S represents the standard deviation of the distance between the data values and the fitted values. S is measured in the units of the response. Because R2 is meaningless outside the linear model context, S is an important measure of the goodness-of-fit for a nonlinear model. Because S is expressed in the same units as the response variable, S is generally more intuitive to interpret than the Final SEE.
Use S to assess how well the model describes the response. S is measured in the units of the response variable and represents how far the data values fall from the fitted values. The lower the value of S, the better the model describes the response. However, a low S value by itself does not indicate that the model meets the model assumptions. You should check the residual plots to verify the assumptions.
For example, you work for a potato chip company that examines the factors that affect the percentage of crumbled potato chips per container. You reduce the model to the significant predictors, and S is calculated as 1.79. This result indicates that the standard deviation of the data points around the fitted values is 1.79. If you are comparing models, values that are lower than 1.79 indicate a better fit, and higher values indicate a worse fit.