Prediction from an integrated regression equation: a forestry application

Models to depict the tapering of a tree bole abound in the literature of forest science, and such models are widely used in forestry practice. One important use is the integration of a taper equation to predict the volume of the tree bole. The statistical properties of volume prediction from an integrated taper equation have been obscure. Based on the statistical characteristics of a taper model for the bole's cross-sectional area, we derive the first two moments of the volume predictor and the prediction error. Bias from the integration is nil. The importance of a reasonable model of the error structure is demonstrated.