Consider the case that the values of V are not completely given. Construct an estimator of B and derive its variance-covariance matrix. Can the variance-covariance matrix be unbiasedly estimated? 2. Consider the multiple regression model for n y-data yı, .., Yn, (n is sample size)y = X,B1 + X2B2 + ɛwhere y = (y1,..., yn)', X1 and X2 are random except the intercept term (i.e., thevector of 1) included in X1. Conditional on X1 and X2, the random error vectorɛ is jointly normal with zero expectation and variance-covariance matrix V,which does not depend on X1 and X2. V is not a diagonal matrix (i.e., someoff-diagonal elements are nonzero). B1 and B2 are vectors of two differentsets of regression coefficients; B1 has two regression coefficients and B2 hasfour regression coefficients. B = (B1 , B½)'; that is, B is a column vector of%3Dsix regression coefficients.

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Answered: 2. Consider the multiple regression…

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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Question

Consider the case that the values of V are not completely given.
Construct an estimator of B and derive its variance-covariance matrix.
Can the variance-covariance matrix be unbiasedly estimated?

2. Consider the multiple regression model for n y-data yı, .., Yn, (n is sample size)
y = X,B1 + X2B2 + ɛ
where y = (y1,..., yn)', X1 and X2 are random except the intercept term (i.e., the
vector of 1) included in X1. Conditional on X1 and X2, the random error vector
ɛ is jointly normal with zero expectation and variance-covariance matrix V,
which does not depend on X1 and X2. V is not a diagonal matrix (i.e., some
off-diagonal elements are nonzero). B1 and B2 are vectors of two different
sets of regression coefficients; B1 has two regression coefficients and B2 has
four regression coefficients. B = (B1 , B½)'; that is, B is a column vector of
%3D
six regression coefficients.

Definition Definition Measure of how two random variables change together. Covariance indicates the joint variability or the directional relationship between two variables. When two variables change in the same direction (i.e., if they either increase or decrease together), they have a positive covariance. When the change is in opposite directions (i.e., if one increases and the other decreases), the two variables have a a negative covariance.

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