Question: Partial correlation (see Exercise 5.8): (a) Illustrate how the partial correlation rY1j2 can be represented using geometric vectors. Draw the vectors y(; x( 1, and

Partial correlation (see Exercise 5.8):

(a) Illustrate how the partial correlation rY1j2 can be represented using geometric vectors.

Draw the vectors y(; x(

1, and x(

2, and define e1 [ fEi1j2g and eY [ fEiYj2g (where i is the subscript for observations).

(b) (Use the vector diagram in part

(a) to show that the incremental F-test for the hypothesis H0: β1 = 0 can be written as F0 = ðn & k & 1Þr2 Y1j2 1 & r2 Y1j2 Recalling part

(b) of Exercise 5.8, why is this result intuitively plausible?

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