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...

2. V is completely known (i.e., the values of all elements of V are given).
 Construct an estimator of ? and discuss the statistical properties (e.g.,
 bias, variance) of your estimator.

Extracted text: 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.