Which of the following represents a strong negative correlation?
A -0.9
B -0.2
C +0.2
D +0.9
The Correct Answer and Explanation is :
The correct answer is A: -0.9.
In statistics, correlation measures the strength and direction of a linear relationship between two variables. The correlation coefficient, denoted as ( r ), ranges from -1 to +1. A coefficient of -1 indicates a perfect negative correlation, meaning that as one variable increases, the other decreases in a perfectly linear manner. Conversely, a coefficient of +1 indicates a perfect positive correlation, where both variables increase together.
Here’s how to interpret the given options:
- A: -0.9: This value indicates a very strong negative correlation. It suggests that there is a significant inverse relationship between the two variables. For instance, if one variable increases, the other tends to decrease substantially. A correlation of -0.9 implies that the relationship is quite consistent and predictable.
- B: -0.2: This indicates a weak negative correlation. The relationship between the two variables exists but is not strong; changes in one variable do not consistently relate to changes in the other.
- C: +0.2: This indicates a weak positive correlation, suggesting that as one variable increases, the other also tends to increase, but not strongly.
- D: +0.9: This indicates a strong positive correlation. As one variable increases, the other increases significantly as well.
In summary, a strong negative correlation (like -0.9) suggests a robust and predictable relationship where an increase in one variable leads to a notable decrease in the other. Understanding this concept is crucial in various fields, such as economics, psychology, and health sciences, where relationships between different factors are analyzed to inform decision-making and predictions.