Variance Explained in Correlation (1 of 1)

The proportion of variance in variable Y explained by variable X is defined as the ratio of the explained variation in Y to the total variation. The section on partitioning the variance in prediction shows that:

r² = SSY'/SSY

where r is the correlation between the two variables, SSY' is the sum of squares explained, and SSY is the total sum of squares Y. Therefore, r² is a measure of the proportion of variance explained.

In multiple regression, the best measure of the proportion of variance explained by the predictor variables is the adjusted R² (corrected for shrinkage).