Question: Let bn X 0 nX n 1 X 0 nY n denote the OLS estimate when Y n is n1 and X n

Let b¯n Æ

X 0 nX n

¢¡1 X 0 nY n denote the OLS estimate when Y n is n£1 and X n is n£k. A new observation (YnÅ1,XnÅ1) becomes available. Prove that the OLS estimate computed using this additional observation is b¯nÅ1 Æ b¯n Å

1 1ÅX0 nÅ1

X 0 nX n

¢¡1 XnÅ1

X 0 nX n

¢¡1 XnÅ1

YnÅ1 ¡X0 nÅ1 b¯n

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