To determine which correlation coefficient indicates a weak negative correlation, let's review the characteristics of correlation coefficients. A correlation coefficient, [tex]\(r\)[/tex], measures the strength and direction of a linear relationship between two variables. The value of [tex]\(r\)[/tex] 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
When the correlation coefficient is close to 0, it indicates a weak correlation, whether positive or negative. Specifically for a weak negative correlation, the value of [tex]\(r\)[/tex] will be close to 0 but negative.
Now, let's analyze each of the given options:
A. [tex]\( r = 0.5 \)[/tex]
- This indicates a moderate positive correlation, not a negative one.
B. [tex]\( r = -2.0 \)[/tex]
- This is not a valid correlation coefficient because correlation coefficients must be between -1 and 1.
C. [tex]\( r = -0.8 \)[/tex]
- This indicates a strong negative correlation because the value is much closer to -1.
D. [tex]\( r = -0.2 \)[/tex]
- This indicates a weak negative correlation because the value is close to 0 and negative.
Therefore, the correlation coefficient that indicates a weak negative correlation is:
D. [tex]\( r = -0.2 \)[/tex]
