6. Let Y~ N(YIXO, ²1), where X equals:X =HHHL1[11-120 -30And is the 3 x 1 regression coefficient matrix. If Y- [6 1 11 3]', compute themaximum likelihood estimate 0ML, and o- Show all matrix calculations.ELEC

We have Y~NY|Xθ, σ2I X=11 21-1 210-310-1 Y=61113 θ=θ0θ1θ2 is the regression coefficient matrix.

Answered: Let Y~ N(YXO, o²I), where X equals: X =…

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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Let Y=Z3+ € 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 × 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 (e) E(Σ) = Σ (f) cov(₁,3)=0 1 n-p-1
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Only for b and c show the calculation please
. 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 € 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 dij. Define the sample covariance matrix of the residuals by = Prove (a) E(3) = 3 (b) cov (3,3)= Σ (3₁3) = Oik (Z'Z)-¹ 1 n-p-1
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Let Y~ N(YXO, o²I), where X equals: X = TTLE 1 1 1 -1 22 0 21 0-3 ܚ ܝ And is the 3 x 1 regression coefficient matrix. If Y= [6 1 11 3]', compute the maximum likelihood estimate 0ML, and o- Show all matrix calculations. ML