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Residual standard error of a return line

The descriptive residual standard-error calculation is √(SSE/(n−2)) for this two-parameter line.

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Count the fitted coefficients

The straight-line model fits an intercept and slope, so p=2 parameters. With n supplied pairs, the usual residual variance estimate uses n−p rather than the sample variance divisor for returns around their own mean.

Restore the response-return scale

s=∑i(yi−y^i)2n−2s=\sqrt{\frac{\sum_i(y_i-\widehat{y}_i)^2}{n-2}}

At least three pairs are required for a positive residual denominator.

Calculate the original five-period value

SSE is 1.2 percentage points squared and n−2=3. The square root of 0.4 gives approximately 0.632456 percentage points per supplied period.

Keep the population interpretation qualified

The computed value describes this fitted record. Interpreting it as an error-distribution scale or using it for uncertainty intervals needs the model’s inferential assumptions. It is not the standard error of beta itself or tracking error against a unit benchmark holding.

Further references