residual sum of squares

The residual sum of squares is a measure of the fit of a model for a dataset. It is the sum of the squares of the residuals, that is the differences between the modelled value and the actual value in the dataset. Many statistical measures (including linear regression and the simple mean) and data analysis methods (including backpropagation) directly or indirectly minimise the residual sum of squares. When the underlying data is Normally distributed minimisjng residual sum of squares has particularly good properties and often gives the same result as a maximum likelihood estimator.

As an example, consider a set of pairs of values (x_i,y_i) where we want to see how well the line y=mx+c fits the data. This equation gives a modelled value mx_i+c for each data item; so the residual sum of squares is:
      Σ_i (y_i − (mx_i+c))²

Linear regression chooses m and c to mimimise this.