Identifying and Evaluating the Components of Non-Measurement Error in the Application of Standard Volume Equations

We consider the prediction of stem volume of a tree by means of simple linear regression wherein the explanatory variable is D2H; D is the bole diameter measured outside bark at breast height and H is the total height of the tree. Given a fitted equation, a tree whose volume is to be predicted must be measured for D and H. Two sources of error account for the deviation of predicted tree volume from V' the actual tree volume, i.e. (1) error in the estimated coefficients of the volume function and (2) variation of V around its expected value conditional upon D2H. Owing to the greater difficulty and expense of measuring H in forest conditions, a standard practice is to predict its value from a regression on diameter. Consequently the prediction of V, V say, is subject to additional sources of error due to (1) the error in the estimated coefficients of the height-diameter function and (2) the variation of H around its expected value conditional on D. An empirical study of a population of more than 14 000 loblolly pine trees was undertaken with the objective of quantifying the average proportion of overall prediction error which was due to these components. The exact mean square error of the vector of predicted volume, V, is also derived.