A linear program to detect extrapolation in predicting new responses of a multiple linear regression model

A region of interpolation is defined as the smallest convex set containing all original n data points used to build a regression model. In this paper, we present a linear program with n variables and (k + 1) constraints whose feasibility exactly determines whether or not a given new point, at which a response is predicted, is an extrapolation. Here k is the number of regressor variables used to build the regression model. This method has an advantage over the other methods used in the literature for the determination of extrapolation, in that, whenever a new point is indeed an extrapolation point, the developed method identifies it as an extrapolation, while the other methods may fail to identify it as an extrapolation point.