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In statistics, an explained sum of squares (ESS) is the sum of squared predicted values in a standard regression model (for example ), where is the response variable, is the explanatory variable, and are coefficients, indexes the observations from to , and is the error term.

If and are the estimated coefficients, then

is the predicted variable. The ESS is the sum of the squares of the differences of the predicted values and the grand mean:

In general: total sum of squares = explained sum of squares + residual sum of squares.