Let H = X(X^T - X') be the "hat" matrix in the multiple regression model, with Y = HY.Show thatH' = HH(I - H) = 0. H' = H(I - HYH) = 0.Hence, show that He = 0 where YY is the residual vector: If He is the part that can be explained by X, what does this result imply? Vectors and matrices are perpendicular if their dot product is zero. Confirm that ad and aIC are perpendicular.

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