The results for yellow pine indicated that most of the independent variables were stable. 

 Two exceptions are the independent variables D and ln(D) . Their behavior was common to all 

 data sets and to all models, and was expected because of the high correlation between the two. 

 Disappointingly, ridge regression did not change the sign on in(S). For blackjack pine fitted 

 to the uneven-aged data alone, the results were similar. The sign of in(S) did not change, 

 and the four independent variables involving D all showed instability. This last was the 

 most notable feature of the ridge trace for blackjack pine fitted to both the even- and uneven- 

 aged data sets. 



Because of the desire to have a model that was applicable over the range of site indices 

 found in the habitat type, the results of the ridge regression runs were unacceptable. I 

 decided, therefore, to force a reasonable value of ln(S) on the models, which was done by 

 fitting a new dependent variable of ir2(BAG/S). This has the same effect as forcing the 

 independent In(S) onto the log of basal area growth model with a regression coefficient of 

 one. The choice of one as the regression coefficient was made because, fixing other factors, 

 growth increased in direct proportion to an increase in site index (W. H. Meyer 1938; Larson 

 and Minor 1968; Ek 1974; and Myers and others 1976). 



Given this new dependent variable, a final set of screening runs was made utilizing the 

 same strategy as that used for the third set. Promising models were chosen from these runs 

 and additional runs were made to determine their regression coefficients. Ridge regression 

 was then used to examine the stability of the various independent variables. 



As with the ridge trace for the log of basal area growth, the independent variables 



showing the greatest amount of instability are those involving D. For both blackjack pine 



equations, a moderate amount of instability was also exhibited by those variables involving 

 the same basic variables (for example A3*UBA2 and UBA2) . 



The instability between D and ln(D) was expected because of their high correlation, but 

 this was acceptable because the two independent variables are necessary to provide the desired 

 "peaking" effect over diameter class size. For those independent variables involving time- 

 since-last-cutting, however, 1 decided to eliminate those that were highly unstable and 

 therefore did not greatly improve the least squares regression equations. This resulted in no 

 independent variables being removed for yellow pine, but it did result in three independent 

 variables being removed from both blackjack pine equations. The ridge traces for the finished 

 equations are found in figures 10, 11, and 12. 



For two reasons, the independent variable In(GRF) was also eliminated. First, the fact 

 that the variable was negative for the blackjack pine equation with the even-aged data was 

 cause for concern. The even-aged data were collected 40 years later than the uneven-aged 

 data. The sign change caused by the incorporation of the even-aged data might therefore 

 signal that the influence of rainfall was not uniform over time. Also, the data needed to 

 compute Ir!(GRF) are not readily available. The data source used in this study came from the 

 Fort Valley Experimental Forest, which has a weather station. 



62 



