RESULTS 



Final equations for predicting the various types of tree volume follow, along with 

 an explanation of how to apply them. Details concerning the methodology can be found 

 in the appendixes. 



A statistic that will be presented whenever possible is the relative mean-squared 

 residuals (RMSQR) of the final equation. RMSQR is the quotient of mean-squared resid- 

 uals divided by the variance of the dependent variable and, as such, is an index of fit 

 similar to the coefficient of determination (R^) . In the case of Rf-ISQR, however, 

 perfect fit would result in a value of 0. A fit that would not reduce the squared 

 residuals below the value around the mean would result in a value of 1, and a value 

 greater than 1 would indicate that the model has increased variability. The advantage 

 of RMSQR over R^ is that only the former will reflect the loss in degrees of freedom 

 that results from adding another independent variable; therefore, it serves as a better 

 measure for comparing equations of different numbers of independent variables to see if 

 the added variable (s) reduced variance about the regression model. 



The standard error of the estimate is not reported here because the methodology 

 used precluded the calculation of a meaningful statistic. 



Gross volioves . --The appropriate equations for computing gross volume are chosen by 

 the user on a tree-by-tree basis. If the tree is unforked, then the unforked tree vol- 

 ume equation is chosen based on the sp-NF combination of the tree. If the tree is 

 forked, the unforked tree volume is first computed for the tree and then corrected for 

 forking by the appropriate forked tree equation for the sp-NF combination of the tree. 

 These seemingly trivial facts are brought out because the choice of which net volume 

 equation to use is not on a tree-by-tree basis, but instead is determined for an entire 

 data set. 



A tree is considered forked if a fork of any severity occurs between breast height 

 and the tip of the tree. For most of the species, two equations are given. The first 

 equation utilizes tree size information only, while the second equation incorporates 

 two independent variables that relate to the severity of forking. In all cases, the 

 second equation has a lower RMSQR value. The position of the first fork variable, P, 

 is defined as the height to the first fork divided by total tree height. The number of 

 tips variable, T, can be counted directly or computed by adding 1 to the number of 

 forks. All forks between breast height and the tip of the tree should be counted 

 regardless of their severity. 



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