Using the value of h, the resulting regression coefficients of Y were modeled as 

 functions of top diameter to obtain the final equations of Y^ in the model: 



Y 



FC = hil.O - e ^) (30) 



m 



where 



FC = Predicted fraction cull in merchantable cubic foot volume given the tree is 

 unsound 



Y = A function of the tree's attributes and top diameter 

 h = An intermediate constant value. 



Model (30) was then fitted to the data set incorporating all top diameters with least 

 squares regression to obtain a slope correction to adjust the model for possible log 

 bias, and this slope correction was incorporated with k to give the final value, h , in 

 the standard form: 



Y 



FC = ;z (1.0 - e ^) (31) 



m m 



where 



h = A final constant value. 



m - 



The final models were tabulated and checked for reasonableness. This procedure 

 proved to work well on all data sets except Engelmann spruce and Douglas-fir. On these 

 two data sets, a model of the form: 



Y 



FC = fco - hie ^ (32) 



was fitted. Tabulation of these runs indicated that they performed well. They were 

 then converted to the standard form of model (32) using the fact that equals h and 

 by adding ln(2?i/fco) 



Because of the high values of RMSQR, it was decided to provide an optional model 

 to predict mean FC as a function of top diameter. Plots of the means over top diameter 

 indicated that power functions of top diameter would be appropriate. The means were 

 then weighted by their number of observations and screened with numerous power trans- 

 forms on top diameter. The maximum number of independent variables in the screening 

 run was limited to the value of 1 plus the number of maxima or minima the plots had 

 shown. A final model was selected based on its behavior and the magnitude of its RMSQR. 



XIII. Probability of Tree Being Unsound in Board Foot Volume — Unforked and Forked Trees 



An examination of the data indicated that International 1/4- inch and Scribner board 

 foot volumes were always sound or unsound together. Therefore, one model was developed 

 that is applicable to both. 



The techniques used were basically the same as those used for cubic foot volume. 

 The damage information did prove, however, to be statistically significant at the 95 

 percent level on the blackjack pine and Douglas-fir data sets. The model with damage 

 for white fir was almost significant and, because it behaved reasonably, it was also 

 included . 



Again, all curves were plotted as a final check. 



42 



