S is the estimated standard deviation of the error term. The lower the value of S, the better the conditional fitted equation describes the response at the selected factor settings. However, an S value by itself doesn't completely describe model adequacy. Also examine the key results from other tables and the residual plots.
R^{2} is the percentage of variation in the response that is explained by the model. It is calculated as 1 minus the ratio of the error sum of squares (which is the variation that is not explained by model) to the total sum of squares (which is the total variation in the model).
Use R^{2} to determine how well the model fits your data. The higher the R^{2} value, the more variation in the response values is explained by the model. R^{2} is always between 0% and 100%.
Assuming the models have the same covariance structure, R^{2} increases when you add additional fixed factors or covariates. Therefore, R^{2} is most useful when you compare models of the same size.
Small samples do not provide a precise estimate of the strength of the relationship between the response and predictors. If you need R^{2} to be more precise, you should use a larger sample (typically, 40 or more).
R^{2} is just one measure of how well the model fits the data. Even when a model has a high R^{2}, you should check the residual plots to verify that the model meets the model assumptions.
Use adjusted R^{2} when you want to compare models with the same covariance structure but have a different number of fixed factors and covariates. Assuming the models have the same covariance structure, R^{2} increases when you add additional fixed factors or covariates. The adjusted R^{2} value incorporates the number of fixed factors and covariates in the model to help you choose the correct model.