Question

which r-value suggests a strong negative correlation?
a. r = 0.1859
b. r = -0.1859
c. r = 0.9874
d. r = -0.9874

Explanation:

Step1: Recall the properties of correlation coefficient \( r \)

The correlation coefficient \( r \) ranges from \(- 1\) to \(1\). A negative \( r \) - value indicates a negative correlation. The closer \(|r|\) is to \(1\), the stronger the correlation.

Step2: Analyze each option

• Option A: \(r = 0.1859\) is positive. So, it does not represent a negative correlation.
• Option B: \(r=-0.1859\). Here, \(|r|=0.1859\) which is far from \(1\). So, the negative correlation is weak.
• Option C: \(r = 0.9874\) is positive. So, it does not represent a negative correlation.
• Option D: \(r=-0.9874\). Here, \(|r| = 0.9874\) which is close to \(1\) and \(r\) is negative. So, it represents a strong negative correlation.

Answer:

D. \(r=-0.9874\)