Which of these r-values represents the weakest correlation?
A. 0.2
B. 0.5
c.0.4
D. 0.3
The Correct Answer and Explanation is :
The correct answer is A. 0.2.
Explanation:
In statistics, the correlation coefficient (denoted as r) measures the strength and direction of the linear relationship between two variables. The value of r ranges from -1 to +1, where:
- +1 indicates a perfect positive correlation (as one variable increases, the other also increases in a perfectly linear manner),
- -1 indicates a perfect negative correlation (as one variable increases, the other decreases in a perfectly linear manner),
- 0 indicates no linear correlation (no predictable relationship between the two variables).
The strength of the correlation can be interpreted as follows:
- 0 to 0.1 or -0.1 to 0: Very weak or negligible correlation.
- 0.1 to 0.3 or -0.3 to -0.1: Weak correlation.
- 0.3 to 0.5 or -0.5 to -0.3: Moderate correlation.
- 0.5 to 0.7 or -0.7 to -0.5: Strong correlation.
- 0.7 to 1.0 or -1.0 to -0.7: Very strong correlation.
Now, let’s analyze the given options:
- Option A (0.2): This represents a weak correlation. The value is relatively close to 0, suggesting a low degree of association between the variables. The closer the value is to 0, the weaker the correlation.
- Option B (0.5): This represents a moderate correlation. A value of 0.5 indicates a moderate strength of linear association between the two variables.
- Option C (0.4): This also represents a moderate correlation, though slightly weaker than 0.5, it still indicates a noticeable relationship between the variables.
- Option D (0.3): This represents a weak correlation, but it is stronger than 0.2, which means it indicates a slightly more significant relationship than the one in option A.
Thus, Option A (0.2) has the weakest correlation because it is the lowest value and indicates the least linear association between the variables. The closer the absolute value of r is to 0, the weaker the correlation.
