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In the context of multiple regression, define the n X n matrix M =- X(XX)-X. (i) Show that M is symmetric and idempotent.

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So - I m = In - X (XX)X - Saph is show that m is symmetric and idempotent. M = In - X (XIX)7x! .. In - In m = [In - x (Solo i) M = In - x (xx) x In-/100...ol -100....0 I - the diagonal elements of Ina 1 and we also know that the diagonal elesoln chic Since y = xß t u is satisfies the Grauss-Markov Assumptions I = Xß t u ; Elu)=0 O and varlu) = r2In and Pals = (x1xSoln live under Glause m 1 Under Gause maakone Asumptions Y = XB tu, Ely) = 0 and var (4) = 02 In . mes = (xx)xly > Ols resi

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