Abstract
Several error structures for weighted regression equations used for predicting volume were examined for 2 large data sets of felled and standing loblolly pine trees (
Pinus taeda L.). The generally accepted model with variance of error proportional to the value of the covariate squared ( D
2H = diameter squared times height or D
2 = diameter squared) remains the best. Although D
2H is a better covariate than D
2, we found no significant difference between them when testing model accuracy for felled trees, but there were significant differences for standing trees. When we predicted the total volume of a population using equations based on felled tree data, assuming known frequencies for diameter classes and using D
2H as the covariate, we obtained essentially the same estimate as that predicted using D
2 (0.1 % difference). Using the conventional approach of D
2H for all trees (standing and felled) yielded an estimate of volume of 5.6% less than using the equation with D
2H for felled trees only. Trees are more accurately measured for volume when felled, and total heights are often not measured accurately on standing trees. Therefore, we recommend that volume equations be based on felled tree data only and that when they are intended to be applied to standing trees, D
2 be used as the covariate in prediction.
Keywords
best volume equations,
felled trees,
standing trees,
measured heights,
basal area
Citation
Schreuder, Hans T.; Williams, Michael S. 1998. Weighted linear regression using D2H and D2 as the independent variables. Res. Pap. RMRS-RP-6. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station. 10 p.