= Adjusted coefficient of determination
{title2=$\overline R^2$}
= Adjusted R-squared
{synonym}
In a <normal linear model> with an intercept, $n$ observations and $p$ independent mean coefficients, adjusted $R^2$ is
$$
\overline R^2=1-\frac{\operatorname{RSS}/(n-p)}{\operatorname{SST}/(n-1)}.
$$
It compares the residual <variance> estimate with the unmodelled <sample variance>, adjusting the raw <coefficient of determination> for fitted dimension. It can be negative and is not guaranteed to increase when another regressor is added. In penalized regression a related convention uses the fit's <effective degrees of freedom> instead of $p$; the precise smoothing-software <variance> convention should be specified.
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