When no iterative reweighting is done, the “Smoothing Matrix” denoted by defines the linear relationship between the fitted and observed dependent variable values of a loess model. You can obtain the predicted values of a loess fit from the observed values via

where is the vector of observed values and is the corresponding vector of predicted values of the dependent variable. Note that is an n by n matrix, where n is the number of observations in the analysis. PROC LOESS does not explicitly form if the DFMETHOD=EXACT option is not explicitly or implicitly selected.