S, R and adjusted R are measures of how well the model fits the data. These values can help you select the model with the best fit.

·    S is measured in the units of the response variable and represents the standard distance that data values fall from the regression line. For a given study, the better the equation predicts the response, the lower S is.

·    R (R-Sq) describes the amount of variation in the observed response values that is explained by the predictor(s). R always increases with additional predictors. For example, the best five-predictor model will always have a higher R than the best four-predictor model. Therefore, R is most useful when comparing models of the same size.

·    Adjusted R is a modified R that has been adjusted for the number of terms in the model. If you include unnecessary terms, R can be artificially high. Unlike R, adjusted R may get smaller when you add terms to the model. Use adjusted R to compare models with different numbers of predictors.

·    R (pred) indicates how well the model predicts responses for new observations. Predicted R can prevent overfitting the model. This statistic is more useful than adjusted R for comparing models because it is calculated with observations not included in the model calculation. Larger values of predicted R suggest models of greater predictive ability.

For the paint data, R is 47.44% and adjusted R equals 39.56%. If you are comparing different paint hardness models, then you generally look for models that minimize S and maximize the three R values.