The criteria used to judge a model as "best" were: (1) check of normality and 

 independence assumptions, (2) check of variables against the physical constraints of 

 the system, (3) R-squared (coefficient of determination) , (4) the F value being four 

 times the value of the selected percentage point of the F distribution (Wetz 1966) , 

 (5) ease of use of these models, and (6) smallest variance. 



The normality assumptions were checked by plotting the dependent variable and the 

 residuals for each model constructed. Plots of observed values versus residuals and 

 predicted values versus residuals were used to check for any predictive faults in the 

 models. Plots of the order of the observation as recorded versus the residuals were 

 used to check for lack of independence. The criterion of Wetz' as discussed in 

 Draper and Smith (1966) , "suggests that in order that an equation should be regarded 

 as a satisfactory predictor (in the sense that the range of response values predicted 

 by the equation is substantial compared with the standard error of the response) , the 

 observed F ratio (regression mean square) / (residual mean square) should exceed not 

 merely the selected percentage point of the F distribution, but about four times the 

 selected percentage point." 1 



During the model building process many mathematical forms of the variables were 

 screened in order to improve the regression equations. Three of the independent 

 variables, SLO, LDI, and LSLO had quadratic relationships. This was verified with 

 plots of the data and other physical relationships determined from studying the logging 

 system. These three quadratic forms appear in many of the selected models along with 

 various combinations of interaction terms. The following discussion presents a summary 

 of the best model for each element and presents other models which were close contenders. 



RESULTS 



Five good TT models (fig. 4) were found using the six criteria discussed above. 

 None of the five models violated the normality or independence assumptions. In fact, 

 the plots for each model were quite similar, and no one model could be judged "better" 

 than the others. Since the five models were composed of two dominant variables, DI 

 and LDI, model number one was chosen as the "best" model because of its simplicity: 



TT = 3.43 + 0.00391DI + 0.0036LDI 



with an R-squared of 42.69 percent. 



Other variables were not included in the final model because they did not have a 

 strong enough influence on the cumulative R-squared. Note that distance and lateral 

 distance are the only variables that are included. Other expected relationships such 

 as number of logs, volume in board feet, weight, and slope were found not to be signi- 

 ficant in the total model. 



draper, N. R., and H. Smith. 1966. Applied regression analysis, p. 64. John 

 Wiley and Sons, Inc: New York, London, Sidney. 



7 



