Question: (a) Using the fact that R2 = n i=1 y2 i / n i=1 y2 i ; yi = OLSxi; and OLS = n i=1

(a) Using the fact that R2 =

n i=1 y2 i /

n i=1 y2 i ; yi = βOLSxi; and βOLS =

n i=1 xiyi/

n i=1 x2i

, show that R2 = r2 xy where, r2 xy = (

n i=1 xiyi)2/(

n i=1 x2i

)(

n i=1 y2 i ).

(b) Using the fact that yi = yi + ei, show that

n i=1 yiyi =

n i=1 y2 i , and hence, deduce that r2 yˆy = (

n i=1 yiyi)2/(

n i=1 y2 i )(

n i=1 y2 i ) is equal to R2.

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