Table 3 presents height projection equations for 

 general use. The natural logarithm transformation of age 

 was found to be the nonlinear transformation most con- 

 sistently producing low standard errors from the regres- 

 sion equation and large explained variances. In addition, 

 when residuals were examined, no curvilinear trends 

 were detected, and the error components appeared to 

 have equal variances over the range of the data. The 

 behavior of equations with natural logarithm terms dis- 

 pla5'ed a gradual decrease in height growth over time, 

 whereas other transformations were occasionally erratic. 



Some species comparisons that produced site index 

 regression equations were not used in height projection 

 regressions because sample size was inadequate or the 

 range in ages was limited. These equations have been 

 omitted. 



Comparative Study Results 



Despite this study's attempt to encompass a broader 

 range of environments and a more extensive geographi- 

 cal area than have previous studies of this nature, our 

 results (tables 2 and 3) are nonetheless comparable to 

 those of the preceding studies. Deitschman and Green's 

 (1965) regression equations predicting western white pine 

 site index from environmental variables, heights, and 

 ages of associated species explained 37 to 50 percent of 

 the variation in site index, with standard deviation 

 about regression ranging from 9.7 to 12.0 feet. For west- 

 ern white pine, our results (table 2) for these statistical 

 measures were, respectively, 34 to 76 percent and 7.1 to 

 9.2 feet. Their regression equations predicting tree 

 heights for other species from western white pine site 



Table 3.— Projecting age-specific heiglit for a given species from tlie site index of associated species 



Standard Site index 



List of 



List of species (Y) 



Number 









deviation 





Age range of 



range of 



observed 



whose height 



of paired 









about 



Coefficient of 



predicted 



observed 



species (X) 



is predicted 



observations 





Equations^ 





regression 



determination 



species 



species 















Feet 



R2 . 



Years 



Feet 



Douglas- 



Engelmann spruce 



22 



Y = 



— 295.68 + 1.43X — 0.1 2A -i- 



70.54Ln(A) 



7.49 



0.89 



50-156 



39-76 



fir 



Grand fir 



35 



Y = 



-114.41 +1.10X + 0.61A + 



22.31 Ln(A) 



12.71 



.71 



40-127 



59-100 





Lodgepole pine 



41 



Y = 



-287.69 -f1.02X-0.32A-h 



77.13Ln(A) 



5.65 



.82 



47-143 



39-86 





Ponderosa pine 



36 



Y = 



-252.34 -h0.81X-0.37A-(- 



74.44Ln(A) 



8.66 



.69 



42-200 



51-90 





Western larch 



50 



Y = 



-268.95 -F 0.91 X-0.25A-f 



74.75Ln(A) 



5.72 



.89 



40-155 



41-100 





Western white pine 



24 



Y = 



-447.29 -^1.18X-0.84A + 



124.29Ln(A) 



8.34 



88 



44-110 



39-98 





Subalpine fir 



14 



Y = 



- 1 78.87 -^1.25X-f0.14A + 



40.47Ln(A) 



6.33 



.89 



39-145 



39-78 



Engelmann 



Douglas-fir 



22 



Y = 



-173.81 -^0.94X-f0.03A-^ 



44.50Ln(A) 



5.92 



.93 



45-162 



41-90 



spruce 



Grand fir 



11 



Y = 



- 58.32 -^1.08X-f0.56A + 



7.76Ln(A) 



7.00 



.93 



44-127 



50-85 





Lodgepole pine 



39 



Y = 



- 153.92 -^0.99X-0.02A-h 



39.83Ln(A) 



7.12 



.82 



52-144 



38-90 





Mountain hemlock 



16 



Y = 



-164.30-F0.92X-(-0.01A-f 



40.47Ln(A) 



11.24 



.82 



41-163 



39-81 





Subalpine fir 



36 



Y = 



-229.69 -^ 1.02X-0.30A + 



62.18Ln(A) 



7.23 



.85 



40-145 



39-85 





Western larch 



25 



Y = 



-136.81 -^0.77X-f0.01A-h 



40.04Ln(A) 



6.80 



.91 



40-163 



48-90 



Grand fir 



Douglas-fir 



35 



Y = 



-298.76 -^0.63X-0.37A + 



90.08Ln(A) 



