Coefficient of Determination (R-Squared)

R-squared shows how well a regression line fits the data. An R-squared of 0 means the model explains none of the variation; an R-squared of 1 means it explains all of it.

For simple linear regression, R-squared equals the square of the correlation coefficient. If two funds' returns have a correlation of about 0.92, the R-squared is about 0.85, meaning about 85% of the variation in one fund's returns can be explained by the other's.

In investing, R-squared is often used to show how closely a fund follows its benchmark. A fund with an R-squared of 0.95 against an index moves very much in line with that index. A low R-squared suggests the fund's performance is driven by other factors.

A high R-squared does not mean a model is correct or useful for prediction. It can be high by coincidence, especially with trending data, and adding more variables to a model always increases R-squared, even if they add no real explanatory power. Adjusted R-squared corrects for this by penalising extra variables. A low R-squared can still be meaningful in fields where outcomes are naturally noisy, such as share price movements.