Because the first data set included only 

 trees that were grade 3 or better, we used a 

 second set so that we could calculate the 

 probability of a tree of a given species and 

 diameter being at least grade 3. This second 

 data set was collected from complete inven- 

 tories of seven additional cherry-maple stands. 

 A total of 3,650 trees greater than 10 inches 

 in dbh were recorded by species and dbh, and 

 each tree was classified as grade 3 and better 

 or less than grade 3. Thus, the two data sets 

 provided a means of calculating — for each 

 diameter class and species — the probability of 

 a tree being grade 1 or 2 or 3. 



Each of these probabilities were plotted 

 separately as a function of diameter for each 

 species. Species with similar distributions were 

 grouped. These groups were: (1) black cherry 

 and yellow-poplar; (2) sugar maple and red 

 maple, (3) beech and birch. 



Three regression equations were developed 

 for each species group. Each equation related 

 diameter to: (1) The proportion of trees 

 grade 3 and better: (2) The proportion of 

 grade 3 and better trees that were grade 1: 

 and (3) The proportion of grade 3 and better 

 trees that were grade 3. The proportion of 

 grade 3 and better trees that were grade 2 

 was obtained by subtracting the values for 

 equations 2 and 3 from equation 1. 



Predicted values derived from these equa- 

 tions were tabulated and plotted for each 

 species group. 



RESULTS 



The regression statistics for tree grade dis- 

 tribution and the diameter range over which 

 these equations are valid are shown in Tables 

 1-3. The lower limit is the minimum dbh re- 

 quirement for a particular grade. The upper 



Table 1. — Regression statistics for dependent variable 

 of percent of trees grade 3 or better. 



Species Regression j^. Range in 



Equation Diameter 



Black cherry and inches 



yellow-poplar 135.5- 806.5D-1 73 10-22 

 Sugar maple and 



red maple 140.9- 1083.5D-1 84 10.22 



Beech and birch 111.9- 980.2D-1 87 10-22 



Table 2. — Regression statistics for dependent variable 

 of percent of grade 3 or better trees in grade 1. 



Sopcips Regression Range in 



^ Equation Diameter 



Black cherry and inches 



yellow-poplar 127.8- 839.7D-1 65 16-26 

 Sugar maple and 



red maple 157.8- 1777D-1 77 16-26 



Beech and birch 178.4- 2408.30-^ 84 16-26 



Table 3. — Regression statistics for the dependent variable 

 of percent of grade 3 or better trees in grade 3. 



Species 



Regression 

 Equation 



R= 



Range in 

 Diameter 



Black cherry and 







inches 



yellow-poplar 



-17.4-J-43l.6D-i 



62 



13-23 



Sugar maple and 









red maple 



-31.8-f 755.9D-1 



64 



13-22 



Beech and birch 



-42.5 + 896.6D-1 



32 



13-20 



2 



