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 by matrix, where 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.