Let(,)

(X,Y)be a random pair and let

Y^be the least squares linear predictor of

Ybased on

X. Assume that(,)0

r(X,Y)0.

a)Without calculation, say what the sign of the correlation(,

)

r(Y,Y^)should be and explain your answer.

b)Now find(,

)

r(Y,Y^)and confirm that it is consistent with your answer to Parta.