The approach in SVM-Classification was extended to regression by defining a new criterion containing an acceptable error of a regression model ε. Points outside this interval are penalized with a linear loss function with the loss coefficient C > 0. The model should then minimize

The coefficient vector w corresponds to regression parameters of a linear model, b is the absolute term. The user-tuned parameter ε is the half-width of the band in which errors are acceptable, ε is the maximal acceptable absolute error. This criterion has some “robustness” in it since it forces the model to “squeeze” as much data as possible into a narrow band f(x) +- ε around the model and discard the data that do not fit in the band. This makes SVM regression a suitable alternative to robust regression methods in case of heavily contaminated data. The criterion can be rewritten using parameter ν (0<ν<1), corresponding to the probability of a given point to lie inside the acceptable region f(x) +- ε. The resulting criterion can be written as a constrained minimization with respect to w, b, ξ, ξ*, ε:
As with any regression, the regression model can be used to predict expected value of the independent (response) variable for given values of the independent (predictor) variables. The following plot shows the effect on the parameter ε on the regression model in a univariate case and the effect of robustness.