Question

match the correlation coefficient to the interpretation of its value.
letter correlation coefficient number interpretation
a r = 0.88 1 weak negative linear correlation
b r = 0.52 2 strong negative linear correlation
c r = -0.91 3 moderate negative linear correlation
d r = -0.19 4 moderate positive linear correlation
5 strong positive linear correlation
a) r = 0.88
b) r = 0.52
c) r = -0.91
d) r = -0.19

Explanation:

• The correlation coefficient \(r\) measures the strength and direction of a linear relationship.
• If \(r>0\), it is a positive linear correlation. If \(r < 0\), it is a negative linear correlation.
• The closer \(|r|\) is to \(1\), the stronger the linear correlation. When \(|r|\) is around \(0.5\), it is a moderate linear correlation. When \(|r|\) is close to \(0\), it is a weak linear correlation.
• For \(r = 0.88\), since \(r>0\) and \(|r|\) is close to \(1\), it is a strong positive linear correlation (matches with \(5\)).
• For \(r=0.52\), since \(r > 0\) and \(|r|\) is around \(0.5\), it is a moderate positive linear correlation (matches with \(4\)).
• For \(r=-0.91\), since \(r<0\) and \(|r|\) is close to \(1\), it is a strong negative linear correlation (matches with \(2\)).
• For \(r = - 0.19\), since \(r<0\) and \(|r|\) is close to \(0\), it is a weak negative linear correlation (matches with \(1\)).

Answer:

A) \(r = 0.88\) → 5. Strong positive linear correlation
B) \(r = 0.52\) → 4. Moderate positive linear correlation
C) \(r=-0.91\) → 2. Strong negative linear correlation
D) \(r=-0.19\) → 1. Weak negative linear correlation