Choose the weakest correlation

Choose the weakest correlation:

A. -.28

B. +.58

C. +.12

D. -.31

The Correct Answer and Explanation is :

The correct answer is C. +.12.

Explanation:

The correlation coefficient is a measure that indicates the relationship between two variables. It can range from -1 to +1, where:

• +1 indicates a perfect positive relationship.
• -1 indicates a perfect negative relationship.
• 0 indicates no linear relationship.

When interpreting correlation coefficients:

• Positive values (+) indicate that as one variable increases, the other also increases.
• Negative values (-) indicate that as one variable increases, the other decreases.
• The closer the value is to +1 or -1, the stronger the relationship between the two variables.
• The closer the value is to 0, the weaker the relationship.

Now, let’s analyze the options:

1. A. -.28: This is a small negative correlation. The negative sign indicates that as one variable increases, the other tends to decrease. The magnitude of the correlation (0.28) suggests a weak relationship.
2. B. +.58: This is a moderate positive correlation. The positive sign means that as one variable increases, the other also tends to increase. The magnitude of 0.58 indicates a moderate strength of the relationship.
3. C. +.12: This is a very weak positive correlation. The positive sign indicates that as one variable increases, the other slightly increases, but the magnitude of 0.12 is very close to 0, meaning the relationship is very weak.
4. D. -.31: This is a weak negative correlation. Similar to option A, the magnitude (0.31) is weak, but the negative sign indicates an inverse relationship.

Why C is the weakest:

• C (+0.12) has the smallest magnitude among all options. A correlation coefficient of +0.12 is very close to 0, indicating that there is almost no linear relationship between the two variables. This makes it the weakest correlation, as the closer a correlation is to 0, the weaker the relationship. In contrast, all other options have stronger correlations (whether positive or negative) than +0.12, so C is indeed the weakest.