ADAPTING REGRESSION EQUATIONS TO MINIMIZE THE MEAN SQUARED ERROR OF PREDICTIONS MADE USING COVARIATE DATA FROM A GIS

Regression equations between a response variable and candidate explana tory variables are often estimated using a training set of data from c losely observed locations but are then applied using covariate data he ld in a GIS to predict the response variable at locations throughout a region. When the regression assumptions hold and the GIS data are fre e from error, this procedure gives unbiased estimates of the response variable and minimizes the prediction mean squared error. However, whe n the explanatory variables in the GIS are recorded with substantially greater errors than were present in the training set, this procedure does not minimize the prediction mean squared error. A theoretical arg ument leads to the proposal of an adaptation for regression equations to minimize the prediction mean squared error. The effectiveness of th is adaptation is demonstrated by a simulation study and by its applica tion to an equation for tree growth rate.