Residual sum of squares

In statistics, the residual sum of squares (RSS) is the sum of squares of residuals,

${\displaystyle RSS=\sum _{i=1}^{n}(y_{i}-f(x_{i}))^{2}.}$

In a standard regression model ${\displaystyle y_{i}=a+bx_{i}+\varepsilon _{i}\,}$, where a and b are coefficients, y and x are the regressand and the regressor, respectively, and ε is the error term. The sum of squares of residuals is the sum of squares of estimates of ε_i, that is

${\displaystyle RSS=\sum _{i=1}^{n}(y_{i}-(a+bx_{i}))^{2}.}$

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