Overview#Residual Sum of Squares (RSS) (also called Sum of Squared Errors) is the sum of the squares of residuals (deviations predicted from actual empirical values of data).
Residual Sum of Squares is a measure of the discrepancy between the data and an estimation model. A small RSS indicates a tight fit of the model to the data.
Residual Sum of Squares is used as an optimality criterion in parameter selection and model selection.
In general, total sum of squares = explained sum of squares + residual sum of squares. For a proof of this in the multivariate Ordinary Least Squares (OLS) case, see partitioning in the general OLS model.