Let be the least squares estimator of 3 in the regression model y = X3+u, where...

  

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Let be the least squares estimator of 3 in the regression model y = X3+u, where X is a n x k matrix with rank k and u~ N(0,021). (a) Find the non-random matrices A and B such that - can be written in the form Au and the sum of squared residuals can be written as u'Bu. (b) Show that B is idempotent and that AB = 0. (c) Indicate how these results enable one to obtain the distribution of (3-3)'X'X(6-8) n-k (y-XB)'(y-XB) k 687 x 26 Let be the least squares estimator of 3 in the regression model y = X3+u, where X is a n x k matrix with rank k and u~ N(0,021). (a) Find the non-random matrices A and B such that - can be written in the form Au and the sum of squared residuals can be written as u'Bu. (b) Show that B is idempotent and that AB = 0. (c) Indicate how these results enable one to obtain the distribution of (3-3)'X'X(6-8) n-k (y-XB)'(y-XB) k 687 x 26