Question

9 which value of r represents data with a strong negative correlation between two variables? a 0.99 b -0.14 c -0.92 d -1.07

Explanation:

Step1: Recall correlation coefficient rules

The correlation coefficient \( r \) ranges between \(-1\) and \( 1 \). A negative \( r \) means negative correlation, and the closer \( |r| \) is to \( 1 \), the stronger the correlation.

Step2: Analyze each option

• Option A: \( 0.99 \) is positive, so strong positive correlation, not negative. Eliminate.
• Option B: \( -0.14 \), \( |r| = 0.14 \), weak negative correlation. Eliminate.
• Option C: \( -0.92 \), \( |r| = 0.92 \), close to \( 1 \), negative, so strong negative correlation.
• Option D: \( -1.07 \) is outside \([-1, 1]\), invalid. Eliminate.

Answer:

C. -0.92