The basic model for the ordinary least squares regression approach is: 



Y. = 



a + bY . + e . 



1 



1 1 



where 



Y . 



2 



actual value of a variable [or actual output of the model) 



Y . 



2 



predicted value of a variable (or predicted output of the model) 



a,b 



regression coefficients 



£ . 



2 



a random deviate. 



An intercept (a) of zero and a slope (Jb) of one would indicate, presumably, that the predicted 

 output of the model is an unbiased estimate of the actual output of the model (Cohen and Cyert 

 1961; Kleijnen 1974). If the random deviates are distributed normally with mean zero and 

 hemogeneous variance, then standard tests can be used to determine if the intercept is signifi- 

 cantly different from zero, and if the slope is significantly different from one (Draper and 



Smith 1966). Aigner (1972) has shown that the predictive model Y must be deterministic for 

 this approach to be legitimate; and the simulator developed in this study is deterministic. 



In applying this technique to actual and predicted number of trees in a diameter class, 

 the t-tests for determining the significance of the intercept and slope from zero and one, 

 respectively, did not prove to be very useful for making comparisons and decisions. Tests 

 were found in which the intercept and slope were greatly different from their expected values, 

 but, because of the high degree of impreciseness between actual and predicted values (that is, 

 because of the high MSE of the regression), the tests were "insignificant." Conversely, an 

 intercept and/or slope not greatly different from its expected value was often found to be 

 "significantly" different if a low MSE existed (that is, where predictions were highly precise). 

 This limitation of the regression t-tests is the same as attributed by Freese (1960) to the 

 paired t-test. 



Another statistical test considered for use in validation was the Kolmogorov-Smirnov (K- 

 S) test. The standard K-S test was developed for continuous distributions. Because the 

 diameter distribution data are discrete, application of the standard K-S test to it would have 

 resulted in conservative tests (Conover 1971) . A discrete K-S test had been reported in the 

 literature (Conover 1972; Horn 1977), but the time and expense of developing and applying the 

 required computer program was judged too great for this study. 



90 



