I Fiance Apicultural

Appendix 1
Methodology
Proof that Equations (14) and (15)
are the Same
Let the estimated two variable imfitiple regression be
Let
Let
A AA
Y= a+ P X+ 2X, + E,. (1)
x= X, - A'
X2 = ,, -
y=Y-F, and
xI x 2 = ('X - X 1 ) (XI - g2).
A () (EX, y) - (Exx.) (Exy) and (2)
= ( - x)
)( ~) (EX
A, (Ex )_(L.. y) - P2 = ¢E~ )cr_) (1.xx - (ra 2) ,x2) (Ex- 1 y) (3)
U2 = E( y_- A)2/?, _k,
where k is the number of parameters estimated and Y- is the
measure of the failure of the X's to predict Y.
The standard error of
I =se/-E,
F ) -(yI/[2
]
(J3)se A[ ) = A(l) (Ex) - (xx,)2 , and (4)
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