 

In these results, the relationships between rating and concentration, ratio, and temperature are statistically significant because the pvalues for these terms are less than the significance level of 0.05. The relationship between rating and time is not statistically significant at the significance level of 0.05.
Use S to assess how well the model describes the response. Use S instead of the R^{2} statistics to compare the fit of models that have no constant.
S is measured in the units of the response variable and represents the standard deviation of 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.
R^{2} is the percentage of variation in the response that is explained by the model. The higher the R^{2} value, the better the model fits your data. R^{2} is always between 0% and 100%.
R^{2} always increases when you add additional predictors to a model. For example, the best fivepredictor model will always have an R^{2} that is at least as high the best fourpredictor model. Therefore, R^{2} is most useful when you compare models of the same size.
Use adjusted R^{2} when you want to compare models that have different numbers of predictors. R^{2} always increases when you add a predictor to the model, even when there is no real improvement to the model. The adjusted R^{2} value incorporates the number of predictors in the model to help you choose the correct model.
Use predicted R^{2} to determine how well your model predicts the response for new observations. Models that have larger predicted R^{2} values have better predictive ability.
A predicted R^{2} that is substantially less than R^{2} may indicate that the model is overfit. An overfit model occurs when you add terms for effects that are not important in the population, although they may appear important in the sample data. The model becomes tailored to the sample data and therefore, may not be useful for making predictions about the population.
Predicted R^{2} can also be more useful than adjusted R^{2} for comparing models because it is calculated with observations that are not included in the model calculation.
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.
 

In these results, the model explains 72.92% of the variation in the wrinkle resistance rating of the cloth samples. For these data, the R^{2} value indicates the model provides a good fit to the data. If additional models are fit with different predictors, use the adjusted R^{2} values and the predicted R^{2} values to compare how well the models fit the data.
Use the residual plots to help you determine whether the model is adequate and meets the assumptions of the analysis. If the assumptions are not met, the model may not fit the data well and you should use caution when you interpret the results.
Use the residuals versus fits plot to verify the assumption that the residuals are randomly distributed and have constant variance. Ideally, the points should fall randomly on both sides of 0, with no recognizable patterns in the points.
Pattern  What the pattern may indicate 

Fanning or uneven spreading of residuals across fitted values  Nonconstant variance 
Curvilinear  A missing higherorder term 
A point that is far away from zero  An outlier 
A point that is far away from the other points in the xdirection  An influential point 
In this residuals versus fits plot, the data do not appear to be randomly distributed about zero. There appear to be clusters of points that may represent different groups in the data. Investigate the groups to determine their cause.
In this residuals versus order plot, the residuals do not appear to be randomly distributed about zero. The residuals appear to systematically decrease as the observation order increases. You should investigate the trend to determine the cause.
For more information on how to handle patterns in the residual plots, go to Interpret all statistics and graphs for Multiple Regression and click the name of the residual plot in the list at the top of the page.
Use the normal probability plot of residuals to verify the assumption that the residuals are normally distributed. The normal probability plot of the residuals should approximately follow a straight line.
Pattern  What the pattern may indicate 

Not a straight line  Nonnormality 
A point that is far away from the line  An outlier 
Changing slope  An unidentified variable 
In this normal probability plot, the points generally follow a straight line. There is no evidence of nonnormality, outliers, or unidentified variables.