fa]
ar
1
uth)s
4
ne
|
>|
wo
3
a
a]
ia
ot le
At) g
»
a
+l
W
The variance and confidence {interval are
n
/yY,?
n
f=1
Vy
i=
v(R,) = {% (=) -
n
n
v,\7/ ¥ x}/cmn ox?
i=l
int
w
and
R, + tW(R,),
respectively, where te is defined above.
i=l
—
Ratio Estimation When Var(¥) is Independent of X.
FIGURE 4.
Ratio Estimation When Var(Y) is Proportional to X .
|.
n
»
xX
FICURE 3.
os
sim
n
En
A third situation (Figure 5} is when the standard deviation of Y is
proportional to X.
The optimal estimator of the slope of the
regression line (average ratio} is then
i
Its variance is estimated by
n
/¥, 2
V(R,) = {> (z
i=l
i
fay 2
ae x } Joon),
i=1
"i
and its confidence interval by
X
606
607