Question: Suppose in the model Y i = 1 + 2 X 2i + 3 X 3i + u i that r 23

Suppose in the model

Yi = β1 + β2X2i + β3X3i + ui

that r23, the coefficient of correlation between X2 and X3, is zero. Therefore, someone suggests that you run the following regressions:

Yi = α1 + α2X2i + u1i

Yi = γ1 + γ3X3i + u2i


a. Will α̂2 = β̂2 and γ̂3 = β̂3? Why?

b. Will β̂1 equal α̂1 or γ̂1 or some combination thereof?

c. Will var (β̂2) = var (α̂2) and var (β̂3) = var (γ̂3)?

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