To determine which correlation coefficient represents a moderate negative correlation, we need to understand the classification of correlation coefficients. Here's a brief overview:
- A correlation coefficient (r) measures the strength and direction of the linear relationship between two variables.
- The value of r ranges from -1 to 1.
- [tex]\( r = 1 \)[/tex] indicates a perfect positive correlation.
- [tex]\( r = -1 \)[/tex] indicates a perfect negative correlation.
- [tex]\( r = 0 \)[/tex] indicates no correlation.
For negative correlations, we categorize them as follows:
- Weak negative correlation: [tex]\( -0.3 < r < 0 \)[/tex]
- Moderate negative correlation: [tex]\( -0.7 \leq r \leq -0.5 \)[/tex]
- Strong negative correlation: [tex]\( -1 \leq r < -0.7 \)[/tex]
Let's examine the given correlation coefficients:
- [tex]\( r = -0.04 \)[/tex]: This value is close to 0, indicating almost no negative correlation.
- [tex]\( r = -0.24 \)[/tex]: This value is more negative but still falls under a weak negative correlation.
- [tex]\( r = -0.64 \)[/tex]: This value is within the range [tex]\(-0.7 \leq r \leq -0.5\)[/tex], which indicates a moderate negative correlation.
- [tex]\( r = -0.94 \)[/tex]: This value is lower than -0.7, indicating a strong negative correlation.
Thus, the correlation coefficient that represents a moderate negative correlation is:
[tex]\[
r = -0.64
\][/tex]
