Question

Can you please show how the “hint” matrix is achieved using the two theorems below

Hint: Use Theorems 6.9 and 6.3. For any vectors z1 and z2, you can write I heorem The system Ax g is consistent if and only if the rank of A g is equal to the rank of A ear statistical models: The less than full rank model sification σ2 Conditional inverses Normal equations Estimability Interval esti olving the normal equations Proof. ) Since r( Ag combination of the columns of A (A), g must be a linear Therefore there exist constants 1, 2, . Ip, not all zero, so that where a, is the ith column of A Theorem In the general linear model y = X β + ε, tTß įs estimable if and only if there is a solution to the linear system XTXz t. t and put c-Xzo Proof. ( ) Let zo be a solution to XTXz Then so tß is estimable

Answer 1