MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Transcribed Image Text:Let Y Z3+ e denote the standard form of the multivariate regression
model where Y is a matrix of n observations on m dependent variables, Z
is the nx (r + 1) design matrix, 3 is the matrix of regression coefficients
and denotes the error matrix. Let Σ denote the m x m covariance
matrix of any row of e and assume the rows are independent. The least
square estimate for 3 is 3 = (Z'Z)-¹Z'Y. The projection matrix is
H = Z(Z'Z)-¹Z'. Let the ith column of 3 be denoted by 3, and the
i, jth element of Σ by oij. Define the sample covariance matrix of the
residuals by
Prove
Σ
=
1
n-p-1
(g) Z'(I-H) = 0
(h) Qê= (I-11')ê = ê.
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