MSE = mean squared error from weighted regression 



WT = regression weight (DSQH raised to the -1.5 

 power) 



n = desired number trees for confidence interval 

 computations 



H = leverage or xiJC'X) x\ as computed by S AS 

 (1985, p. 663) for weighted regression. 



DISCUSSION 



All equations were compared graphically (fig. 2) for simi- 

 larities and differences. The multiple-stem equations 

 showed less volume for given DSQH values than did single- 

 stem counterparts for all species groups. Of all the equa- 

 tions, single-stem mesquite appeared most different. How- 

 ever, extrapolation error may be the main cause, because 

 few mesquite trees in the data exceeded a DSQH of 2. 



Volume equations from this study (labeled Arizona) were 

 then compared to equations from Hualapai/Havasupai 

 Gabeled H & H) and Fort Apache/San Carlos (labeled 

 Apache) Indian Reservations (Chojnacky 1988; Chojnacky 

 and Ott 1986). Also compared were Olson's (1940) and 

 Andrew's (1988) mesquite equations and volume tables 

 given by Barger and Ffolliott (1972, tables 30, 31, and 32). 



The Barger and Ffolliott tables required "smoothing" of 

 the tabulated data for graphic comparison. A spline inter- 

 polation (SAS 1985, p. 70) was used to plot tabulated data 

 for Utah juniper (labeled B & F JUOS), alligator juniper 

 Gabeled B & F JUDE), pinyon Gabeled B & F), and oak 

 Gabeled B & F). 



Because some of the Barger and Ffolliott tables were 

 based on diameter at breast height (d.b.h.), compatible 

 graphic comparison required a conversion equation relat- 

 ing DRC to d.b.h. Data from single-stem trees measured 

 on the San Carlos Indian Reservation (Chojnacky 1988) 

 were used to develop the following equations: 



Juniper: DRC = 2.62 + 0.8314 (d.b.h.) + 0.0135 (d.b.h. 2 ) (6) 



n = 78, R 2 = 0.96 



Pinyon: DRC = 1.04 + 1.1181 (d.b.h.) - 0.0029 (d.b.h. 2 ) (7) 



n =102, R 2 = 0.94 



Oak: DRC = 0.41 + 1.3552 (d.b.h.) -0.0122 (d.b.h. 2 ) (8) 



n =76, # 2 = 0.92 



Comparison of the juniper equations for single-stem 

 trees showed large differences between Barger and 

 Ffolliott's (B & F) work and the rest (fig. 3). However, 

 these differences are probably due to volume definition 

 standards. All equations, except Barger and Ffolliott's, 

 included volume of all wood pieces at least 1-foot long and 

 larger than 1 .5 inches in diameter. Barger and Ffolliott's 

 definition resulted in less volume per tree by including 

 wood pieces with diameter standards similar to the others 

 but omitting all pieces less than 4 feet long. 



The pinyon volume equation from this study (Arizona) 

 was found similar to the Hualapai/Havasupai (H & H) 

 equation (fig. 4). Because Barger and Ffolliott's pinyon 

 volume table appeared to be in error, a modification was 

 made. In their table 31, diameter is defined at stump 

 height for all trees, but it appears the volumes best 

 correspond to d.b.h. for trees smaller than 10 inches and 



0123456789 10 

 DSQH (DRC squared times HT in 1000's) 



Figure 2 — Comparison of the seven woodland 

 volume equations from this study. 



Single-stem Juniper 



0123456789 10 



DSQH (DRC squared times HT in 1000's) 



Figure 3 — Comparison of this study's single-stem 

 juniper equation (Arizona) with other single-stem 

 juniper equations. 



5 



