (Victor) is closest to 1. So Victor has the best model.

Answer:

B. Victor