For certain designs with replicates at the levels of the predictor variables, the residual sum of squares can be further partitioned into meaningful parts which are relevant for testing hypotheses. Specifically, the residual sums of squares can be partitioned into lack-of-fit and pure-error components. This involves determining the part of the residual sum of squares that can be predicted by including additional terms for the predictor variables in the model (for example, higher-order polynomial or interaction terms), and the part of the residual sum of squares that cannot be predicted by any additional terms (i.e., the sum of squares for pure error). A test of lack-of-fit for the model without the additional terms can then be performed, using the mean square pure error as the error term. This provides a more sensitive test of model fit, because the effects of the additional higher-order terms is removed from the error.

See also: pure error, design matrix; or the General Linear Model (GLM), General Regression Models (GRM), or Experimental Design methods of analysis.