chapter  19
50 Pages

Ratio Estimation

When two random variables are correlated and the relationship between them can be described on a straight line, the regression equation is

m

=

Y

=

b

+

b

X

According to Equation 15.59,

b

=

m

b

m

Thus, if the regression line passes through the origin,

b

= 0 and

b

=

m

/

m

As can be seen,

b

is a ratio of the means of the two random variables. Then,

(19.1)

(19.2)

(19.3)

Ratios of this sort are not uncommon in forestry. In some cases the ratios themselves are of interest while in others the ratios are used to obtain estimates of parameters that otherwise would be excessively difficult and/or expensive to obtain directly. Some examples are ratios of wood volume to wood weight, which are used to estimate wood volume on trucks; ratios of present volumes of timber per unit land area to past volumes, which are used to update timber cruises; ratios of dbh to crown diameter, which are used to estimate dbh from crown images on aerial photographs; and ratios of basal area per unit land area to percent crown closure, which are used to estimate stand density, in terms of basal area per unit land area, from aerial photographic evidence.