To determine which correlation coefficient indicates a weak negative correlation, let's analyze the options:
1. Understanding Correlation Coefficients:
- Correlation coefficients (denoted by [tex]\( r \)[/tex]) can vary between -1 and 1.
- A correlation of [tex]\( r = 1 \)[/tex] indicates a perfect positive linear relationship.
- A correlation of [tex]\( r = -1 \)[/tex] indicates a perfect negative linear relationship.
- A correlation of [tex]\( r = 0 \)[/tex] indicates no linear relationship.
2. Categories of Correlation Strength:
- Strong Correlation: [tex]\( |r| \)[/tex] is close to 1 (for example, [tex]\( r > 0.7 \)[/tex] or [tex]\( r < -0.7 \)[/tex]).
- Moderate Correlation: [tex]\( |r| \)[/tex] is around 0.4 to 0.7.
- Weak Correlation: [tex]\( |r| \)[/tex] is less than 0.3.
3. Analyzing the Options:
- Option A: [tex]\( r = 0.5 \)[/tex]
- This indicates a moderate positive correlation.
- Option B: [tex]\( r = -0.2 \)[/tex]
- This indicates a weak negative correlation (since [tex]\( |r| < 0.3 \)[/tex] and the sign is negative).
- Option C: [tex]\( r = -2.0 \)[/tex]
- This is not a valid correlation coefficient since correlation coefficients must be between -1 and 1.
- Option D: [tex]\( r = -0.8 \)[/tex]
- This indicates a strong negative correlation (since [tex]\( |r| > 0.7 \)[/tex] and sign is negative).
4. Conclusion:
- The correlation coefficient that indicates a weak negative correlation is [tex]\( r = -0.2 \)[/tex].
Therefore, the correct answer is:
B. [tex]\( r = -0.2 \)[/tex]
