Economics · Ch 12 — Introduction to Statistical Methods and Econometrics
Correlation
Correlation
Correlation measures the degree and direction of the linear relationship between two variables — for instance, between income and expenditure, or between rainfall and agricultural output. Correlation can be:
- Positive — both variables move in the same direction (e.g. income rises, expenditure rises).
- Negative — the variables move in opposite directions (e.g. price rises, quantity demanded falls).
- Zero (no correlation) — the variables show no consistent linear relationship at all.
| Type of correlation | What a scatter diagram of the data would show |
|---|---|
| Positive | Points cluster around a line sloping upward from left to right |
| Negative | Points cluster around a line sloping downward from left to right |
| Zero (no correlation) | Points form a shapeless cloud with no visible upward or downward trend |
The most widely used measure is Karl Pearson's Coefficient of Correlation (r):
r always lies between −1 and +1. A value close to +1 indicates strong positive correlation, close to −1 indicates strong negative correlation, and a value near 0 indicates little or no linear relationship. …
A number between −1 and +1 measuring the strength and direction of the linear relationship between two variables, computed as the ratio of their covariance-type sum to the geometric mean of …