9.29 



.77 



44-159 



41-107 





Engelmann spruce 



11 



Y = 



-1 80.93 + 0.72X-^0.02A-h 



53.88Ln(A) 



11.13 



.79 



47-145 



33-70 





Western larch 



21 



Y = 



-1 16.80 0. 49X-^ 0.01 A 



43.15Ln(A) 



8.06 



.74 



50-167 



39-84 



Lodgepole 



Douglas-fir 



41 



Y = 



-232. 14-^1. 30X-0.17A + 



58.50Ln(A) 



6.63 



.84 



44-144 



45-78 



pine 



Engelmann spruce 



39 



Y = 



-294.86 -^1.33X-0.43A-F 



77.86Ln(A) 



8.14 



.86 



44-200 



38-78 





Mountain hemlock 



15 



Y = 



-147.85 + 1.02X-0.02A-^ 



35.91 Ln(A) 



5.20 



.85 



41-130 



38-61 





Subalpine fir 



26 



Y = 



-106. 02 + 1. 30X + 0.14A + 



22.24Ln(A) 



7.99 



.74 



39-145 



38-78 





Western larch 



34 



Y = 



-296.44 + 1. 64X-0.36A + 



73.48Ln(A) 



7.09 



.81 



53-147 



49-78 





Western white pine 



16 



Y = 



-149.83 + 1. 82X + 0.14A + 



28.51 Ln(A) 



6 16 



.82 



44-135 



45-69 



Mountain 



Engelmann spruce 



16 



Y = 



-238.78 + 1.03X-0.34A + 



67.93Ln(A) 



11.44 



.83 



44-146 



26-67 



hemlocl< 



Lodgepole pine 



15 



Y = 



-192. 92 + 1. 12X-0.29A + 



54.90Ln(A) 



6.16 



.75 



51-144 



38-61 





Subalpine fir 



24 



Y = 



-207. 57 + 1. 14X-0.26A + 



56.77Ln(A) 



7.15 



.85 



43-155 



26-67 



Ponderosa 



Douglas-fir 



36 



Y = 



-122. 57 + 0. 81X + 0.05A + 



35.18Ln(A) 



8.27 



.70 



48-178 



38-92 



pine 



Subalpine 



Engelmann spruce 



36 



Y = 



-209. 79 + 1. 03X-0.08A + 



54.31 Ln(A) 



8.03 



.88 



44-152 



28-87 



fir 



Lodgepole pine 



26 



Y = 



-233.38 + 0.82X-0.34A + 



66.77Ln(A) 



7.22 



.75 



51-147 



28-87 





Mountain hemlock 



24 



Y = 



-148. 02 + 1. 01X + 0.12A- 



33.76Ln(A) 



6.99 



.87 



41-147 



28-74 



Western 



Douglas-fir 



50 



Y = 



-331.12 + 1.47X-0.32A + 



80.77Ln{A) 



6.09 



.89 



44-162 



47-90 



larch 



Engelmann spruce 



25 



Y = 



- 460.1 + 1 .05X-0.82A + 1 27.25Ln(A) 



8.69 



.90 



44-162 



43-75 





Grand fir 



21 



Y = 



-413.43 + 1.12X-0.81A + 116. 53Ln(A) 



11.68 



.65 



40-107 



58-90 





Lodgepole pine 



34 



Y = 



-174.42 + 0.84X-0.07A + 



48.90Ln(A) 



4.84 



.86 



54-143 



43-83 





Western white pine 



27 



Y = 



-281.61 +1.79X-0.06A + 



6l.78Ln(A) 



7.55 



.92 



44-146 



47-86 



Western 



Douglas-fir 



24 



Y = 



-495. 87 + 1. 18X-0.84A + 



133.79Ln(A) 



10.66 



.77 



45-145 



39-97 



white 



Western larch 



27 



Y = 



-571. 46 + 1. 17X-1.03A + 



155.76Ln(A) 



6.41 



.92 



46-165 



39-97 



pine 



is the mean stand site index of the observed species; A is the age of the species whose height is being protected; Ln(A) is the natural logarithm of A. 



