Appendix 13a

13A.1 THE PROOF THAT E(b12) = $2 + fab32 [EQUATION (13.3.3)]

In the deviation form the three-variable population regression model can be written as yi = 02X2i + 03X3i + (Ui - U) (1)

First multiplying by x2 and then by x3, the usual normal equations are yiX2i = 02^2 X2i + 03^2, X2iX3i + ^ X2i (Ui - U) (2)

yiX3i = 02^2 X2iX3i + 03^2 X3i +^2 X3i (Ui - U) (3)

Dividing (2) by Y, X^i on both sides, we obtain

2i 2i 2i

X22i

X2iX3i

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