Table 4 — The average moisture content of the total tree and of the various size fractions 



Diameter Sample Total Size fractions (cm) 



Species class trees tree > 7.6 2.5 to 7.6 0.64 to 2.5 < 0.64 Foliage Deadwood 



cm No. Percent green weight 



Pinyon 



> -in 



A 



4 



A c; 



40 







en 

 DU 



4 l 



A Q 



4o 



1 o 





10-20 



19 



47 



44 



47 



52 



51 



50 



12 





20-30 



17 



45 



43 



45 



49 



50 



50 



13 





30-40 



17 



43 



44 



42 



47 



50 



50 



13 





> 40 



19 



42 



43 



41 



47 



51 



51 



11 



Juniper 



10-20 



7 



47 



50 



51 



53 



42 



42 



10 





20-30 



8 



46 



48 



48 



49 



43 



43 



12 





30-40 



7 



46 



47 



49 



49 



45 



45 



12 





>40 



11 



45 



49 



49 



49 



43 



43 



12 



Regression Analysis 



The relationships between tree variables and ovendry 

 weights were evaluated by screening all possible combina- 

 tions of variables and weights using forward and reverse 

 stepwise multiple regression techniques. Since all the 

 relationships were nonlinear, logarithmic transformations 

 (base e) were used throughout the analysis. The improve- 

 ment in the standard error of the estimate and the 

 sequential and partial F-test critera were used to select 

 the number of tree variables to be included in the final 

 prediction equations (Draper and Smith 1966). For most 

 weight categories, the final equations have two tree 

 variables. The addition of more variables did not signifi- 

 cantly improve the prediction equations and also would not 

 lend itself to the construction of weight tables. 



Although the use of logarithmic equations for predicting 

 weights is acceptable, the bias encountered when the 

 logarithmic estimates are converted back to original units 

 has been questioned. Baskerville (1972) suggested the use 

 of a correction factor for this downward bias. However, 

 Magwick and Satoo (1975) pointed out that the bias using 

 logarithmic equations is of minor importance compared 

 with the variation among samples. Although Brown 

 (1978) applied correction factors for the logarithmic trans- 

 formation bias to most of his crown weight equations, he 

 omitted the correction factor in some cases because it con- 

 tributed more bias than it eliminated. In this study, the bias 

 encountered was low and the use of a correction factor 

 introduced greater bias. Thus, a correction factor was not 

 applied to the logarithmic estimates. 



In order to express the precision of the predictive 

 equations, coefficient of determination (Ft 2 ), standard 

 error of the estimate, percent mean error, and the percent 

 bias are reported for each equation. For predictive 

 purposes, most investigators presently use some measure 

 of the actual deviation between the predicted and observed 

 weights (Brown 1978; Faurot 1977; Whittaker and 



Woodwell 1968). The percent mean error is an indication 

 of the average variation of the sample. Faurot (1977) 

 states that expressing the deviation in percentage over- 

 comes the inherent problem of heterogeneous variance. 

 The percent mean error is analogous to the standard 

 deviation of the regression and is also similar to the 

 estimate of the relative error reported by Whittaker 

 and Woodwell (1968). Percent mean error is obtained as 

 follows (Faurot 1977): 

 n 



[i = 1 ({ Y.-Y. [100/K) 2 ln - k - 1 V 2 

 Percent bias is obtained as follows (Faurot 1977): 



100(2 Y. - ZYjj/XY. 



where 



Y- = observed value 



/. = arithmetic estimated value 



n = number of observations 



k - number of independent variables. 



Equations 



The prediction equations for the various size fractions 

 are presented in table 5 for pinyon and in table6for juniper. 

 All equations are logarithmic (base e) and follow the model: 



LnW = f(LnH, LnDSH or LnDBH, LnC, LnD'LnC, LnS) 



where 



W = weight, kilograms 



H = height, meters 

 DSH = diameter at stump height (30 cm), centimeters 

 DBH = diameter at breast height, centimeters 



C = average crown diameter, meters 



S = number of stems at breast height. 



5 



