Let Y Z3+ e denote the standard form of the multivariate regressionmodel where Y is a matrix of n observations on m dependent variables, Zis the nx (r + 1) design matrix, 3 is the matrix of regression coefficientsand denotes the error matrix. Let Σ denote the m x m covariancematrix of any row of e and assume the rows are independent. The leastsquare estimate for 3 is 3 = (Z'Z)-¹Z'Y. The projection matrix isH = Z(Z'Z)-¹Z'. Let the ith column of 3 be denoted by 3, and thei, jth element of Σ by oij. Define the sample covariance matrix of theresiduals byProveΣ=1n-p-1(g) Z'(I-H) = 0(h) Qê= (I-11')ê = ê.

Given the standard form of multivariate regression model as Y=Zβ+ε β^=Z'Z-1Z'Y H=ZZ'Z-1Z'

Answered: Let Y=Z3+ e denote the standard form of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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