There are many statistical tools for model validation, but the primary tool for most process modeling applications is graphical residual analysis. Different types of plots of the residuals (see definition below) from a FITTED model provide information on the adequacy of different aspects of the model. Numerical methods for model validation, such as the R2 statistic, are also useful, but usually to a lesser degree than graphical methods.

Unfortunately, a high R2 (coefficient of determination) does not guarantee that the model fits the DATA well, because as Anscombe's quartet SHOWS, a high R2 can occur in the presence of misspecification of the functional form of a relationship or in the presence of outliers that DISTORT the true relationship.

One problem with the R2 as a measure of model validity is that it can always be increased by adding more variables into the model, except in the unlikely event that the additional variables are EXACTLY uncorrelated with the dependent variable in the data sample being used. To avoid such spurious increases of the R2, one can instead use the adjusted R2, which penalizes the use of additional explanatory variables in accordance with the amount that they are likely to spuriously increase the R2.