Because of the behavior of the residuals, it was concluded that a weighted nonlinear 

 regression model was the most appropriate model for total ingrowth. Using the model form 

 and initial parameter values of model (7) and the weights derived from model (8), a weighted, 

 nonlinear regression run was made to provide the following model: 



Total ingrowth = coS(BACLi (BACLz)^^ ^C^sBA + cgAjBA '+) 

 where 



Co = 



0.42994711 





^1 = 



0.66118156 





C2 = 



-0.46026739 





^3 = 



-4.8091408E- 



06 



= 



2.7316853 





c-5 = 



-1 .6118274E- 



06 



This model behaves well except when BACL2 approaches zero, which causes the model to 

 "blow up." To control this, a value of 1.0 was added to BACL2, and the final weighted, non- 

 linear model was fitted. 



Through-Growth Model Development 



Program RISK was used to develop the through-growth model. It was hypothesized that 

 through-growth would most likely be correlated with predicted basal area growth in the 4-inch 

 diameter class (BJBAGl-4" and BJBAG2-4") and with predicted total ingrowth (TINGRO) . Using 

 these two independent variables and the time-since-cutting variable, Aj , RISK runs 1 through 

 10 listed in table 36 were made. Analysis of these runs indicated that the two best independ- 

 ent variables for predicting through-growth were BJBAGl-4" (or BJBAG2-4") and A^ *TINGRO. 

 Using these independent variables, runs 11 and 12 were made, and the chi-square "goodness-of- 

 fit" statistics across predicted basal area growth classes and across predicted through-growth 

 classes were computed. Across predicted basal area growth classes, the tests were insignif- 

 icant at the 99 percent testing level (tables 37 and 38) . Across predicted through-growth 

 classes, the model with BJBAGl-4" was also insignificant; however, the model with BJBAG2-4" 

 was significant. This latter test result was very surprising because, up to this point, the 

 two blackjack pine basal area growth equations behaved consistently in relation to each other. 

 Comparison of the mean squared errors, "t"-values, regression coefficients, and mean predicted 

 basal area growths all indicate that the two independent variables, BJBAGl-4" and BJBAG2-4", 

 and the two models do not differ greatly. This conclusion is further substantiated by the 

 similarity of the results for chi-square tests across predicted basal area growth classes. 

 It was decided, therefore, to ignore this chi-square test and accept model 12 as being the 

 final model for BJBAG2-4". 



84 



