## Question

###### Problem 5 (3+3 pts) Consider multiple regression modelYi = Bo + B1xli + + Bprpi + â‚¬i for i = 1, n . Let Y (Y;:Yn)T , â‚¬ = (â‚¬1,- en)T , 8 (Bo, B1, Bp)T and X [1,X1,.. Xp] where (1, 1)T and Xj (1j1. Tjn)T for j 1, ~p. Then one can rewrite the model asY =XB +e.Let 8 is the ordinary least squares estimator of BShow that, for any product in R"RP+l <XB,Y >=< XB,XB >_ Here a,6 >= aTb is the usual inner2. Show that the vector XB has the least angle with the vector Y among the v

Problem 5 (3+3 pts) Consider multiple regression model Yi = Bo + B1xli + + Bprpi + â‚¬i for i = 1, n . Let Y (Y;:Yn)T , â‚¬ = (â‚¬1,- en)T , 8 (Bo, B1, Bp)T and X [1,X1,.. Xp] where (1, 1)T and Xj (1j1. Tjn)T for j 1, ~p. Then one can rewrite the model as Y =XB +e. Let 8 is the ordinary least squares estimator of B Show that, for any product in R" RP+l <XB,Y >=< XB,XB >_ Here a,6 >= aTb is the usual inner 2. Show that the vector XB has the least angle with the vector Y among the vectors in the column space of X. (Hint_ a,6 >= llallllbll cos 0 where 0 is the angle between vector a and b.)

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