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R-squared

The share of a variable's variance explained by the model, from 0 to 1. High R-squared on financial return data usually means you have made a mistake.

Real return-predicting regressions in liquid markets have R-squared values around 0.01 or lower, and those can still be very profitable, because a tiny predictable component applied thousands of times compounds. An R-squared of 0.85 on next-day returns means data-leakage, not genius.

R-squared also rises mechanically when you add inputs, regardless of whether they help. Adjusted R-squared penalises the extra degrees-of-freedom and is the right one to compare models of different sizes.

The number says nothing about whether a relationship is causal or stable. Two unrelated trending series can produce an R-squared above 0.9, which is the spurious regression trap that stationarity exists to prevent.

Related: ols-regression, residuals, overfitting, stationarity

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