The measure of a linear relationship is the correlation coefficient, often denoted as r.
This numerical value quantifies both the strength and direction of a linear association between two variables. The correlation coefficient ranges from -1 to +1, where:
- +1 indicates a perfect positive linear relationship: As one variable increases, the other increases proportionally.
- -1 indicates a perfect negative linear relationship: As one variable increases, the other decreases proportionally.
- 0 indicates no linear relationship: There is no apparent linear trend between the two variables.
The closer r is to +1 or -1, the stronger the linear relationship. Values closer to 0 suggest a weak or non-existent linear relationship.
Here's a breakdown:
| Correlation Coefficient (r) | Strength of Linear Relationship | Direction of Relationship |
|---|---|---|
| -1.0 | Perfect Negative | Negative |
| -0.7 to -0.9 | Strong Negative | Negative |
| -0.5 to -0.7 | Moderate Negative | Negative |
| -0.3 to -0.5 | Weak Negative | Negative |
| 0 | No Linear Relationship | None |
| 0.3 to 0.5 | Weak Positive | Positive |
| 0.5 to 0.7 | Moderate Positive | Positive |
| 0.7 to 0.9 | Strong Positive | Positive |
| 1.0 | Perfect Positive | Positive |
It's crucial to remember that correlation does not imply causation. Even if two variables have a strong correlation, it does not necessarily mean that one variable causes the other. There could be lurking variables influencing both. Also, the correlation coefficient only measures the linear relationship. There might be a strong non-linear relationship between variables that would not be captured by r.
