- Interpret a correlation coefficient.
- Describe the strength of a linear relationship.
- Relate correlation coefficients to scatter plots.
Goal: formalize the concept of the strength of a linear relationship.
The correlation (or correlation coefficient) \(R\) between two variables describes the strength of their linear relationship.
\[R = \frac{1}{n-1}\sum_{i=1}^n\left(\frac{x_i - \bar{x}}{s_x}\times\frac{y_i - \bar{y}}{s_y}\right)\]
This is a pretty involved formula! We’ll let a computer handle this one.
Correlations
Note: the sign of the correlation will match the sign of the slope!
When two variables are highly correlated (\(R\) close to \(-1\) or \(1\))
That is, correlation does not imply causation.
A final note:
Section 3.2 Exercise 1