in(Total Ingrowth) = bQ + ijinCBACLi) + 2)2in(BACL2) + b^BA^ + 



2)i,AjBA1-5 + In(S) (6) 



where 



bo 



= -7.75817566 





i>l 



= 0.706329932 





b2 



= 1.97156496 





i>3 



= -8.04453668E- 



-03 



bk 



- -2.69619979E- 



-03 



BACL^ = basal area in the 4- through 6-inch diameter classes 

 BACL2 = basal area in the 7+-inch diameter classes 

 BA = total basal area 



A^ = time-since-last-cutting transform 



S = Minor's site index. 



The skewTiess statistic for this model was 1.10468, and the kurtosis statistic was 3.55524. 

 These statistics indicate a moderate amount of "nonnormality . " Examination shows the 

 residuals were divided into two groups. One group represented the zero valued ingrowth 

 observations (which has been set to a very small positive number when fitting the log models). 



The strange behavior of the residuals did not appear reasonable. Therefore, the anti- 

 log of model 6 was fitted to the total ingrowth data through linear, least squares regression 

 through the origin, to produce the following model: 



Total ingrowth = aoS(BACLi)^l (BACL2)^2 ,^^0 - b,BA^'' - b,A,BA^ 



where 



ao = 1.41650289 



bQ, bi, . . . , bi^ = regression coefficients from model (6). 



The skewness statistic for this model was 0.818989, and the kurtosis statistic was 2.44519. 

 These values indicate that the residuals about model (7) are more normally distributed than 

 those about model (6). Also, the residuals were in one group about the model, and they 

 increased, indicating a necessity to weight the model. 



To determine the proper weighting scheme, the residuals were divided into seven predicted 

 total ingrowth classes, and the variance for each class was then computed. Using these data, 

 the following model was then developed: 



Variance = 8.42590476 + 3 . 11147074 (YHAT) ° " ^^"^^^^^^^ (8) 



where 



YHAT = predicted ingrowth from model (7) . 

 The reciprocal of predicted variance then provides the weights necessary in weighted regression. 



83 



