1. Range of Values
The correlation coefficient (often represented as "r") ranges from -1 to +1.
- A value of +1 indicates a perfect positive linear relationship between two variables.
- A value of -1 indicates a perfect negative linear relationship.
- A value of 0 signifies no linear relationship at all.
2. Direction of Relationship
The sign of the correlation coefficient indicates the direction of the relationship between the variables.
- A positive value means that as one variable increases, the other variable also tends to increase.
- Conversely, a negative value indicates that as one variable increases, the other variable tends to decrease.
3. Strength of Relationship
The absolute value of the correlation coefficient reflects the strength of the linear relationship.
- Values close to +1 or -1 indicate a strong relationship.
- Values near 0 suggest a weak relationship.
- For example, an r value of 0.9 indicates a strong positive correlation, while an r value of -0.2 indicates a weak negative correlation.
4. Sensitivity to Outliers
The correlation coefficient is sensitive to outliers, which can significantly affect its value.
- A single extreme value can distort the correlation, making it appear stronger or weaker than it actually is.
- It's crucial to analyze data for outliers before relying on the correlation coefficient to draw conclusions.
Understanding these properties helps in effectively interpreting the correlation coefficient and its implications for data analysis in commerce.