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To determine whether each correlation coefficient shows a strong, moderate, or weak correlation, we can follow these guidelines:
1. Strong Correlation: If the absolute value of the correlation coefficient ([tex]\( |r| \)[/tex]) is greater than 0.7.
2. Moderate Correlation: If the absolute value of the correlation coefficient ([tex]\( |r| \)[/tex]) is between 0.3 and 0.7.
3. Weak Correlation: If the absolute value of the correlation coefficient ([tex]\( |r| \)[/tex]) is less than or equal to 0.3.
Now, let's analyze each given correlation coefficient step-by-step.
### 1. Correlation Coefficient [tex]\( r = -0.91 \)[/tex]
- The absolute value is [tex]\( |-0.91| = 0.91 \)[/tex].
- Since 0.91 is greater than 0.7, this indicates a Strong Correlation.
### 2. Correlation Coefficient [tex]\( r = 0.82 \)[/tex]
- The absolute value is [tex]\( |0.82| = 0.82 \)[/tex].
- Since 0.82 is greater than 0.7, this indicates a Strong Correlation.
### 3. Correlation Coefficient [tex]\( r = -0.49 \)[/tex]
- The absolute value is [tex]\( |-0.49| = 0.49 \)[/tex].
- Since 0.49 is between 0.3 and 0.7, this indicates a Moderate Correlation.
### 4. Correlation Coefficient [tex]\( r = 0.26 \)[/tex]
- The absolute value is [tex]\( |0.26| = 0.26 \)[/tex].
- Since 0.26 is less than or equal to 0.3, this indicates a Weak Correlation.
### 5. Correlation Coefficient [tex]\( r = 0.54 \)[/tex]
- The absolute value is [tex]\( |0.54| = 0.54 \)[/tex].
- Since 0.54 is between 0.3 and 0.7, this indicates a Moderate Correlation.
### 6. Correlation Coefficient [tex]\( r = -0.18 \)[/tex]
- The absolute value is [tex]\( |-0.18| = 0.18 \)[/tex].
- Since 0.18 is less than or equal to 0.3, this indicates a Weak Correlation.
In summary:
- [tex]\( r = -0.91 \)[/tex]: Strong Correlation
- [tex]\( r = 0.82 \)[/tex]: Strong Correlation
- [tex]\( r = -0.49 \)[/tex]: Moderate Correlation
- [tex]\( r = 0.26 \)[/tex]: Weak Correlation
- [tex]\( r = 0.54 \)[/tex]: Moderate Correlation
- [tex]\( r = -0.18 \)[/tex]: Weak Correlation
These results provide a detailed categorization of the given correlation coefficients based on their strengths.
1. Strong Correlation: If the absolute value of the correlation coefficient ([tex]\( |r| \)[/tex]) is greater than 0.7.
2. Moderate Correlation: If the absolute value of the correlation coefficient ([tex]\( |r| \)[/tex]) is between 0.3 and 0.7.
3. Weak Correlation: If the absolute value of the correlation coefficient ([tex]\( |r| \)[/tex]) is less than or equal to 0.3.
Now, let's analyze each given correlation coefficient step-by-step.
### 1. Correlation Coefficient [tex]\( r = -0.91 \)[/tex]
- The absolute value is [tex]\( |-0.91| = 0.91 \)[/tex].
- Since 0.91 is greater than 0.7, this indicates a Strong Correlation.
### 2. Correlation Coefficient [tex]\( r = 0.82 \)[/tex]
- The absolute value is [tex]\( |0.82| = 0.82 \)[/tex].
- Since 0.82 is greater than 0.7, this indicates a Strong Correlation.
### 3. Correlation Coefficient [tex]\( r = -0.49 \)[/tex]
- The absolute value is [tex]\( |-0.49| = 0.49 \)[/tex].
- Since 0.49 is between 0.3 and 0.7, this indicates a Moderate Correlation.
### 4. Correlation Coefficient [tex]\( r = 0.26 \)[/tex]
- The absolute value is [tex]\( |0.26| = 0.26 \)[/tex].
- Since 0.26 is less than or equal to 0.3, this indicates a Weak Correlation.
### 5. Correlation Coefficient [tex]\( r = 0.54 \)[/tex]
- The absolute value is [tex]\( |0.54| = 0.54 \)[/tex].
- Since 0.54 is between 0.3 and 0.7, this indicates a Moderate Correlation.
### 6. Correlation Coefficient [tex]\( r = -0.18 \)[/tex]
- The absolute value is [tex]\( |-0.18| = 0.18 \)[/tex].
- Since 0.18 is less than or equal to 0.3, this indicates a Weak Correlation.
In summary:
- [tex]\( r = -0.91 \)[/tex]: Strong Correlation
- [tex]\( r = 0.82 \)[/tex]: Strong Correlation
- [tex]\( r = -0.49 \)[/tex]: Moderate Correlation
- [tex]\( r = 0.26 \)[/tex]: Weak Correlation
- [tex]\( r = 0.54 \)[/tex]: Moderate Correlation
- [tex]\( r = -0.18 \)[/tex]: Weak Correlation
These results provide a detailed categorization of the given correlation coefficients based on their strengths.
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